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List of regular polytopes

This article lists the regular polytopes in Euclidean, spherical and hyperbolic spaces.

Overview
This table shows a summary of regular polytope counts by rank.

There are no Euclidean regular star tessellations in any number of dimensions.

1-polytopes
There is only one polytope of rank 1 (1-polytope), the closed line segment bounded by its two endpoints. Every realization of this 1-polytope is regular. It has the Schläfli symbol { }, or a Coxeter diagram with a single ringed node,. Norman Johnson calls it a dion and gives it the Schläfli symbol { }.

Although trivial as a polytope, it appears as the edges of polygons and other higher dimensional polytopes. It is used in the definition of uniform prisms like Schläfli symbol { }×{p}, or Coxeter diagram as a Cartesian product of a line segment and a regular polygon.

2-polytopes (polygons)
The polytopes of rank 2 (2-polytopes) are called polygons. Regular polygons are equilateral and cyclic. A $p$-gonal regular polygon is represented by Schläfli symbol {p}.

Many sources only consider convex polygons, but star polygons, like the pentagram, when considered, can also be regular. They use the same vertices as the convex forms, but connect in an alternate connectivity which passes around the circle more than once to be completed.

Convex
The Schläfli symbol {p} represents a regular $p'$-gon.

Spherical
The regular digon {2} can be considered to be a degenerate regular polygon. It can be realized non-degenerately in some non-Euclidean spaces, such as on the surface of a sphere or torus. For example, digon can be realised non-degenerately as a spherical lune. A monogon {1} could also be realised on the sphere as a single point with a great circle through it. However, a monogon is not a valid abstract polytope because its single edge is incident to only one vertex rather than two.

Stars
There exist infinitely many regular star polytopes in two dimensions, whose Schläfli symbols consist of rational numbers $\{n/m\}$. They are called star polygons and share the same vertex arrangements of the convex regular polygons.

In general, for any natural number $p$, there are regular $p$-pointed stars with Schläfli symbols $\{n/m\}$ for all $n$ such that $m < n/2$ (strictly speaking $\{n/m\} = \{n/(n − m)\}$) and $n$ and $m$ are coprime (as such, all stellations of a polygon with a prime number of sides will be regular stars). Symbols where $m$ and $n$ are not coprime may be used to represent compound polygons.

Star polygons that can only exist as spherical tilings, similarly to the monogon and digon, may exist (for example: {3/2}, {5/3}, {5/4}, {7/4}, {9/5}), however these do not appear to have been studied in detail.

There also exist failed star polygons, such as the piangle, which do not cover the surface of a circle finitely many times.

Skew polygons
In addition to the planar regular polygons there are infinitely many regular skew polygons. Skew polygons can be created via the blending operation.

The blend of two polygons $m$ and $n$, written $P#Q$, can be constructed as follows: Alternatively, the blend is the polygon $VP × VQ$ where $P$ and $Q$ are the generating mirrors of $P$ and $Q$ placed in orthogonal subspaces. The blending operation is commutative, associative and idempotent.
 * 1) take the cartesian product of their vertices $(p0 × q0, p1 × q1)$.
 * 2) add edges $(p0, p1)$ where $(q0, q1)$ is an edge of $ρ$ and $⟨ρ0σ0, ρ1σ1⟩$ is an edge of $σ$.
 * 3) select an arbitrary connected component of the result.

Every regular skew polygon can be expressed as the blend of a unique set of planar polygons. If $P$ and $Q$ share no factors then $Dim(P#Q) = Dim(P) + Dim(Q)$.

In 3 space
The regular finite polygons in 3 dimensions are exactly the blends of the planar polygons (dimension 2) with the digon (dimension 1). They have vertices corresponding to a prism ($\{n/m\}#$ where $P$ is odd) or an antiprism ($\{n/m\}#$ where $Q$ is even). All polygons in 3 space have an even number of vertices and edges.

Several of these appear as the Petrie polygons of regular polyhedra.

In 4 space
The regular finite polygons in 4 dimensions are exactly the polygons formed as a blend of two distinct planar polygons. They have vertices lying on a Clifford torus and related by a Clifford displacement. Unlike 3-dimensional polygons, skew polygons on double rotations can include an odd-number of sides.

3-polytopes (polyhedra)
Polytopes of rank 3 are called polyhedra:

A regular polyhedron with Schläfli symbol $\{p, q\}$, Coxeter diagrams, has a regular face type $\{p\}$, and regular vertex figure $\{1\}$.

A vertex figure (of a polyhedron) is a polygon, seen by connecting those vertices which are one edge away from a given vertex. For regular polyhedra, this vertex figure is always a regular (and planar) polygon.

Existence of a regular polyhedron $\{p, q\}$ is constrained by an inequality, related to the vertex figure's angle defect: $$ \begin{align} & \frac{1}{p} + \frac{1}{q} > \frac{1}{2} : \text{Polyhedron (existing in Euclidean 3-space)} \\[6pt] & \frac{1}{p} + \frac{1}{q} = \frac{1}{2} : \text{Euclidean plane tiling} \\[6pt] & \frac{1}{p} + \frac{1}{q} < \frac{1}{2} : \text{Hyperbolic plane tiling} \end{align} $$

By enumerating the permutations, we find five convex forms, four star forms and three plane tilings, all with polygons $\{p\}$ and $\{q\}$ limited to: {3}, {4}, {5}, {5/2}, and {6}.

Beyond Euclidean space, there is an infinite set of regular hyperbolic tilings.

Convex
The five convex regular polyhedra are called the Platonic solids. The vertex figure is given with each vertex count. All these polyhedra have an Euler characteristic (χ) of 2.

Spherical
In spherical geometry, regular spherical polyhedra (tilings of the sphere) exist that would otherwise be degenerate as polytopes. These are the hosohedra {2,n} and their dual dihedra {n,2}. Coxeter calls these cases "improper" tessellations.

The first few cases (n from 2 to 6) are listed below.

Star-dihedra and hosohedra $\{p, q\}$ and $\{p\}$ also exist for any star polygon $\{q\}$.

Stars
The regular star polyhedra are called the Kepler–Poinsot polyhedra and there are four of them, based on the vertex arrangements of the dodecahedron {5,3} and icosahedron {3,5}:

As spherical tilings, these star forms overlap the sphere multiple times, called its density, being 3 or 7 for these forms. The tiling images show a single spherical polygon face in yellow.

There are infinitely many failed star polyhedra. These are also spherical tilings with star polygons in their Schläfli symbols, but they do not cover a sphere finitely many times. Some examples are {5/2,4}, {5/2,9}, {7/2,3}, {5/2,5/2}, {7/2,7/3}, {4,5/2}, and {3,7/3}.

Skew polyhedra
Regular skew polyhedra are generalizations to the set of regular polyhedron which include the possibility of nonplanar vertex figures.

For 4-dimensional skew polyhedra, Coxeter offered a modified Schläfli symbol {l,m|n} for these figures, with {l,m} implying the vertex figure, m l-gons around a vertex, and $n$-gonal holes. Their vertex figures are skew polygons, zig-zagging between two planes.

The regular skew polyhedra, represented by {l,m|n}, follow this equation:

$$2 \sin\left(\frac{\pi}{l}\right) \sin\left(\frac{\pi}{m}\right) = \cos\left(\frac{\pi}{n}\right)$$

Four of them can be seen in 4-dimensions as a subset of faces of four regular 4-polytopes, sharing the same vertex arrangement and edge arrangement:

4-polytopes
Regular 4-polytopes with Schläfli symbol $$\{p,q,r\}$$ have cells of type $$\{p,q\}$$, faces of type $$\{p\}$$, edge figures $$\{r\}$$, and vertex figures $$\{q,r\}$$.
 * A vertex figure (of a 4-polytope) is a polyhedron, seen by the arrangement of neighboring vertices around a given vertex. For regular 4-polytopes, this vertex figure is a regular polyhedron.
 * An edge figure is a polygon, seen by the arrangement of faces around an edge. For regular 4-polytopes, this edge figure will always be a regular polygon.

The existence of a regular 4-polytope $$\{p,q,r\}$$ is constrained by the existence of the regular polyhedra $$\{p,q\}, \{q,r\}$$. A suggested name for 4-polytopes is "polychoron".

Each will exist in a space dependent upon this expression:
 * $$\sin \left ( \frac{\pi}{p} \right ) \sin \left(\frac{\pi}{r}\right) - \cos\left(\frac{\pi}{q}\right)$$
 * $$> 0$$ : Hyperspherical 3-space honeycomb or 4-polytope
 * $$= 0$$ : Euclidean 3-space honeycomb
 * $$< 0$$ : Hyperbolic 3-space honeycomb

These constraints allow for 21 forms: 6 are convex, 10 are nonconvex, one is a Euclidean 3-space honeycomb, and 4 are hyperbolic honeycombs.

The Euler characteristic $$\chi$$ for convex 4-polytopes is zero: $$\chi = V+F-E-C = 0$$

Convex
The 6 convex regular 4-polytopes are shown in the table below. All these 4-polytopes have an Euler characteristic (χ) of 0.

Spherical
Di-4-topes and hoso-4-topes exist as regular tessellations of the 3-sphere.

Regular di-4-topes (2 facets) include: {3,3,2}, {3,4,2}, {4,3,2}, {5,3,2}, {3,5,2}, {p,2,2}, and their hoso-4-tope duals (2 vertices): {2,3,3}, {2,4,3}, {2,3,4}, {2,3,5}, {2,5,3}, {2,2,p}. 4-polytopes of the form {2,p,2} are the same as {2,2,p}. There are also the cases {p,2,q} which have dihedral cells and hosohedral vertex figures.

Stars
There are ten regular star 4-polytopes, which are called the Schläfli–Hess 4-polytopes. Their vertices are based on the convex 120-cell {5,3,3} and 600-cell {3,3,5}.

Ludwig Schläfli found four of them and skipped the last six because he would not allow forms that failed the Euler characteristic on cells or vertex figures (for zero-hole tori: F+V−E=2). Edmund Hess (1843–1903) completed the full list of ten in his German book Einleitung in die Lehre von der Kugelteilung mit besonderer Berücksichtigung ihrer Anwendung auf die Theorie der Gleichflächigen und der gleicheckigen Polyeder (1883).

There are 4 unique edge arrangements and 7 unique face arrangements from these 10 regular star 4-polytopes, shown as orthogonal projections:

There are 4 failed potential regular star 4-polytopes permutations: {3,5/2,3}, {4,3,5/2}, {5/2,3,4}, {5/2,3,5/2}. Their cells and vertex figures exist, but they do not cover a hypersphere with a finite number of repetitions.

Skew 4-polytopes
In addition to the 16 planar 4-polytopes above there are 18 finite skew polytopes. One of these is obtained as the Petrial of the tesseract, and the other 17 can be formed by applying the kappa operation to the planar polytopes and the Petrial of the tesseract.

Ranks 5 and higher
5-polytopes can be given the symbol $$\{p,q,r,s\}$$ where $$\{p,q,r\}$$ is the 4-face type, $$\{p,q\}$$ is the cell type, $$\{p\}$$ is the face type, and $$\{s\}$$ is the face figure, $$\{r,s\}$$ is the edge figure, and $$\{q,r,s\}$$ is the vertex figure.

