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Stroud District

Stroud District is a local government district in Gloucestershire, England. The district is named after its largest town of Stroud. The council is based at Ebley Mill in Cainscross. The district also includes the towns of Berkeley, Dursley, Nailsworth, Stonehouse and Wotton-under-Edge, along with numerous villages and surrounding rural areas. Over half of the district lies within the Cotswolds Area of Outstanding Natural Beauty.

The neighbouring districts are Forest of Dean, Tewkesbury, Gloucester, Cotswold and South Gloucestershire.

History
The area is rich in Iron Age and Roman remnants and is of particular interest to archaeologists for its Neolithic burial grounds, of which there are over a hundred. Much of its wealth was built on the cloth industry during the Victorian era, and its many mills, most of which are now listed buildings, survive as testament to this. Much of the landscape in this area is designated as an Area of Outstanding Natural Beauty. The Cotswold Way walk leads through the area. There are gliding clubs at Aston Down and Nympsfield.

The district was formed on 1 April 1974 under the Local Government Act 1972. It covered the whole area of four former districts and parts of another three, which were all abolished at the same time: The new district was named Stroud after its largest town.
 * Dursley Rural District
 * Gloucester Rural District (part, rest split between Forest of Dean and Tewkesbury)
 * Nailsworth Urban District
 * Sodbury Rural District (parish of Alderley only, rest went to Northavon)
 * Stroud Rural District
 * Stroud Urban District
 * Thornbury Rural District (parishes of Alkington, Berkeley, Ham and Stone, Hamfallow and Hinton only, rest went to Northavon)

Boundary reviews in 1991 saw the district gain the parish of Hillesley and Tresham from Northavon and cede the parish of Quedgeley to Gloucester.

Governance
Stroud District Council provides district-level services. County-level services are provided by Gloucestershire County Council. The whole district is also covered by civil parishes, which form a third tier of local government.

Political control
The council has been under no overall control since 2011. Following the 2024 election a Green minority administration formed to run the council.

The first election to the council was held in 1973, initially operating as a shadow authority alongside the outgoing authorities until the new arrangements took effect on 1 April 1974. Political control of the council since 1974 has been as follows:

Leadership
The leaders of the council since 2001 have been:

Composition
Following the 2024 election the composition of the council was:

The next election is due in May 2028.

Premises
The council is based at Ebley Mill in the parish of Cainscross, a suburban town adjoining the west side of the town of Stroud. The mill was built as a woollen mill in 1818 and is a grade II* listed building. It was converted to become the council's offices between 1987 and 1990.

Elections
Since the last full review of boundaries in 2016 the council has comprised 51 councillors representing 27 wards, with each ward electing one, two or three councillors. Elections are held every four years.

Towns and parishes
The district is entirely covered by civil parishes. The parish councils for Berkeley, Cainscross, Dursley, Nailsworth, Stonehouse, Stroud and Wotton-under-Edge take the style "town council". Some of the smaller parishes have a parish meeting rather than a parish council.

Notable Members of Stroud District Council (and predecessors)
Margaret Hills (née Robertson) was the first woman elected to Stroud Urban District Council in 1928. where she stood as a representative of the Stroud Women's Citizens Association (SWCA). She remained a member until 1936 when the council was expanded to cover Cainscross and Rodborough.

David Drew is also a former member of the council originally representing the Stonehouse Ward and more recently the Paganhill and Farmhill Ward. Tom Levitt is also a former member and served for a short time before moving to High Peak in the early 1990s.

title: Stroud District


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Hold

Hold may refer to:

Physical spaces

 * Hold (compartment), interior cargo space
 * Baggage hold, cargo space on an airplane
 * Stronghold, a castle or other fortified place