 * A vertex figure (of a 5-polytope) is a 4-polytope, seen by the arrangement of neighboring vertices to each vertex.
 * An edge figure (of a 5-polytope) is a polyhedron, seen by the arrangement of faces around each edge.
 * A face figure (of a 5-polytope) is a polygon, seen by the arrangement of cells around each face.

A regular 5-polytope $$\{p,q,r,s\}$$ exists only if $$\{p,q,r\}$$ and $$\{q,r,s\}$$ are regular 4-polytopes.

The space it fits in is based on the expression:
 * $$\frac{\cos^2\left(\frac{\pi}{q}\right)}{\sin^2\left(\frac{\pi}{p}\right)} + \frac{\cos^2\left(\frac{\pi}{r}\right)}{\sin^2\left(\frac{\pi}{s}\right)}$$
 * $$< 1$$ : Spherical 4-space tessellation or 5-space polytope
 * $$= 1$$ : Euclidean 4-space tessellation
 * $$> 1$$ : hyperbolic 4-space tessellation

Enumeration of these constraints produce 3 convex polytopes, no star polytopes, 3 tessellations of Euclidean 4-space, and 5 tessellations of paracompact hyperbolic 4-space. The only no non-convex regular polytopes for ranks 5 and higher are skews.

Convex
In dimensions 5 and higher, there are only three kinds of convex regular polytopes.

There are also improper cases where some numbers in the Schläfli symbol are 2. For example, {p,q,r,...2} is an improper regular spherical polytope whenever {p,q,r...} is a regular spherical polytope, and {2,...p,q,r} is an improper regular spherical polytope whenever {...p,q,r} is a regular spherical polytope. Such polytopes may also be used as facets, yielding forms such as {p,q,...2...y,z}.

Star polytopes
There are no regular star polytopes of rank 5 or higher, with the exception of degenerate polytopes created by the star product of lower rank star polytopes. e.g. hosotopes and ditopes.

Regular projective polytopes
A projective regular $\{p/q, 2\}$-polytope exists when an original regular $n$-spherical tessellation, {p,q,...}, is centrally symmetric. Such a polytope is named hemi- {p,q,...}, and contain half as many elements. Coxeter gives a symbol {p,q,...}/2, while McMullen writes {p,q,...}h/2 with h as the coxeter number.

Even-sided regular polygons have hemi-2n-gon projective polygons, {2p}/2.

There are 4 regular projective polyhedra related to 4 of 5 Platonic solids.

The hemi-cube and hemi-octahedron generalize as hemi-$n$-cubes and hemi-$n$-orthoplexes to any rank.

Regular projective 4-polytopes
5 of 6 convex regular 4-polytopes are centrally symmetric generating projective 4-polytopes. The 3 special cases are hemi-24-cell, hemi-600-cell, and hemi-120-cell.

Regular projective 5-polytopes
Only 2 of 3 regular spherical polytopes are centrally symmetric for ranks 5 or higher: they are the hemi versions of the regular hypercube and orthoplex. They are tabulated below for rank 5, for example:

Apeirotopes
An apeirotope or infinite polytope is a polytope which has infinitely many facets. An $n$-apeirotope is an infinite $n$-polytope: a 2-apeirotope or apeirogon is an infinite polygon, a 3-apeirotope or apeirohedron is an infinite polyhedron, etc.

There are two main geometric classes of apeirotope:
 * Regular honeycombs in $n$ dimensions, which completely fill an $n$-dimensional space.
 * Regular skew apeirotopes, comprising an $n$-dimensional manifold in a higher space.

2-apeirotopes (apeirogons)
The straight apeirogon is a regular tessellation of the line, subdividing it into infinitely many equal segments. It has infinitely many vertices and edges. Its Schläfli symbol is {∞}, and Coxeter diagram.

......

It exists as the limit of the $n$-gon as $n$ tends to infinity, as follows:

Apeirogons in the hyperbolic plane, most notably the regular apeirogon, {∞}, can have a curvature just like finite polygons of the Euclidean plane, with the vertices circumscribed by horocycles or hypercycles rather than circles.

Regular apeirogons that are scaled to converge at infinity have the symbol {∞} and exist on horocycles, while more generally they can exist on hypercycles.

Above are two regular hyperbolic apeirogons in the Poincaré disk model, the right one shows perpendicular reflection lines of divergent fundamental domains, separated by length λ.

Skew apeirogons
A skew apeirogon in two dimensions forms a zig-zag line in the plane. If the zig-zag is even and symmetrical, then the apeirogon is regular.

Skew apeirogons can be constructed in any number of dimensions. In three dimensions, a regular skew apeirogon traces out a helical spiral and may be either left- or right-handed.

Euclidean tilings
There are three regular tessellations of the plane.

There are two improper regular tilings: {∞,2}, an apeirogonal dihedron, made from two apeirogons, each filling half the plane; and secondly, its dual, {2,∞}, an apeirogonal hosohedron, seen as an infinite set of parallel lines.

Euclidean star-tilings
There are no regular plane tilings of star polygons. There are many enumerations that fit in the plane (1/p + 1/q = 1/2), like {8/3,8}, {10/3,5}, {5/2,10}, {12/5,12}, etc., but none repeat periodically.

Hyperbolic tilings
Tessellations of hyperbolic 2-space are hyperbolic tilings. There are infinitely many regular tilings in H2. As stated above, every positive integer pair {p,q} such that 1/p + 1/q < 1/2 gives a hyperbolic tiling. In fact, for the general Schwarz triangle (p, q, r) the same holds true for 1/p + 1/q + 1/r < 1.

There are a number of different ways to display the hyperbolic plane, including the Poincaré disc model which maps the plane into a circle, as shown below. It should be recognized that all of the polygon faces in the tilings below are equal-sized and only appear to get smaller near the edges due to the projection applied, very similar to the effect of a camera fisheye lens.

There are infinitely many flat regular 3-apeirotopes (apeirohedra) as regular tilings of the hyperbolic plane, of the form {p,q}, with p+q<pq/2.
 * {3,7}, {3,8}, {3,9} ... {3,∞}
 * {4,5}, {4,6}, {4,7} ... {4,∞}
 * {5,4}, {5,5}, {5,6} ... {5,∞}
 * {6,4}, {6,5}, {6,6} ... {6,∞}
 * {7,3}, {7,4}, {7,5} ... {7,∞}
 * {8,3}, {8,4}, {8,5} ... {8,∞}
 * {9,3}, {9,4}, {9,5} ... {9,∞}
 * {∞,3}, {∞,4}, {∞,5} ... {∞,∞}
 * {∞,3}, {∞,4}, {∞,5} ... {∞,∞}

A sampling:

The tilings {p, ∞} have ideal vertices, on the edge of the Poincaré disc model. Their duals {∞, p} have ideal apeirogonal faces, meaning that they are inscribed in horocycles. One could go further (as is done in the table above) and find tilings with ultra-ideal vertices, outside the Poincaré disc, which are dual to tiles inscribed in hypercycles; in what is symbolised {p, iπ/λ} above, infinitely many tiles still fit around each ultra-ideal vertex. (Parallel lines in extended hyperbolic space meet at an ideal point; ultraparallel lines meet at an ultra-ideal point.)

Hyperbolic star-tilings
There are 2 infinite forms of hyperbolic tilings whose faces or vertex figures are star polygons: {m/2, m} and their duals {m, m/2} with m = 7, 9, 11, .... The {m/2, m} tilings are stellations of the {m, 3} tilings while the {m, m/2} dual tilings are facetings of the {3, m} tilings and greatenings of the {m, 3} tilings.

The patterns {m/2, m} and {m, m/2} continue for odd m < 7 as polyhedra: when m = 5, we obtain the small stellated dodecahedron and great dodecahedron, and when m = 3, the case degenerates to a tetrahedron. The other two Kepler–Poinsot polyhedra (the great stellated dodecahedron and great icosahedron) do not have regular hyperbolic tiling analogues. If m is even, depending on how we choose to define {m/2}, we can either obtain degenerate double covers of other tilings or compound tilings.

Skew apeirohedra in Euclidean 3-space
There are three regular skew apeirohedra in Euclidean 3-space, with planar faces. They share the same vertex arrangement and edge arrangement of 3 convex uniform honeycombs. Allowing for skew faces, there are 24 regular apeirohedra in Euclidean 3-space. These include 12 apeirhedra created by blends with the Euclidean apeirohedra, and 12 pure apeirohedra, including the 3 above, which cannot be expressed as a non-trivial blend.
 * 6 squares around each vertex: {4,6|4}
 * 4 hexagons around each vertex: {6,4|4}
 * 6 hexagons around each vertex: {6,6|3}

Those pure apeirohedra are:
 * $\{2, p/q\}$, the mucube
 * $\{p/q\}$, the Petrial of the mucube
 * $\{p, q\}$, the mutetrahedron
 * $\{p\}$, the Petrial of the mutetrahedron
 * $\{q\}$, the muoctahedron
 * $(n+1)$, the Petrial of the muoctahedron
 * $\{4,6|4\}$, the halving of the mucube
 * ${∞,6}4,4$, the Petrial of $\{6,6|3\}$
 * ${∞,6}6,3$, the skewing of the muoctahedron
 * $\{6,4|4\}$, the Petrial of ${∞,4}6,4$

Skew apeirohedra in hyperbolic 3-space
There are 31 regular skew apeirohedra with convex faces in hyperbolic 3-space with compact or paracompact symmetry:
 * 14 are compact: {8,10|3}, {10,8|3}, {10,4|3}, {4,10|3}, {6,4|5}, {4,6|5}, {10,6|3}, {6,10|3}, {8,8|3}, {6,6|4}, {10,10|3},{6,6|5}, {8,6|3}, and {6,8|3}.
 * 17 are paracompact: {12,10|3}, {10,12|3}, {12,4|3}, {4,12|3}, {6,4|6}, {4,6|6}, {8,4|4}, {4,8|4}, {12,6|3}, {6,12|3}, {12,12|3}, {6,6|6}, {8,6|4}, {6,8|4}, {12,8|3}, {8,12|3}, and {8,8|4}.

Tessellations of Euclidean 3-space

There is only one non-degenerate regular tessellation of 3-space (honeycombs), {4, 3, 4}:

Improper tessellations of Euclidean 3-space
There are six improper regular tessellations, pairs based on the three regular Euclidean tilings. Their cells and vertex figures are all regular hosohedra {2,n}, dihedra, {n,2}, and Euclidean tilings. These improper regular tilings are constructionally related to prismatic uniform honeycombs by truncation operations. They are higher-dimensional analogues of the order-2 apeirogonal tiling and apeirogonal hosohedron.

Tessellations of hyperbolic 3-space
There are ten flat regular honeycombs of hyperbolic 3-space:
 * 4 are compact: {3,5,3}, {4,3,5}, {5,3,4}, and {5,3,5}
 * while 6 are paracompact: {3,3,6}, {6,3,3}, {3,4,4}, {4,4,3}, {3,6,3}, {4,3,6}, {6,3,4}, {4,4,4}, {5,3,6}, {6,3,5}, and {6,3,6}.

Tessellations of hyperbolic 3-space can be called hyperbolic honeycombs. There are 15 hyperbolic honeycombs in H3, 4 compact and 11 paracompact.

There are also 11 paracompact H3 honeycombs (those with infinite (Euclidean) cells and/or vertex figures): {3,3,6}, {6,3,3}, {3,4,4}, {4,4,3}, {3,6,3}, {4,3,6}, {6,3,4}, {4,4,4}, {5,3,6}, {6,3,5}, and {6,3,6}.

Noncompact solutions exist as Lorentzian Coxeter groups, and can be visualized with open domains in hyperbolic space (the fundamental tetrahedron having ultra-ideal vertices). All honeycombs with hyperbolic cells or vertex figures and do not have 2 in their Schläfli symbol are noncompact.

There are no regular hyperbolic star-honeycombs in H3: all forms with a regular star polyhedron as cell, vertex figure or both end up being spherical.

Ideal vertices now appear when the vertex figure is a Euclidean tiling, becoming inscribable in a horosphere rather than a sphere. They are dual to ideal cells (Euclidean tilings rather than finite polyhedra). As the last number in the Schläfli symbol rises further, the vertex figure becomes hyperbolic, and vertices become ultra-ideal (so the edges do not meet within hyperbolic space). In honeycombs {p, q, ∞} the edges intersect the Poincaré ball only in one ideal point; the rest of the edge has become ultra-ideal. Continuing further would lead to edges that are completely ultra-ideal, both for the honeycomb and for the fundamental simplex (though still infinitely many {p, q} would meet at such edges). In general, when the last number of the Schläfli symbol becomes ∞, faces of codimension two intersect the Poincaré hyperball only in one ideal point.

Tessellations of Euclidean 4-space
There are three kinds of infinite regular tessellations (honeycombs) that can tessellate Euclidean four-dimensional space:

There are also the two improper cases {4,3,4,2} and {2,4,3,4}.

There are three flat regular honeycombs of Euclidean 4-space:
 * {4,3,3,4}, {3,3,4,3}, and {3,4,3,3}.

There are seven flat regular convex honeycombs of hyperbolic 4-space:
 * 5 are compact: {3,3,3,5}, {5,3,3,3}, {4,3,3,5}, {5,3,3,4}, {5,3,3,5}
 * 2 are paracompact: {3,4,3,4}, and {4,3,4,3}.

There are four flat regular star honeycombs of hyperbolic 4-space:
 * {5/2,5,3,3}, {3,3,5,5/2}, {3,5,5/2,5}, and {5,5/2,5,3}.

Tessellations of hyperbolic 4-space
There are seven convex regular honeycombs and four star-honeycombs in H4 space. Five convex ones are compact, and two are paracompact.

Five compact regular honeycombs in H4:

The two paracompact regular H4 honeycombs are: {3,4,3,4}, {4,3,4,3}.

Noncompact solutions exist as Lorentzian Coxeter groups, and can be visualized with open domains in hyperbolic space (the fundamental 5-cell having some parts inaccessible beyond infinity). All honeycombs which are not shown in the set of tables below and do not have 2 in their Schläfli symbol are noncompact.

Star tessellations of hyperbolic 4-space
There are four regular star-honeycombs in H4 space, all compact:

6-apeirotopes
There is only one flat regular honeycomb of Euclidean 5-space: (previously listed above as tessellations)
 * {4,3,3,3,4}

There are five flat regular regular honeycombs of hyperbolic 5-space, all paracompact: (previously listed above as tessellations)
 * {3,3,3,4,3}, {3,4,3,3,3}, {3,3,4,3,3}, {3,4,3,3,4}, and {4,3,3,4,3}

Tessellations of Euclidean 5-space
The hypercubic honeycomb is the only family of regular honeycombs that can tessellate each dimension, five or higher, formed by hypercube facets, four around every ridge.

In E5, there are also the improper cases {4,3,3,4,2}, {2,4,3,3,4}, {3,3,4,3,2}, {2,3,3,4,3}, {3,4,3,3,2}, and {2,3,4,3,3}. In En, {4,3n−3,4,2} and {2,4,3n−3,4} are always improper Euclidean tessellations.

Tessellations of hyperbolic 5-space
There are 5 regular honeycombs in H5, all paracompact, which include infinite (Euclidean) facets or vertex figures: {3,4,3,3,3}, {3,3,4,3,3}, {3,3,3,4,3}, {3,4,3,3,4}, and {4,3,3,4,3}.

There are no compact regular tessellations of hyperbolic space of dimension 5 or higher and no paracompact regular tessellations in hyperbolic space of dimension 6 or higher.

Since there are no regular star n-polytopes for n ≥ 5, that could be potential cells or vertex figures, there are no more hyperbolic star honeycombs in Hn for n ≥ 5.

Tessellations of hyperbolic 6-space and higher
There are no regular compact or paracompact tessellations of hyperbolic space of dimension 6 or higher. However, any Schläfli symbol of the form {p,q,r,s,...} not covered above (p,q,r,s,... natural numbers above 2, or infinity) will form a noncompact tessellation of hyperbolic n-space.

Abstract polytopes
The abstract polytopes arose out of an attempt to study polytopes apart from the geometrical space they are embedded in. They include the tessellations of spherical, Euclidean and hyperbolic space, and of other manifolds. There are infinitely many of every rank greater than 1. See this atlas for a sample. Some notable examples of abstract regular polytopes that do not appear elsewhere in this list are the 11-cell, {3,5,3}, and the 57-cell, {5,3,5}, which have regular projective polyhedra as cells and vertex figures.

The elements of an abstract polyhedron are its body (the maximal element), its faces, edges, vertices and the null polytope or empty set. These abstract elements can be mapped into ordinary space or realised as geometrical figures. Some abstract polyhedra have well-formed or faithful realisations, others do not. A flag is a connected set of elements of each rank - for a polyhedron that is the body, a face, an edge of the face, a vertex of the edge, and the null polytope. An abstract polytope is said to be regular if its combinatorial symmetries are transitive on its flags - that is to say, that any flag can be mapped onto any other under a symmetry of the polyhedron. Abstract regular polytopes remain an active area of research.

Five such regular abstract polyhedra, which can not be realised faithfully and symmetrically, were identified by H. S. M. Coxeter in his book Regular Polytopes (1977) and again by J. M. Wills in his paper "The combinatorially regular polyhedra of index 2" (1987). They are all topologically equivalent to toroids. Their construction, by arranging n faces around each vertex, can be repeated indefinitely as tilings of the hyperbolic plane. In the diagrams below, the hyperbolic tiling images have colors corresponding to those of the polyhedra images.

 * {| class="wikitable" width=400

! Polyhedron Medial rhombic triacontahedron Dodecadodecahedron Medial triambic icosahedron Ditrigonal dodecadodecahedron Excavated dodecahedron !Vertex figure !Faces 12 pentagrams 12 pentagrams ! Tiling {4, 5} {5, 4} {6, 5} {5, 6} {6, 6} ! χ
 * - align=center
 * [[Image:DU36 medial rhombic triacontahedron.png|100px]]
 * [[Image:Dodecadodecahedron.png|100px]]
 * [[Image:DU41 medial triambic icosahedron.png|100px]]
 * [[Image:Ditrigonal dodecadodecahedron.png|100px]]
 * [[Image:Excavated dodecahedron.png|100px]]
 * - align=center
 * {5}, {5/2}
 * (5.5/2)2
 * {5}, {5/2}
 * (5.5/3)3
 * Medial triambic icosahedron face.svg
 * - align=center valign=top
 * 30 rhombi
 * 12 pentagons
 * 20 hexagons
 * 12 pentagons
 * 20 hexagrams
 * - align=center
 * [[Image:Uniform tiling 45-t0.png|100px]]
 * [[Image:Uniform tiling 552-t1.png|100px]]
 * [[Image:Uniform tiling 65-t0.png|100px]]
 * [[Image:Uniform tiling 553-t1.png|100px]]
 * [[Image:Uniform tiling 66-t2.png|100px]]
 * - align=center
 * −6
 * −6
 * −16
 * −16
 * −20
 * }

These occur as dual pairs as follows:
 * The medial rhombic triacontahedron and dodecadodecahedron are dual to each other.
 * The medial triambic icosahedron and ditrigonal dodecadodecahedron are dual to each other.
 * The excavated dodecahedron is self-dual.

title: List of regular polytopes


text:
Almyros

Almyros or Halmyros (Αλμυρός, lit. 'salty') is a town and a municipality of the regional unit of Magnesia, region of Thessaly, Greece. It lies in the center of prosperous fertile plain known as 'Krokio Pedio', which is crossed by torrents. Almyros is an important agricultural and commercial center of Magnesia, and is also developing as a tourist center for the area. The main agricultural products are tomatoes, cotton, wheat, almonds, peanuts and pistachio nuts.

History
The history of Almyros begins with the ancient city of Halos (about 10 km [6.2 mi] south of Almyros), the ruins of which can still be visited. Halos was a very important and populous town, famous for its port and for its role in the Persian Wars. After the Byzantine Empire, because of pirate raids, they built the town in the place that it is today.

Ancient Halos is still mentioned in the works of Stephanus of Byzantium (6th century). The medieval successor settlement of Halmyros is first mentioned in the 11th century, when it was listed as a Christian diocese. During the middle ages, sources refer to "two Halmyroi" (δύο Άλμυροι): one of these was at the same site as ancient Halos, 6 km southeast of the present-day town of Almyros, while the other was an associated port on the Pagasitic Gulf.

At the old acropolis of Halos, the remains of a couple of stone towers (one at the highest point of the acropolis, the other at the base, overlooking the modern motorway) attest to the site's continued existence in the middle ages. The lower town of Halmyros existed between two fortresses, one at the mouth of the Platanorrema and the other at the site of present-day Tsengeli (which is now inaccessible due to being the site of an airport). Almost nothing remains of either fortress. Remains of the old city walls have been found in the area between the two fortresses.

Medieval Halmyros owed a lot of its prosperity to the presence of Italian merchant groups who settled here (originally from places like Venice, Pisa, and Genoa). Several medieval Christian churches are attributed to these Italian communities: the church of St. George was built by the Venetians, and possibly also the now-gone church of St. Mark, while the former church of St. Jacob was built by the Pisans. There was also a strong Jewish community in medieval Halmyros. Warren Treadgold estimates the size of Halmyros's Jewish community at about 400 people during the 12th century.

In 1158, Halmyros was attacked and plundered by a naval force commanded by William I of Sicily. The Pisan church of St. Jacob was burned down in the attack. Halmyros's Venetian community was hit badly by the arrest of all Venetians living in Byzantine territory in 1171. In 1198, the "two Halmyroi" were mentioned for the first time, in a document under Alexios III Angelos granting special privileges to the Venetians. In the 1204 Partitio terrarum imperii Romaniae after the sack of Constantinople, the "duo Almiri" are mentioned among the Thessalian possessions of Alexios's wife, Euphrosyne Doukaina Kamatera. Halmyros was then assigned by Boniface of Montferrat as the place where the former Alexios III would reside as a private citizen. Later, Halmyros became a property of William of Larissa and later still was assigned to Margaret of Hungary, Boniface of Montferrat's widow.