Arts, entertainment, and media

 * Hold (musical term), a pause, also called a Fermata
 * Hold (album), 2023 album by Wild Nothing
 * "Hold" (song), a song by Vera Blue
 * "Hold", a song by Axium from Blindsided
 * "Hold", a song by Saves the Day from I'm Sorry I'm Leaving
 * Hold, in a card game (e.g., blackjack or poker, the cards that are kept in a hand, not those discarded and replaced
 * Handhold (dance), a type of hold in dance
 * Hold (novel) a novel by Michael Donkor

Law

 * Legal hold, a legal ruling or official declaration
 * Senate hold, a US parliamentary procedure

Sports

 * Hold (baseball), a statistic that may be awarded to a relief pitcher
 * Climbing hold, on climbing walls
 * Grappling hold, a specific grip applied to an opponent in wrestling or martial arts

Technology

 * Hold (aviation), a manoeuvre designed to delay an aircraft already in flight while keeping it within a specified airspace
 * Hold (telephone), a condition wherein a call is not terminated, but the connection is held and no speech can take place
 * Authorization hold, a now common practice by bankers and retailers (especially gas stations)

Other uses

 * Hold (title), an ancient Anglo-Danish and Norwegian title
 * holD, a bacterial gene
 * Hold or on hold, library books or other borrowed materials reserved for a particular borrower's use
 * Marianne Hold (1933–1994), German actress
 * Trevor Hold (1939-2004), English composer, poet and author

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

title: Hold


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Romeo Beckham

Romeo James Beckham (born 1 September 2002) is an English footballer who plays as a forward for Brentford B. He is the second son of former footballer David Beckham and fashion designer and former Spice Girls member, Victoria Beckham.

Early life
Beckham was born in Portland Hospital in the City of Westminster, London. He is the son of the former England international captain David Beckham and the singer-turned-fashion designer Victoria Beckham. His brothers, Brooklyn and Cruz, also played football with him for Arsenal, however, both were released from the club's youth system. He remains an Arsenal supporter. He attended Wetherby School in London and, then, Millfield School in Street, Somerset.

In 2014, Beckham joined Arsenal's Academy but was released the following year. After his release, he admitted that he no longer wished to pursue a career in football, instead taking up tennis training with Andy Murray. However, in 2020, Beckham announced that he was looking to return to football after a five-year absence. In support of the decision, his father replaced the tennis court he had previously built at the family home with a football pitch.

Club career
In September 2021, after turning 19, Beckham joined USL League One club Fort Lauderdale CF (renamed Inter Miami II in 2022), the reserve affiliate of his father's Major League Soccer club Inter Miami. This came after he had been seen training with the Inter Miami team in February. On 19 September, Beckham made his professional debut in a 2–2 draw against Tormenta FC. In that match, he appeared alongside Harvey Neville, the son of his father's former Manchester United teammate Phil Neville. On 26 January 2022, Beckham made his non-competitive senior debut for Inter Miami during a 4–0 pre-season win against Club Universitario de Deportes.

In October 2022, Beckham began training in England with Brentford B, who he joined in January 2023 on a six-month loan. He made his debut four days later, coming on as a second-half sub in a London Senior Cup game against Erith & Belvedere at Park View Road. He scored his first goal on 14 February 2023, in a Middlesex Senior Cup game against Wealdstone, scoring a 93rd minute winning goal in a 3-2 victory. In May 2023, Beckham was part of the Brentford B squad that won the 2022–23 Premier League Cup, although he was an unused substitute in the cup final. He made 15 appearances for Brentford B during the 2022–23 season. At the conclusion of his loan, he signed a permanent one-year contract with Brentford B.

Personal life
In 2019, Beckham made his relationship with model Mia Regan official via his Instagram account. They allegedly split after three years of dating in the summer of 2022, but got back together later that year. The couple announced they had split again in February 2024.

title: Romeo Beckham


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No. 42 Squadron RNZAF

No. 42 Squadron is an active transport squadron of the Royal New Zealand Air Force (RNZAF). It was formed at Rongotai Airport (Wellington) in December 1943 to provide a communications service around New Zealand, initially using impressed civilian types. It was briefly officially disbanded in 1946, but its aircraft continued with general purpose operations at RNZAF Station Ohakea (near Bulls). When reformed, the squadron was equipped with various numbers of North American Harvard, Auster, Grumman Avenger, Airspeed Oxford, de Havilland Devon, North American P-51 Mustang and Douglas Dakota aircraft.