Halmyros remained under Latin control until 1246, when it was reconquered by Michael II of Epirus. In 1259, Halmyros is attested as a theme. In 1265, a Venetian quarter was re-established in Halmyros, after the Venetians had previously been expelled. Rampant piracy is described as happening in the Halmyros area in the next decade, sometime before 1278. Halmyros was sacked in 1307, and in 1310 it was captured by the Catalan Company along with several other towns in southern Thessaly (namely Domokos, Gardikia, and Pharsalos).

Halmyros was the site of the decisive Battle of Halmyros on 15 March 1311, where the Catalan Company shattered the assembled feudal armies of Frankish Greece and conquered the Duchy of Athens.

In the 1300s, Halmyros began to lose its importance as a port town; the newly founded town of Golos (modern Volos) took its place.

In 1838, the settlement was described as being "a Turkish town, situated on the western coast of the Pagasitic Gulf, half an hour's journey inland, on the Plain of Krokios, and consisting of some 300 dwellings. It is chiefly inhabited by Turks, with only a few Christian settlers, who cultivate the lands of the Turks residing there". The Ottoman Empire ceded most of Thessaly in 1881, followed by development and repopulation by Greeks.

In 1980 a catastrophic magnitude 6.5 earthquake destroyed most of the town.

Municipality
The municipality Almyros was formed at the 2011 local government reform by the merger of the following 4 former municipalities, that became municipal units:
 * Almyros
 * Anavra
 * Pteleos
 * Sourpi

The municipality has an area of 905.4 km2 (349.6 sq mi), the municipal unit 473.940 km2 (183 sq mi).

Subdivisions
The municipal unit of Almyros is divided into the following communities: Almyros, Efxeinoupoli, Anthotopos, Kokkotoi, Kroki, Kofoi, Platanos, and Fylaki.

Province
The province of Almyros (Επαρχία Αλμυρού) was one of the provinces of Magnesia. It had the same territory as the present municipality. It was abolished in 2006.

Landmarks

 * The Archaeological Museum of Almyros includes local artifacts and exhibits from the Neolithic period, through Mycenean, Geometric, Classical, Hellenistic periods, and later Roman years. Opposite the museum is the old High School, the Gymnasium of Almyros, which is a classic monumental building from the beginning of the 20th century. The Museum and Gymnasium are the oldest buildings in the area.
 * The Kouri forest, about 2 km from the town of Almyros, at an elevation of 75 m (246 ft), encompasses 108 ha (266.9 acres) of lowland oak forest. The forest is flat (elevation gradient is less than 2%). Oaks belong to the species: Quercus pubescens, Quercus aegilops, Quercus pedunculiflora. There are footpaths, as well as a miniature train for a brief tour through the woods and over small bridges.
 * The area is important to migratory birds, such as the mute swan, spoonbill, glossy ibis, and various herons.
 * South of the town are the moderately wooded Othrys mountains. 17 km (10.6 mi) from the town of Almyros but still in Almyros province, high in the Othrys mountains, is the 12th century Monastery of Panagia Xenia, with wall paintings, treasuries, and a library.
 * There are several sandy beaches in the municipality of Almyros.
 * Almyros has three main churches: Agios Dimitrios, Agios Nikolaos and Evangelistria.

Geography
Almyros is situated near the western end of the Pagasetic Gulf, 25 km (15.5 mi) southwest of Volos. Motorway 1 (Athens – Thessaloniki) passes east of the town Almyros.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Almyros


text:
Zarma language

Zarma (Zarma Ciine/Sanni; Ajami: زَرْمَ ݘِينٜ / زَرْمَ سَنِّ) is one of the Songhay languages. It is the leading indigenous language of the southwestern lobe of the West African nation of Niger, where the Niger River flows and the capital city, Niamey, is located. Zarma is the second-most common language in the country, after Hausa, which is spoken in south-central Niger. With over 6 million speakers, Zarma is easily the most widely spoken Songhay language.

In earlier decades, Zarma was rendered Djerma, using French orthography, but it is usually now 'Zarma', the form that the Zarma people use in their language.

Alternative names for Zarma are Djerma, Jerma, Dyabarma, Dyarma, Dyerma, Adzerma, Zabarma, Zarbarma, Zarmaci or Zerma.

Geographic distribution
The majority of people who speak Zarma live in Southwestern Niger. It is also spoken in other parts of Niger and in neighbouring countries. Cities where Zarma is spoken include Tillaberi, Dosso, Niamey, Tahoua and Agadez.

In Nigeria, where the Zarma people are usually referred to as Zabarma or Zabarmawa, they are located in bordering States such as Kebbi, near Nguru Road in Yobe State and communities in Niger State.

The name Zabarmawa is derived from the Hausa language word for the Zarma people and the Songhai people.

In Mali, where they are located in bordering Gao Region and Kidal Region, the name is usually spelled Djerma.

In countries where no other Songhai languages are spoken, Zarma is also simply referred to as Songhai or Songhay.

Communities
Outside Niger, Nigeria and Mali, communities of speakers are found in the following other countries:
 * Northern Benin
 * Sahel Region and Est Region, Burkina Faso
 * Urban Areas in Northern Ghana
 * Savanes District, Ivory Coast
 * Kara Region and Savanes Region, Togo
 * Northern Cameroon
 * Sudan

Vowels
There are ten vowels: the five oral vowels and their nasalized counterparts. There is slight variation, both allophonic and dialectal. Vowel length is phonemically distinctive. There are a number of combinations of a vowel with a semivowel or,  the semivowel being initial or final.

Consonants
The combinations and  usually have some palatal quality to them and may even be interchangeable with  and  in the speech of many people.

All consonants may be short, and all consonants except /c/, /h/, /f/ and /z/ may be long. (In some dialects, long /f/ exists in the word goffo.)

Lexical tone and stress
Zarma is a tonal language with four tones: high, low, fall and rise. In Dosso, some linguists (such as Tersis) have observed a dipping (falling-rising) tone for certain words: ma ("the name").

Stress is generally unimportant in Zarma. According to Abdou Hamani (1980), two-syllable words are stressed on their first syllable unless that syllable is just a short vowel: a-, i- or u-. Three-syllable words have stress on their second syllable. The first consonant of a stressed syllable is pronounced a bit more strongly, and the vowel in the preceding syllable is weakened. Only emphasized words have a stressed syllable. There is no change of tone for a stressed syllable.

Orthography
Zarma is primarily written in either Latin alphabet or Arabic alphabet (Ajami). Zarma as well as other Songhay languages, and other indigenous languages of the Sahel such as Fula and Hausa have been written in Arabic alphabet for centuries. The tradition of writing in Arabic dates back to the arrival of Islam via merchants of the Trans-Saharan trade, as early as the 12th century. The tradition of Arabic script in the Sahel and Sub-Saharan Africa came to be known as Ajami. Ajami has its own unique characteristics across various languages that differ from the Perso-Arabic tradition or Jawi tradition of Southeast Asia for example.

Latin alphabet came to be used for Zarma and other indigenous languages of the region in the beginning of the 19th century with the arrival of European Christian Missionaries and colonial administrators.

Latin alphabet
Table below illustrates the letters used in the Zarma Latin alphabet:

Nasal vowels are written with a tilde or a following $⟨n⟩$ or $⟨ŋ⟩$. Officially, the tilde should go under the vowel (so̰ho̰), but many current works write the tilde over the vowel (sõhõ). Also, v may be used in a few words of foreign origin, but many Zarma cannot pronounce it.

Most of the letters are pronounced with the same values as the International Phonetic Alphabet (IPA), the exceptions being $⟨j⟩$ (approximately English j but more palatalized), $⟨y⟩$, $⟨r⟩$  (a flap). The letter is approximately like English ch but more palatalized. The palatal nasal is spelled $⟨ny⟩$ in older works.

Long consonants are written with double letters; $⟨rr⟩$ is a trilled. Long vowels are sometimes but inconsistently written with double letter. In older works, was spelled $⟨ky⟩$ or $⟨ty⟩$. Both $⟨n⟩$ and $⟨m⟩$ are pronounced as a labiodental nasal before $⟨f⟩$.

Tone is not written unless the word is ambiguous. Then, the standard IPA diacritics are used: bá ("to be a lot": high tone), bà ("to share": low tone), bâ ("to want" or "even": falling tone) and bǎ ("to be better": rising tone). However, the meaning is almost always unambiguous in the context so the words are usually all written ba.

Arabic alphabet
Table below illustrates the Arabic (Ajami) alphabet for Zarma, based on UNESCO.BREDA report on standardization of Arabic script in published in 1987 in Bamako.

Arabic alphabet for Songhay languages in Niger differs in 5 characters from that of Mali. Otherwise, the two orthographies are the same, especially in how vowels are written.

Sample text
Below is a sample text, Article 1 of the Universal Declaration of Human Rights.

General
There are many suffixes in Zarma. There are very few prefixes, and only one (a-/i- before adjectives and numbers) is common.

Nouns
Nouns may be singular or plural. There are also three "forms" that indicate whether the noun is indefinite, definite or demonstrative. "Form" and number are indicated conjointly by an enclitic on the noun phrase. The singular definite enclitic is -ǒ or -ǎ. Some authors always write the ending with a rising tone mark even if it is not ambiguous and even if it is not truly a rising tone. The other endings are in the table below. The definite and the demonstrative endings replace any final vowel. See Hamani (1980) for a discussion on when to add -ǒ or -ǎ as well as other irregularities. See Tersis (1981) for a discussion of the complex changes in tone that may occur.

For example, súsúbày means "morning" (indefinite singular); súsúbǎ means "the morning" (definite singular); and súsúbô means "this morning" (demonstrative singular).

The indefinite plural -yáŋ ending is often used like English "some". Ay no leemuyaŋ means "Give me some oranges." Usually, the singular forms are used if the plurality is indicated by a number or other contextual clue, especially for the indefinite form: Soboro ga ba ("There are a lot of mosquitoes"); ay zanka hinkǎ ("my two children"); hasaraw hinko kulu ra ("in both of these catastrophes").

There is no gender or case in Zarma so the third-person singular pronoun a can mean "he", "she", "it", "her", "him", "his", "hers", "its", "one" or "one's", according to the context and its position in the sentence.

Verbs
Verbs do not have tenses and are not conjugated. There are at least three aspects for verbs that are indicated by a modal word before the verb and any object nouns. The aspects are the completive (daahir gasu), the incompletive (daahir gasu si) and the subjunctive (afiri ŋwaaray nufa). (Beginning grammars for foreigners sometimes inaccurately call the first two "past and present tenses".) There is also an imperative and a continuing or progressive construction. Lack of a modal marker indicates either the affirmative completive aspect (if there is a subject and no object) or the singular affirmative imperative (if there is no subject). There is a special modal marker, ka or ga, according to the dialect, to indicate the completive aspect with emphasis on the subject. Different markers are used to indicate a negative sentence.

Linguists do not agree on the tone for ga. Some say that it is high before a low tone and low before a high tone.

There are several words in Zarma to translate the English "to be". The defective verb tí is used to equate two noun phrases, with the emphasized completive ka/ga, as in Ay ma ka ti Yakuba ("My name is Yakuba"). The existential gǒ (negative sí) is not a verb (White-Kaba, 1994, calls it a "verboid") and has no aspect; it means "exist" and usually links a noun phrase to a descriptive term, such as a place, a price or a participle: A go fuwo ra ("She's in the house"). The predicative nô means "it is", "they are", etc. and is one of the most common words in Zarma. It has no aspect or negative form and is placed after a noun phrase, sometimes for emphasis: Ni do no ay ga koy ("It's to your house I'm going"). Other words, such as gòró, cíyà, tíyà and bárà are much rarer and usually express ideas, such as the subjunctive, which gǒ and tí cannot handle.

Participles can be formed with the suffix -ànté, which is similar in meaning to the past participle in English. It can also be added to quantities to form ordinal numbers and to some nouns to form adjectives. A sort of gerund can be formed by adding -yàŋ, which transforms the verb into a noun. There are many other suffixes that can make nouns out of verbs, but only -yàŋ works with all verbs.

Two verbs can be related with the word ká. (In many dialects it is gá, not to be confused with the incompletive aspect marker or the emphasized completive marker.) The connector ká implies that the second verb is a result of the first or that the first is the reason or cause of the second: ka ga ŋwa, "come (in order to) eat." A large number of idiomatic expressions are expressed with it: sintin ga ... or sintin ka means "to begin to ...", ban ga ... means "to have already ...", ba ga ... means "to be about to ..., gay ga ... means "it's been awhile since ...", haw ga ... means "to purposely ..." and so on.

Syntax
Zarma's normal word order is subject–object–verb. The object is normally placed before the verb but may be placed after the verb for emphasis, and a few common verbs require the object after them. Unlike English, which places prepositions before a noun, Zarma has postpositions, which are placed after the noun: fuwo ra (in the house), fuwo jine (in front of the house).

When two nouns are placed together, the first noun modifies the second, showing possession, purpose or description: Fati tirǎ (Fati's book), haŋyaŋ hari (drinking water), fu meeyo (the door of a house). The same construction occurs with a pronoun before a noun: ni baaba ("your father"). All other modifiers of a noun (adjectives, articles, numbers, demonstratives etc.) are placed after the noun: Ay baaba wura muusu boŋey ("My father's gold lion heads", Tersis, 1981).

Here is a proverb in Zarma:

da curo fo hẽ, a-fo mana hẽ, i si jinde kaan-a bay

if bird one cry, NFP-one NEG.COMPL cry, they NEG.INCOMPL voice good-DEF know

"If one bird sings, and another doesn't sing, they won't know which voice is sweetest."

That means that "you need to hear both sides of the story".

title: Zarma language


text:
Terence Frisby

Terence Peter Michael Frisby (performing name Terence Holland; 28 November 1932 – 22 April 2020) was a British playwright, actor, director and producer, best known as the author of the play There's a Girl in My Soup.

Early life
Frisby was born in 1932 in New Cross, south-east London, the second son of William Frisby, who worked on the railways, and Kathleen (née Campbell), who was employed in a department store. He was educated at Dartford Grammar School leaving aged 16 becoming a tailor's apprentice. He remained in the occupation for six years before gaining a place at the Central School of Speech and Drama and training to become an actor. He worked in repertory theatre under the name Terence Holland from 1957 to 1966. Under his stage name, he was also a presenter on the BBC's children's series Play School during the 1960s.

Plays and other work
There's a Girl in My Soup opened in 1966 at the Globe Theatre (now called the Gielgud Theatre) and ran for over 1,000 performances, before transferring to the Comedy Theatre for a further three years. It was a worldwide hit with runs on Broadway, Paris (with Gérard Depardieu), Madrid (with Concha Velasco)Berlin, Stockholm, Sydney, Rome (starring Domenico Modugno), Vienna, Prague and elsewhere. His script for the 1970 film, which starred Peter Sellers and Goldie Hawn, won the Writers' Guild of Great Britain Award in 1970 for the Best British Comedy Screenplay.

His other stage plays include The Subtopians (Arts Theatre 1964), The Bandwagon (Mermaid Theatre 1969), It's All Right If I Do It (Mermaid 1977), Seaside Postcard  (Young Vic 1978), Rough Justice (Apollo Theatre 1994), and Funny About Love (two UK national tours 1999–2000). All his plays are published by Samuel French. The first performance of The Subtopians was in fact at the Guildford Theatre in the week of 26 March 1962. The second production, which transferred to the Arts Theatre in the West End in 1964, was directed by himself at Bromley Repertory Theatre, where he was working as a member of the rep company.

Frisby also wrote many plays for television, two of which were nominated for awards. His comedy series include Lucky Feller (1976) with David Jason (1976) and That's Love (1988–92) with Jimmy Mulville, Diana Hardcastle, and Tony Slattery, which won the Gold Award for Comedy at the 1991 Houston International Film Festival.

His radio play Just Remember Two Things: It's Not Fair And Don't Be Late for BBC Radio 4 won The Giles Cooper Award. A musical stage version was produced at the Queen's Theatre, Barnstaple in 2004 under the title Just Remember Two Things... A second production of the same show, under the title Kisses on a Postcard, was produced in 2011 at the same venue.

Frisby's book, Outrageous Fortune (1998), is an autobiographical account addressed to his son, Dominic Frisby, about his fifteen years as a litigant-in-person in the High Court following his divorce in 1971 from the model Christine Doppelt and his custody claim involving their son, who is now an author and comedian. Terence Frisby's second book is Kisses on a Postcard, published by Bloomsbury.(ISBN 9781408800584). It tells of his experiences as an evacuee as a 7-year-old from London to Cornwall during World War Two. It is based on the musical of the same name.

Frisby worked for over 50 years as an actor, director and producer. He played leads and directed in the West End, at the Young Vic and elsewhere in the UK. A presentation as a producer was the South African, multi-award-winning Woza Albert! at the Criterion Theatre in 1984. It was subsequently performed off-Broadway and worldwide.

Frisby was a founder member of the father's rights and support group Families Need Fathers, but became distant from the group terming it "Nippers Need Nutters". He died in April 2020, aged 87, from the side effects of treatment three years earlier for bladder cancer, which he did not have.

title: Terence Frisby


text:
Frank Knox

William Franklin Knox (January 1, 1874 – April 28, 1944) was an American politician, soldier, newspaper editor, and publisher. He was the Republican vice presidential candidate in 1936 and Secretary of the Navy under Franklin D. Roosevelt during most of World War II. On December 7, 1941, Knox, flanked by his assistant John O’Keefe, walked into Roosevelt's White House study around 1:30 pm EST, and announced that Japan had attacked Pearl Harbor.

Born in Boston, he attended Alma College and served with the Rough Riders during the Spanish–American War. After the war, he became a newspaper editor in Grand Rapids, Michigan, and state chairman of the Republican Party. He was a leading supporter of Theodore Roosevelt, the Progressive candidate for president in 1912. He advocated U.S. entrance into World War I and served as an artillery officer in France. The 1936 Republican National Convention nominated a ticket of Alf Landon and Knox, and they were defeated by Roosevelt and John Nance Garner in the 1936 election.

After World War II broke out in 1939, Knox supported aid to the Allies. In 1940, Roosevelt appointed him as Secretary of the Navy in hopes of building bipartisan support. Knox brought in James Forrestal as the under secretary. They presided over a massive naval buildup but were dissatisfied by the confused chain of command in Hawaii. After the attack on Pearl Harbor, Knox brought in a much more aggressive admiral, Ernest J. King. Roosevelt worked closely with King and largely neglected Knox. During the war, Knox continued his supervision of the Chicago Daily News, while Forrestal expanded his role and supervised the nonmilitary aspects of the department in terms of contracts and recruitment. Knox served as secretary of the Navy until his death in 1944, when Forrestal replaced him.

Early life
William Franklin Knox was born in Boston, Massachusetts. His parents were both Canadian; his mother, Sarah C. (Barnard), was from Charlottetown, Prince Edward Island, and his father, William Edwin Knox, was from New Brunswick. When he was nine, his family moved to Grand Rapids, Michigan, where his father ran a grocery store. He attended Alma College in Michigan, where he was a member of the Zeta Sigma fraternity. He left in his senior year to join the US Army for the Spanish–American War. He later supplemented his studies with additional readings and coursework, and the college's board of trustees awarded him a Bachelor of Arts degree as a member of the class of 1898.

He served in Cuba with Theodore Roosevelt's famous Rough Riders, the First Volunteer Cavalry Regiment. He was a member of Troop D commanded by Captain Robert Huston. As a member of D Troop, Knox fought in Cuba at the Battle of Las Guasimas, and the Battle of San Juan Hill.

Newspapers and politics

After the war, Knox became a newspaper reporter in Grand Rapids, which was the beginning of a career that included ownership of several papers. He changed his first name to Frank around 1900. He was state chairman of the Michigan Republican Party. In 1912, he was a key organizer for the presidential ambitions of Theodore Roosevelt.

In late 1912, Knox helped found the Manchester Leader in New Hampshire. It was financed by Governor Robert P. Bass, a member of the Progressive or Bull Moose Party). The newspaper was so successful that Knox bought out the Manchester Union. The two newspapers merged under the banner of the Union-Leader Corporation July 1913. Both papers espoused a moderate Republican, probusiness stance.

During World War I, Knox was an advocate of U.S. military preparedness and then of participation in the war. When the U.S. declared war on Germany in 1917, he rejoined the Army. He reached the rank of Colonel and served as an artillery officer in France. After the war he returned to the newspaper business.

In 1931, Frank Knox became publisher and part owner of the Chicago Daily News. In the 1936 election, he was the Republican nominee for vice president under Alf Landon. Landon, Knox, and former President Herbert Hoover were the only supporters of Theodore Roosevelt in 1912 who were later named to a Republican ticket. They lost in a landslide, winning just Maine and Vermont against the Democratic ticket of President Franklin D. Roosevelt and Vice President John Nance Garner.

World War II
During World War II, Knox again was an advocate of preparedness. As an internationalist, he supported aid to the Allies and opposed isolationism. In July 1940, he became secretary of the Navy under Roosevelt with Henry L. Stimson as Secretary of War, part of the Democratic president's effort to build bipartisan support for his foreign and defense policies following the defeat of France. Knox carried out Roosevelt's plan to expand the US Navy into a force capable of fighting in both the Atlantic and the Pacific oceans. Knox was mentioned by name in Adolf Hitler's speech of December 11, 1941, in which Hitler asked for a German declaration of war against the United States.

When a new naval officer on Knox's staff told him, "I'm no New Dealer," Knox replied, "I fought the President with every resource at my command. But now I've squared my politics with my conscience and I'm proud to serve under such a great man. At that," Knox added, "it's a good thing to have a couple of fellows around here who aren't New Dealers!" He traveled extensively to Navy installations worldwide. Knox also supported the continued racial segregation in the United States Armed Forces.