TBF Avengers flown by 42 Squadron pilots were involved in the first aerial topdressing trials carried out in the world, spreading superphosphate fertiliser alongside the runways at RNZAF Ohakea. Their main purpose was to tow gunnery targets (drogues and banners) for air-to-air gunnery and for the navy and army. The P-51 Mustang also provided high-speed towing of banner targets, especially for de Havilland Vampire jets, and was used extensively for co-operation in army manoeuvres.

Transformation and VIP role
The role of the squadron gradually changed to VIP flights (Dakota and Devon; the Devons entered service with the RNZAF from 1948), multi-engine conversion courses (Oxford and Devon), and general transport flying around New Zealand and the South Pacific region. During the visit of Queen Elizabeth in 1953/54, 42 Squadron Dakotas carried her around New Zealand. In the late 1950s the squadron's inventory comprised only Dakotas and Devons, and in the mid-1960s the Dakota fleet was enlarged to six aircraft.

The reliable but aging Dakotas were retired in 1977 and replaced by four Hawker Siddeley Andover twin-engine transports. Two were converted to full VIP configuration; one was semi-converted and one remained in the utility configuration.

To accommodate the reformed No. 2 Squadron RNZAF and its Douglas A-4 Skyhawks at Ohakea in 1984, 42 Squadron moved to RNZAF Whenuapai near Auckland and absorbed the Andovers of No. 1 Squadron which was disbanded. The squadron then had ten Andovers.

Peacekeeping role
In 1988 a Hawker Siddeley Andover joined the United Nations Iran–Iraq Military Observer Group (UNIIMOG). The detachment of 17 personnel and aircraft were based at Tehran until withdrawn in December 1990. In 1993 three 42 Squadron Andovers went to Somalia to join the United States-led Unified Task Force (UNTAF). Based at Mogadishu, they flew air transport support missions for the force.

Training Role
Four Andovers were withdrawn from service in 1997 and the remainder in 1998. They were replaced by leased Beechcraft Model B200 King Airs. The leasing of aircraft was a new venture for the RNZAF, with a commercial contractor providing maintenance support to the aircraft on site. The workload for the aircraft is multi-engine conversion training of pilots qualified to fly single engine aircraft, continuation training for multi-engine qualified pilots and a limited VIP transport role around New Zealand.

A photo of NZ2351, the first of the King Airs, at Ohakea in September 2018 can be seen here.

The squadron returned to Ohakea in January 2002. It continued operating four B200 King Airs as part of the flying training wing. In 2018 the RNZAF leased four King Air 350 aircraft to replace the King Air 200 aircraft operated by No.42 Squadron, with the first aircraft arriving at Ohakea in April 2018.

In July 2020, New Zealand Minister of Defence Ron Mark welcomed the delivery of the fourth and final King Air 350 to Ohakea, bringing No.42 Squadron back up to full operating capability. Two of the four aircraft are permanently fitted with sensor suites, allowing for training of aircrew officers as well as multi-engine pilot training. Previously RNZAF aircrew officers were trained in Australia under an agreement with the RAAF.

title: No. 42 Squadron RNZAF


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File:Arms-milton-k.jpg

Arms of Milton Keynes Council. From civicheraldry.co.uk, with permission.