Internment of Japanese Americans
Knox had called for the internment of Japanese Americans as early as 1933, and he continued to do so in his new position. Shortly after the attack on Pearl Harbor, he visited Hawaii to investigate the sabotage that he believed to have taken place there. Upon his return, he issued a public statement that "the most effective Fifth Column work of the entire war was done in Hawaii with the exception of Norway," and he accused Japanese Hawaiians of impeding US defense efforts in a report to the President. Although the FBI and military intelligence later disproved those claims, Knox continued to push for the internment of Japanese Americans and barred them from service in the Navy during the war.

Death
Following a brief series of heart attacks, Secretary Knox died in Washington, DC, on April 28, 1944, while still in office. He was buried on May 1, 1944, at Arlington National Cemetery, in Arlington, Virginia.

Posthumous honors and memorials
The Gearing-class destroyer USS Frank Knox (DD-742), commissioned in December 1944, was named in his honor.

On May 31, 1945, he received posthumously the Medal for Merit from President Harry S. Truman. He also received the Spanish Campaign Medal and the World War I Victory Medal for his previous military service.

In 1948, his widow, Annie Reid Knox (1875–1958) endowed the Frank Knox Memorial Fellowships, which allow scholars from Australia, Canada, New Zealand, the Union of South Africa, and the United Kingdom to pursue graduate study at Harvard University, or by recent graduates of Harvard to travel and research in the countries of the British Commonwealth of Nations.

Frank Knox School on the grounds of the Patuxent River Naval Air Station was named for him.

title: Frank Knox


text:
Pōkarekare Ana

"Pōkarekare Ana" is a traditional New Zealand love song, probably communally composed about the time World War I began in 1914. The song is written in Māori and has been translated into English. It enjoys widespread popularity in New Zealand as well as some popularity in other countries.

Composition
Eastern Maori politicians Paraire Tomoana and Āpirana Ngata published the song in 1919, but neither of them claimed to have composed it. They explained that it had "emanated North of Auckland" and was popularised by Māori soldiers who were training near Auckland before embarking for the war in Europe.

The Māori words have remained virtually unaltered over the decades, with only the waters in the first line being localized. For example, some versions refer to Lake Rotorua in the North Island. It is then associated with the story of Hinemoa swimming across the lake to her forbidden lover, Tūtānekai, on Mokoia Island. However, there have been many different English translations.

"Pōkarekare Ana" was originally written predominantly in triple time, with the verse in duple time, but has been more commonly heard in duple time since World War II.

Use
The song is very popular in New Zealand, and has been adapted for multiple purposes, including in advertising and by sporting groups. Notable uses include:
 * "Sailing Away", which promoted New Zealand's 1987 America's Cup challenge, and featured an ensemble choir of famous New Zealanders recording as "All of Us".
 * It was used in multiple TV advertisements for Air New Zealand in the 1990s (using a recording with Kiri Te Kanawa) and in 2000. Air New Zealand also used the song again in 2020 to mark the 80th birthday of New Zealand's national airline, this time, using a recording from Hayley Westenra.
 * In April 2013, members and spectators in the New Zealand Parliament sang "Pōkarekare Ana" after the house passed the bill legalising same-sex marriage in New Zealand.

In popular culture, "Pōkarekare Ana" was used as the theme song for the 2005 South Korean film Crying Fist.

In the 2019 DLC for Civilization VI, Gathering Storm, the main theme for the added Māori civilization is Pōkarekare Ana and Ka Mate. There are four renditions of the theme, each corresponding to a different era in the game. These renditions were composed by Geoff Knorr and Phill Boucher.

Recordings
Dozens of recording artists throughout the world have performed and recorded the song.

A version of "Pōkarekare Ana" by Rhonda Bryers appears on the 1981 CBS various artists album The Mauri Hikitia.

Richard Clayderman recorded an instrumental version in 1984, which appeared on the album Memories.

Among New Zealand opera singers to record and perform "Pōkarekare Ana" are Kiri Te Kanawa and Malvina Major.

"Pōkarekare Ana" was featured on the 2003 album Pure, by the New Zealand soprano Hayley Westenra.

A version of the song features on the self-titled album by Angelis, a British classical crossover singing group.

On the CD Classical-Crossover Compilation 2011, Hollie Steel sings "Pōkarekare Ana". Steel later released the song as a charity single for those suffering from the 2011 earthquake in Christchurch, New Zealand.

Adaptations
It was known that the song was introduced to South Korea by New Zealand soldiers fighting in the Korean War. It was eventually given Korean lyrics and a Korean title, "Yeonga" (연가), and has become popular across the country.

The melody of "Pōkarekare Ana" was used for an Irish hymn to the Blessed Virgin: "A Mhuire Mháthair, sé seo mo ghuí".

A homophonous translation into Hebrew was composed in 2007 by Ghil'ad Zuckermann. In this translation the approximate sounds of the Māori words are retained while Hebrew words with similar meanings are used. In this translation, however, "Waiapu" is replaced by "Rotorua" (oto rúakh, Hebrew for "that wind").

title: Pōkarekare Ana


text:
Hans Larive

Etienne Henri "Hans" Larive, MWO, DSC and bar, (23 September 1915 – 28 December 1984) was a Dutch naval officer during World War II. He escaped from the prisoner of war camp Oflag IV-C at Colditz Castle in 1941, and spent the rest of the war in England serving aboard Motor Torpedo Boats. He later wrote his memoir Vannacht varen de Hollanders (1950), which was republished translated into English as The Man Who Came in From Colditz (1975) – a pun on the best-selling novel The Spy Who Came in from the Cold.

Early life
Larive was born on 23 September 1915 in Singapore. He entered the Royal Netherlands Naval College (KIM) in 1934, graduating in 1937, and gaining his commission as Luitenant ter Zee (3de klasse) on 13 August that year. He was promoted to Luitenant ter Zee (2de klasse) on 13 August 1939.

World War II
In May 1940, just a few days before the Germans attacked Holland, he returned from his tour of duty in the Dutch East Indies as Navigation Officer aboard the Admiralen class destroyer HNLMS Van Galen. On 10 May 1940 the Germans invaded, and the Van Galen was sent to shell German paratroopers who had landed around Rotterdam and Waalhaven airport. The ship had to steam into the narrow Nieuwe Waterweg, where she was attacked and soon sunk by Stuka dive-bombers.

The 'Singen' route
After the Dutch capitulation, all officers were required to give their not to take part in any hostile activities against the Germans. About 60 officers including Larive, and one rating, refused, and were sent to German POW camps. The first was Oflag VI-A in Soest, Germany, where Larive made his first escape attempt in October 1940. This attempt brought him near to Singen, close to the Swiss border, where he was arrested. Convinced that Germany would soon win the war, the interrogating Gestapo officer arrogantly showed Larive how he would have crossed the Swiss border without problems. Larive later passed this valuable information on, and many Dutch and British prisoners used the "Singen route" to enter Switzerland. After this escape attempt all Dutch POW's were moved to Oflag VIII-C near Juliusburg, but after another successful escape by two officers they were all moved again in July 1941 to the maximum security camp (Sonderlager) Oflag IV-C at Colditz.

Escaping Colditz
At Colditz all Dutch escapes were coordinated by the Dutch escape officer Captain Machiel van den Heuvel, known as "Vandy" by the British. Van den Heuvel quickly recognised the possibilities of the exercise park and soon had his first escape plan ready. On 15 August 1941 Larive and Lieutenant Francis Steinmetz hid under a manhole cover under the cover of a rugby scrum. Lieutenant Gerrit Dames then created a diversion by cutting a hole in the barbed wire fence, before allowing himself to be caught, shouting to imaginary escapers to run, so that the Germans would think that the missing officers had already escaped.

Larive and Steinmetz hid for several hours. The cover was fixed with a heavy bolt, which Van den Heuvel had replaced with a fake made of glass. Once it was dark the two men forced the manhole cover open from below, and replaced the now broken glass bolt with the original one. They then made their way out of the castle. (This escape method was repeated on 20 September 1941 by two other Dutch officers, Conrad Giebel and Oscar Ludwig Drijber. ). At Leisnig Larive and Steinmetz took a train to Nuremberg where they waited for their next train in a nearby park. To avoid attracting unwanted attention, they pretended to be a courting couple, with Steinmetz pulling a blanket down over his shorts so it looked like a skirt. They crossed the Swiss border on 18 August 1941.

Under Swiss neutrality law they were not allowed to leave the country, so the Dutch Legation provided false papers describing them as sugar planters on their way to Cuba. They travelled on a sealed train in which neutrals were able to pass through France into Spain. At Barcelona they boarded the neutral ship, Isla de Teneriffe, sailing for Havana. The ship was intercepted by a Royal Navy cutter in the Strait of Gibraltar and the two men were taken off and arrived in Gibraltar on 4 November. They then sailed to England aboard the submarine HNLMS O 21 and arrived in London on 17 December 1941.

MTB commander
In March 1942 Larive was assigned to command of the Dutch Motor Torpedo Boat MTB 203, part of the Anglo-Dutch 9th MTB Flotilla. Later the 9th Flotilla became wholly Dutch, and Larive commanded it from October 1942 until October 1943. He then became the Senior Officer of all Dutch MTBs (commanding the 2nd and 9th MTB Flotillas) until 16 September 1944, with the rank of Temporary Acting Luitenant ter Zee 1ste klasse. The Dutch MTB service was disbanded on 5 September 1944, and its personnel were reassigned to "Port Parties", operating in liberated areas of the Netherlands. Larive then became head of the Dutch Naval Press Agency MARVO (Marine Voorlichting Dienst), a post he held until leaving the navy on 1 July 1946.

Post-war
Larive was employed by the Royal Dutch Shell company from 1 September 1946. Between December 1951 and May 1954 he was a Deputy Director of N.V. Curaçaose Scheepvaart Maatschappij (Curaçao Shipping Company), a Shell subsidiary.

In 1950, he published his wartime memoirs entitled Vannacht varen de Hollanders ("The Dutch Sail Tonight"), later published in English as The Man Who Came in From Colditz. He died at The Hague on 28 December 1984.

Awards

 * NLD Military Order of William - Knight BAR.png Knight 4th Class of the Military Order of William (Ridder der 4e klasse der Militaire Willems-Orde), awarded on 23 July 1947. The citation read:
 * For outstanding acts of courage, leadership and devotion distinguished by;
 * Firstly, on the night of 14/15 June 1942 off the French coast, as commander of MTB 203, accompanied by two British motor torpedo boats of the flotilla under a British commander, competently, audaciously and successfully attacked an enemy convoy near Calais, and returned to base with only minor damage to his boat.
 * Secondly, on the night of 5 July 1943 as commander of a Flotilla of motor torpedo boats, consisting of MTBs 235 and 240, and a British MTB, in the Strait of Dover, in co-operation with the heavy 35-inch batteries at Dover, attacked two heavily armed enemy destroyers, which were in transit through the channel.
 * Thirdly, on the night of 26/27 September 1943, as Senior Officer of the flotilla, consisting of MTB 202, 204 and 231, he attacked and sank an escorted enemy merchantman, while under fire from the heavily defended French coast.

 * Order of Orange-Nassau ribbon.svg Knight of the Order of Orange-Nassau (Ridder der Orde van Oranje-Nassau)
 * Bronzen Kruis.png Ribbon numeral 2.png Bronze Cross (Bronzen Kruis), awarded 2 September 1942 and 13 July 1944, for successfully escaping from Germany and his actions in May 1940.
 * NLD War Commemorative Cross three clasp.png War Commemorative Cross (Oorlogsherinneringskruis) with 3 bars.
 * UK DSC w bar BAR.svg Distinguished Service Cross and bar (UK), for his attacks on enemy convoys in June 1942 and September 1943.
 * UK MID 1920-94.svg Mentioned in Dispatches (UK)

title: Hans Larive


text: Template:United States S class submarine


text:
Maidenhead Locator System

The Maidenhead Locator System (a.k.a. QTH Locator and IARU Locator) is a geocode system used by amateur radio operators to succinctly describe their geographic coordinates, which replaced the deprecated QRA locator, which was limited to European contacts. Its purpose is to be concise, accurate, and robust in the face of interference and other adverse transmission conditions. The Maidenhead Locator System can describe locations anywhere in the world.

Maidenhead locators are also commonly referred to as QTH locators, grid locators or grid squares, although the "squares" are distorted on any non-equirectangular cartographic projection. Use of the terms QTH locator and QRA locator was initially discouraged, as it caused confusion with the older QRA locator system. The only abbreviation recommended to indicate a Maidenhead reference in Morse code and radio teleprinter transmission was LOC, as in LOC KN28LH.

John Morris G4ANB originally devised the system and it was adopted at a meeting of the IARU VHF Working Group in Maidenhead, England in 1980.

History
Amateur radio contests on VHF and UHF are often scored based on the distance of contacts, typically 1 point per kilometre, so there is a need for amateurs to exchange their locations over the air. To facilitate this, following the growth of the sport in the 1950s, the German QRA locator system was adopted in 1959. The QRA locator system was limited to describing European coordinates, and by the mid-1970s there was growing need for a global locator system.

By the time of their April 1980 meeting, in Maidenhead, England, the VHF Working Group had received twenty different proposals to replace the QRA locator grid. That devised by John Morris (G4ANB) was deemed to be the best.

At the 1999 IARU Conference in Lillehammer it was decided that the latitude and longitude to be used as a reference for the determining of locators should be based on the World Geodetic System 1984 (WGS-84).

Description of the system
A Maidenhead locator compresses latitude and longitude into a short string of characters, which is similar in concept to the World Geographic Reference System or GEOREF. This position information is presented in a limited level of precision to limit the number of characters needed for its transmission using voice, Morse code, or any other operating mode.

The chosen coding uses alternating pairs of letters and digits, like so:

 * BL11BH16

In each pair, the first character encodes longitude and the second character encodes latitude. These character pairs also have traditional names, and in the case of letters, the range of characters (or "encoding base number") used in each pair does vary.

To avoid negative numbers in the input data, the system specifies that latitude is measured from the South Pole to the North Pole, and longitude measured eastward from the antimeridian of Greenwich, giving the prime meridian a false easting of 180° and the equator a false northing of 90°.

To simplify manual encoding, the base for the first pair of letters—traditionally called a field—was chosen to be 18, thus dividing the globe into 18 zones of longitude of 20° each, and 18 zones of latitude 10° each. These zones are encoded with the letters "A" through "R".

The second pair of numbers, called a square and placed after the first pair of letters, uses a base number of 10, and is encoded using the digits "0" to "9". This is where the alternative name "grid squares" comes from. Each of these squares represents 1° of latitude by 2° of longitude. For additional precision, each square can optionally be sub-divided further, into subsquares. These are encoded into a second pair of letters, which should be presented in uppercase, but are sometimes (incorrectly) presented in lowercase as a legacy from the old QRA.The error has unfortunately been incorporated into various software packages, several examples of which can be seen on this page. Again, to make manual calculations from degrees and minutes easier, 24 was chosen as the base number, giving these subsquares dimensions of 2.5' of latitude by 5' of longitude. The letters used are "A" through "X".

The resulting Maidenhead subsquare locator string is hence composed of two letters, two digits, and two more letters. To give an example, W1AW, the American Radio Relay League's Hiram Percy Maxim Memorial Station in Newington, Connecticut, is found in grid locator. Two points within the same Maidenhead subsquare are always less than 10.4 km apart, which means a Maidenhead locator can give adequate precision from only six easily transmissible characters.

For even more precise location mapping, two additional digits were proposed and ratified as an extended locator, making it altogether eight characters long, and dividing subsquares into even smaller ones with dimensions 15" of latitude by 30" of longitude. Such precision has uses in very short communication spans. Beyond this, no common definition exists to extend the system further into even smaller squares. Most often the extending is done by repeating alternating subsquare and square rules (base numbers 24 and 10 respectively). However, other bases for letter encodings have also been observed, and therefore such extended extended locators might not be compatible.

To summarise:
 * Character pairs encode longitude first, and then latitude.
 * The first pair (a field) encodes with base 18 and the letters "A" to "R".
 * The second pair (square) encodes with base 10 and the digits "0" to "9".
 * The third pair (subsquare) encodes with base 24 and the letters "A" to "X".
 * The fourth pair (extended square) encodes with base 10 and the digits "0" to "9".

(The fifth and subsequent pairs are not formally defined, but recursing to the third and fourth pair algorithms is a possibility, e.g.: BL11BH16OO66)

On shortwave frequencies, positions are reported at square precision, and on VHF and UHF, subsquare precision is used. At high microwave frequencies extended square and extended subsquare precision is often used.

Adoption and use
Like the QRA system before it, Maidenhead locators were enthusiastically adopted by radio amateurs beyond contesting, and it is now in widespread use.

Maidenhead locators are still used as part of the formulas for scoring in many VHF amateur radio contests and as the basis of earning awards like the American Radio Relay League's VHF/UHF Century Club, URE TTLOC, etc. operating contests.

Under IARU Region 1 rules, VHF distance calculations are carried out between Maidenhead subsquare centres, assuming a spherical Earth. This results in a small error in distance, but makes calculations simpler and, given the inherent imprecision in the input data used, it is not the biggest error source. Until the adoption of WGS 84 as the official geodetic datum of the Maidenhead locator system in 1999, operators had usually specified their location based on their local national datum. Consequently, stations very near the edges of squares (at denoted precision) may have changed their locators when changing over to the use of WGS 84.

The relatively new FT8 narrowband digital mode transmits Maidenhead locator square as part of standard messages, with the 4 character locator square being efficiently represented within 15 bits of the transmitted string.

In 2019 the IARU clarified the latest position on use of the IARU locator at various levels of precision, including a fifth pair of characters and that all letters should be uppercase.

Hardware and software support
In 1985, the Radio Society of Great Britain published a small set of BASIC language routines to convert from locator references to geographical coordinates (latitude and longitude) for further processing. A complete program in BASIC called Universal Gridlocator was made available the following year by ARRL for a nominal cost of US$3.

Many other utilities exist to convert latitude and longitude to locators, as this is a favourite hack for programmers who are also radio amateurs. Perl supports conversion between geographical coordinates and Maidenhead locators in module Ham::Locator by Andy Smith, available on CPAN.

The Python maidenhead module is on pypi.org for installation via pip.

Many commercially available general purpose (civil) Global Positioning System (GPS) receivers (e.g. Garmin GPS-12) have the option to display positions in Maidenhead Locator format.

title: Maidenhead Locator System


text:
Talk:User-centered design

Well that was a painful learning curve, bogus and SEO marketing citations removed.

Wiki Education Foundation-supported course assignment
This article is or was the subject of a Wiki Education Foundation-supported course assignment. Further details are available on the course page. Student editor(s): Jaswa003, Anoop195.

Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 12:11, 17 January 2022 (UTC)

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Improvement Needed
This page is an awful mess.

The whole thing needs to be re-written with the relevant ISO standards connected.
 * I have made few changes in the article by adding some missing citations and adding a section to describe user-centered design process.Some more actions needed to make this article better are:

 * 1) Move purpose section under user-centered design process, as it is just an example of a phase of the user-centered design process.
 * 2) Add missing citations for subsections about elements, rhetorical situations, and analysis tools.
 * 3) Improve the structure of the article.

I also propose deletion of the sections on purpose ,elements and rhetorical that have been citied from which doesnt meet wikipedia guidelines.These sections have been paraphrased and should be removed or should be cited from reliable sources.--Anoop195 (talk) 00:35, 3 April 2017 (UTC)

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It's a little embarrassing to point this out but User-centered design is spelt wrong the spelling is User-centred design - ISO 13407:1999 Human-centred design processes for interactive systems now revised as ISO 9241-210:2010 Ergonomics of human-system interaction -- Part 210: Human-centred design for interactive systems. All the Legal Frameworks spell it as Centred so do RFP and RFI contractual documents.

How do we get this updated is there a super user who decides?

The Introduction for ISO 9241-210:2010(E);

Introduction

Human-centred design is an approach to interactive systems development that aims to make systems usable and useful by focusing on the users, their needs and requirements, and by applying human factors/ergonomics, and usability knowledge and techniques. This approach enhances effectiveness and efficiency, improves human well-being, user satisfaction, accessibility and sustainability; and counteracts possible adverse effects of use on human health, safety and performance.

There is a substantial body of human factors/ergonomics and usability knowledge about how human-centred design can be organized and used effectively. This part of ISO 9241 aims to make this information available to help those responsible for managing hardware and software design and re-design processes to identify and plan effective and timely human-centred design activities.

The human-centred approach to design described in this part of ISO 9241 complements existing systems design approaches. It can be incorporated in approaches as diverse as object-oriented, waterfall and rapid application development.

The principles of human-centred design and the related activities have not changed substantially since ISO 13407 was produced and have been validated by ten years of application. This part of ISO 9241 reflects this by making requirements as well as recommendations. --Karl — Preceding unsigned comment added by Karlsmithux (talk • contribs) 15:06, 14 August 2015 (UTC)

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This article fails to cite one of the most widely accepted definitions and references for UCD - the ISO standard ISO 13407: Human-centred design process. --Lkantrov (talk) 15:10, 28 March 2008 (UTC) __________________________________________________________________________________________________________________________________________  —Preceding unsigned comment added by Lkantrov (talk • contribs) 15:08, 28 March 2008 (UTC)

This article, along with the article about 'User centered design' needs more reference to the study of Anthropology and Ethnography and its application throughout the design process. UCD focuses on the need to understand physical or cognitive properties of an individual or group, or of a social behavior specific to humanity relative to products, services, interactions, experiences, etc. 'Human centered Design' is a more appropriate title --K.Weigelt March 27, 2008 __________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________ —Preceding unsigned comment added by 130.138.227.10 (talk) 09:05, 27 March 2008 (UTC) This page was blanked soon after creation by its creator, but I can't honestly see any problem with the info, although the article could possibly be moved to a better name. It's not copyvio as far as I can tell. -- Graham :) 23:06, 4 Mar 2004 (UTC)

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should this page have a link to human-centered computing for contrast?