About the civic heraldry images

title: File:Arms-milton-k.jpg


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Gooding

Gooding may refer to:

Places

 * Gooding County, Idaho, a county in the United States
 * Gooding, Colorado, an unincorporated community in the United States
 * Gooding, Idaho, a city in the United States
 * Gooding High School, located within the city
 * Goodings Grove, Illinois, a census-designated place in the United States
 * Gooding Drive, a road in Australia

Other uses

 * Gooding (surname), an English surname
 * Gooding (band), an American rock band
 * Gooding railway station, in Australia
 * Gooding, an old English custom of asking for money during the Feast of St. Thomas

title: Gooding


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Optic Nerve

Optic Nerve may refer to:

 * Optic nerve, the anatomical structure
 * Optic Nerve (GCHQ), a mass surveillance program run by the British intelligence agency GCHQ
 * Optic Nerve (comics), a comic book series
 * Optic Nerve (CD-ROM), a Red Hot Benefit Series tribute to David Wojnarowicz
 * Optic Nerve Studios, a special make-up effects studio run by Glenn Hetrick

title: Optic Nerve


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Amersham Rural District

Amersham Rural District was a rural district in the administrative county of Buckinghamshire, England from 1894 to 1974, covering an area in the south-east of the county.

Origins
The district had its origins in the Amersham Poor Law Union, which had been created in 1835, covering Amersham itself and several surrounding parishes. In 1872 sanitary districts were established, giving public health and local government responsibilities for rural areas to the existing boards of guardians of poor law unions. The Amersham Rural Sanitary District therefore covered the area of the poor law union except for the town of Beaconsfield, which had an urban authority and so became its own urban sanitary district. Chesham was subsequently made its own urban sanitary district in 1884, removing it from the Amersham Rural Sanitary District. The Amersham Rural Sanitary District was administered from Amersham Union Workhouse, which had been built in 1838 on Whielden Road in Amersham.

Under the Local Government Act 1894, rural sanitary districts became rural districts from 28 December 1894. The Amersham Rural District Council held its first meeting on 3 January 1895 at the workhouse. George Weller of Amersham was appointed the first chairman of the council.

Civil parishes
The parishes were originally:

 * Amersham
 * Ashley Green (created 1897 from part of Chesham)
 * Chalfont St Giles
 * Chalfont St Peter
 * Chartridge (created 1899 from part of Chesham)
 * Chenies
 * Chesham Bois
 * Cholesbury-cum-St Leonards (created 1934 from 4 parishes plus parcels of land previously in Aylesbury Rural District)
 * Coleshill
 * Great Missenden
 * Latimer (created 1899 from part of Chesham)
 * Little Missenden (until 1930)
 * Penn
 * Seer Green
 * The Lee

Premises
The council was initially based at the workhouse on Whielden Road, continuing to meet there until the 1930s. In 1931 the council purchased Elmodesham House at 42 High Street in Amersham for £3,300, converting it to become their offices and meeting place. The premises at Elmodesham House were officially opened on 8 October 1931. The council remained based at Elmodesham House until its abolition in 1974.

Abolition
Amersham Rural District was abolished under the Local Government Act 1972, merging with neighbouring Chesham Urban District to become Chiltern District. The former Amersham Rural District Council offices at Elmodesham House subsequently served as the main offices of Chiltern District Council until 1986, when the council moved to a purpose-built office on King George V Road in Amersham. Elmodesham House has subsequently been converted into flats.

title: Amersham Rural District


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Goodland

Goodland may refer to:

United States

 * Goodland, Florida
 * Goodland, Indiana
 * Goodland, Kansas
 * Goodland Township, Michigan
 * Goodland, Minnesota
 * Goodland Township, Itasca County, Minnesota
 * Goodland, Iron County, Missouri
 * Goodland, Knox County, Missouri
 * Goodland, Oklahoma
 * Goodland, Bailey County, Texas
 * Goodland, Robertson County, Texas

Elsewhere

 * Goodland, Barbados
 * Goodlands, Canada, the Canadian side of the Carbury–Goodlands Border Crossing
 * Goodland, County Antrim, a townland in County Antrim, Northern Ireland
 * Goodlands, Mauritius

People

 * Goodland (surname)

Other uses

 * Benton County Wind Farm, Indiana, U.S., also known as Goodland I
 * Goodland Academy, Choctaw County, Oklahoma, U.S.
 * Goodland Field, now Nienhaus Field, in Appleton, Wisconsin, U.S.
 * Goodland Municipal Airport, Goodland, Kansas, U.S.

title: Goodland


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German aircraft production during World War II

The following is a list of aircraft production by Germany during World War II by type and year. Note that some figures may not be accurate, and it is not comprehensive. Aircraft variants of different roles are listed separately. Related types are listed next to each other; see RLM aircraft designation system for an explanation.