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"human-centered design" redirects to this page. i propose removing this redirect and adding a page for "human-centered design." although the two terms are often used interchangeably, they are in my mind substantially distinct. "user-centered" implies an eventual end user for the design, whereas "human-centered" includes the designer. futhermore, not all designers design for "use". in my experience, there are also important distinctions made between the two terms depending on disciplinary perspective. "human-centered computing" is a kind of "human-centered design". "user-centered design", meanwhile, is a term used commonly in business, but not a term used heavily by designers I know.

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It isn't at all clear what the phrase "rather than the opposite way around" means here : what is the opposite of "tries to bend and structure the functioning of a user interface around how people can, want or need to work" - NOT structure the interface around how people need to work? -- Agreed this is awkward and a bit unclear. How about something simpler like "The chief difference from other interface design philosophies is that user-centered design tries to structure a user interface around how people naturally work, rather than requiring users to learn how the interface works." - BMcCarthy 00:03, 20 November 2006 (UTC) (I think I got the time right!)

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I'd like to suggest appending something like: "In product design, this is sometimes referred to as the "out of the box experience," referring to all tasks the user must complete from first opening the box the product is shipped in, through unpacking, reading the directions, assembly, first use and continuing use." In expanding this paragraph, I might also consider removing the parentheses around the restaurant example. - BMcCarthy 00:09, 20 November 2006 (UTC)

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I agree that the article is not in a good state. It lacks crucial definitions and key nuances of the user-centered design concept.
 * 1) The article fails to provide a well-articulated definition and motivation of the concept with reliable references.
 * 2) The User-Centered design concept was coined in Don Norman's lab. He motivates it in his book Design of Everyday Things. First, the need and emotions part does not effectively brings out the issues of usability, the importance of design and the needs of users. Also, the article is incorrectly structured in the way that the Needs paragraph is mentioned at the last. It does not flow properly.

I plan to provide the following changes:
 * 1) Better Definition: As mentioned before, the definition does not have any sought of reference. I plan to rewrite the definition according the the following source: Source: Henry, Shawn Lawton. Just Ask: Integrating Accessibility Throughout Design. Madison, WI: ET\Lawton, 2007. ISBN 978-1430319528
 * 2) Provide better needs and emotions from Don Norman's Design of Everyday Things. We also plan to move Needs and Emotions up and keep it after the definition. I believe that would provide a better structure to the article. Source: http://dl.acm.org/citation.cfm?id=2187809

Jaswa003 (talk) 05:54, 25 March 2017 (UTC)

Models and Approaches
Under this section, the article mentions about the principles that ensure a design is user centered, but it has not been cited nor it is very well elaborated.

I will cite this part of article and will create a user-centered design process sub section which is missing in this article

Reference:

https://www.w3.org/WAI/EO/2003/ucd

https://www.usability.gov/what-and-why/user-centered-design.html

--Anoop195 (talk) 06:05, 25 March 2017 (UTC)

Changing focus citations?
The focus section, though interesting, ignores the very origins of user-centered design in the 80s. I marked it with "citation needed", but figure the "last decade" phrase should just be removed. I certainly don't know of any shift in thinking or application, though I see people new to the field asserting that they are making this shift without knowledge that this type of perspective has always existed. --Ronz 14:58, 27 July 2006 (UTC)
 * Someone removed the "citation needed", so I removed all reference to any supposed change in focus. --Ronz 15:42, 8 August 2006 (UTC)

Consolidation Needed
There are two UCD pages...one with a hyphen, and one without...these should be combined.

 * User Centered Design
 * User-centered design

There are also a number of related pages/topics that should be linked somehow:
 * HCI Human–computer interaction
 * Human factors
 * Usability
 * Web usability
 * Techniques for creating a User Centered Design
 * User interface design
 * User experience

Lkantrov 22:18, 22 January 2007 (UTC)

 * Yep, and more. Merging and moving pages gives details on how to do a merge.  Placing the merge proposal links is fairly easy to do.
 * As for the cross-linking, they are to some degree through internal links within the articles, with "See also" sections, and through categories. It certainly could be improved.
 * Techniques for creating a User Centered Design is a strange article from my perspective. I added a couple of tags to it.  There's a chance that everything in the article is already covered elsewhere. --Ronz 22:33, 22 January 2007 (UTC)

Agreed. User Centered Design, however, refers frequently to "documents" as the object of design, while User-centered design is more general, referring sometimes to software. I think the resulting merged article should be general and explicitly mention it can apply to documents, software, signage, or any artifact meant to be used in some way by a person. BMcCarthy 01:27, 30 January 2007 (UTC)

I agree that consolidation is useful, because the term does exist philosophically above the uses, and I think the hyphenated version is just a convention of use within a particular discourse community rather than a change in the term's meaning or use. BUT, we need to understand that the term does carry nuances of difference within each area: software, hardware, architecture, industrial design, technical writing, web design, etc. I think a single article that starts at the philosophical level then proceeds to discuss UCD within each of those contexts would be the way to go. Mark David Anthony 17:59, 14 June 2007 (UTC)

 * Yes, obviously the articles should be merged. Kla’quot (talk | contribs) 02:42, 1 September 2007 (UTC)

Designing Pleasurable Products
Moved from article for discussion. Neither the book nor the author are notable, nor is any source provided. Without a source, this looks like a NPOV violation: "Other books in a similar vein include 'Designing Pleasurable Products' by Patrick W. Jordan, in which the author suggests that different forms of pleasure should be included in a user-centered approach in addition to traditional definitions of usability." --Ronz 21:10, 3 October 2007 (UTC) Ronz strikes again with an overzealous cut! I support this link being included. Just read the book description on this Amazon link. Also check out the "Buy Together Emotional Design: Why We Love (or Hate) Everyday Things by Donald A. Norman today!" section Amazon Link To Book. Ronz, you state "neither the book nor the author are notable". When does a book become such? Are there any guides-line other than Ronz's feeling that a book or author become notable? -Buttysquirrel 16:38, 20 October 2007 (UTC)
 * Please see WP:TALK. --Ronz 17:15, 20 October 2007 (UTC)
 * ronz, don't be a douche. The article is tech biased; if the source would tip it to other direction, it's good. I mean, I'm not arguing for or against the book; I haven't read it or heard about it, but, well, if it exists and is relevant, it's good for the article. --Sigmundur (talk) 12:19, 26 November 2009 (UTC)

People keep forgetting that verifiability is one of Five pillars, while notability isn't. Given that notability guidelines do not directly limit article content, deleting the link on the basis of notability is spurious. On the other hand, WP:NPOV requires us to document significant viewpoints in reliable sources, so I say this link is a must because of the raised concerns of technical bias in the article.Diego (talk) 12:51, 26 November 2009 (UTC)

Overly focused on software and 'documents'
Coming fresh to this article I found it strangely focused on software design (or at least 'interface' design) and design of 'documents'. Are these 'documents' meant to be screen-based ones? A lot of the entry about 'document' design seems common information design principles, except some of the 'legibility' section. I think someone (a web-page designer?) has written this from their perspective, ignoring wider applications and relevance of user-centred-design. Notwithstanding the section on 'Focus on more than just computers. . ', this article could do with a broader orientation and less-blinkered view. At least, the intro shouldn't just be limited to 'interface or document' design. I also think the Jordan book (see entries above) is very relevant to user-centred design. Bristolian46 (talk) 15:58, 24 March 2008 (UTC)

UCD works for more than just web sites!
Quite annoying, the "elements of UCD" were obviously some web site examples; they spoke of the product as "document"; come on, if I'm designing a truck, I don't really consider "bold and italics" in my design, do I? Product design isn't just Flash and Javascript. --Sigmundur (talk) 12:16, 26 November 2009 (UTC)

Diagram
Maybe a diagram could be beneficial. I have created an educational infographic illustrating the iterative cycle of the user centred design process and released it under CC license. This is the infographic: http://lh4.ggpht.com/_h6EgYdPOxGo/S_78gXn0qCI/AAAAAAAABl4/1wf9AZB-bHE/User-Centred-Design.jpg

Feel free to include it if you think it's beneficial for the article.Jazzpazz (talk) 21:49, 15 June 2010 (UTC)
 * Unfortunately the CC license by which you published the image makes it incompatible with the Wikipedia preferred licenses. The Non-Commercial clause makes it not a "free cultural work" as per the definition in Licensing policy.
 * On a technical note, the diagram is too low resolution to be read with comfort.
 * If you could provide the SVG source code and release it as CC-BY-SA, I think the diagram would be a nice addition. Diego Moya (talk) 13:21, 16 June 2010 (UTC)

 * ok, this is interesting. Sorry, I'm new to wikipedia and have yet to figure out how to do things right. Maybe you can explain how to provide the SVG source code? I have the image as PDF and JPEG and Adobe Illustrator file. I'd be happy to release it as CC-BY-SA. —Preceding unsigned comment added by 86.131.58.78 (talk) 22:26, 18 June 2010 (UTC)
 * oops, sorry that last comment was me but I didn't notice that I wasn't logged in. Sorry for being a n00b.Jazzpazz (talk) 00:30, 21 June 2010 (UTC)
 * You should be able to "export" or "save as SVG" the Adobe Ilulustrator file from your graphic editor of choice. The file produced is the "source code" I referred to, since the SVG format is a readable open documented standard. You can then upload that SVG file to Wikimedia Commons under a Free license. You could also create a PNG high resolution (at least 300ppp) version of your design for bonus points ;-) Diego Moya (talk) 10:28, 21 June 2010 (UTC)

Analysis tools
The article is wonderful. What is bad, is that the section 5 Analysis tools used in user-centered design - does not obey the UCD principles, that is it contains large texts you can't grasp the idea, and it would be better to split those sections into chunks! --Yaroslav Nikitenko (talk) 08:14, 8 November 2011 (UTC)

Merge with human-centered design
It was suggested to merge this article with human-centered design.

There is a difference in the meaning, like you can read here: https://tubikstudio.com/faq-design-platform-human-centered-vs-user-centered-are-the-terms-different/

>human-centered design is the process of creating things deeply based on general natural characteristics and peculiarities of human psychology and perception.

>user-centered design is more focused and concise version of human-centered design with deeper analysis of target audience

I'm no expert in this field but i think that two different articles are ok, but the other article should be linked and the difference explained.

--Davidak (talk) 05:22, 13 October 2019 (UTC)
 * Added a missing hatnote template (and closed the merge proposal). Klbrain (talk) 09:29, 24 May 2020 (UTC)

title: Talk:User-centered design


text:
GNN

GNN can stand for:

 * GNNradio, a Christian radio network in the southeastern United States
 * GNN (news channel), Pakistani news channel
 * Garde Nationale et Nomade du Tchad (National and Nomadic Guard), a state security force in Chad
 * Genome News Network, an online magazine focused on genomics news
 * Global Network Navigator, an early commercial Web publication
 * Global News Network, a news channel in the Philippines
 * Goodnight Nurse, a New Zealand alternative rock band
 * Graph neural network, a class of neural network for processing data best represented by graph data structures
 * Guerrilla News Network, a defunct news website and TV studio
 * JA:GNN Web News, Japanese Web newsmagazine

title: GNN


text: User talk:64.12.96.168

title: User talk:64.12.96.168