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Shroud

Shroud usually refers to an item, such as a cloth, that covers or protects some other object. The term is most often used in reference to burial sheets, mound shroud, grave clothes, winding-cloths or winding-sheets, such as the famous Shroud of Turin, tachrichim (burial shrouds) that Jews are dressed in for burial, or the white cotton kaffan sheets Muslims are wrapped in for burial.

A traditional Orthodox Jewish shroud consists of a tunic; a hood; pants that are extra-long and sewn shut at the bottom, so that separate foot coverings are not required; and a belt, which is tied in a knot shaped like the Hebrew letter shin, mnemonic of one of God's names, Shaddai. Traditionally, mound shrouds are made of white cotton, wool or linen, though any material can be used so long as it is made of natural fibre. Intermixture of two or more such fibres is forbidden, a proscription that ultimately derives from the Torah, viz., Deut. 22:11. An especially pious Jewish man may next be enwrapped in either his kittel or his tallit, one tassel of which is defaced to render the garment ritually unfit, symbolizing the fact that the decedent is free from the stringent requirements of the 613 mitzvot (commandments). The shrouded body is wrapped in a winding sheet, termed a sovev in Hebrew (a cognate of svivon, the spinning Hanukkah toy that is familiar under its Yiddish name, dreidel), before being placed either in a plain coffin of soft wood (where required by governing health codes) or directly in the earth.

The Early Christian Church also strongly encouraged the use of winding-sheets, except for monarchs and bishops. The rich were wrapped in cerecloths, which are fine fabrics soaked or painted in wax to hold the fabric close to the flesh. Early Christian shrouds incorporated a cloth, the sudarium, that covered the face, as depicted in traditional artistic representations of the entombed Jesus or his friend, Lazarus (John 11, q.v.). An account of the opening of the coffin of Edward I says that the "innermost covering seems to have been a very fine linen cerecloth, dressed close to every part of the body". The use of burial shrouds was general until at least the Renaissance – for much of history, a new set of clothing was an expensive purchase, so preparing the deceased in this manner ensured that a good set of clothes could be retained for further use by the family. In Europe in the Middle Ages, coarse linen shrouds were used to bury most poor without a coffin. In poetry shrouds have been described as of sable, and they were later embroidered in black, becoming more elaborate and cut like shirts or shifts.

Orthodox Christians still use a burial shroud, usually decorated with a cross and the Trisagion. The special shroud that is used during the Orthodox Holy Week services is called an Epitaphios. Some Christians also use the burial shroud, particularly the Catholics (Roman/Eastern), among others.

Muslims as well use burial shrouds that are made of white cotton or linen. The Burying in Woollen Acts 1666–80 in England were meant to support the production of woollen cloth.

title: Shroud


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User:Robblind

Welcome to my Wikipedia Homepage!

I am a student at Stanford University in Palo Alto, California, and I am writing a paper analyzing Wikipedia as on Online Learning Community.

Here is a picture from my home state of Minnesota:

title: User:Robblind


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Giovanni Battista Moroni

Giovanni Battista Moroni (c. 1520-1524 – 5 February 1578) was an Italian painter of the Mannerism. He also is called Giambattista Moroni. Best known for his elegantly realistic portraits of the local nobility and clergy, he is considered one of the great portrait painters of the Cinquecento.

Biography
Moroni was the son of architect Andrea Moroni. He trained under Alessandro Bonvicino in Brescia, where he was the main studio assistant during the 1540s, and worked in Trento, Bergamo and his home town of Albino, near Bergamo, where he was born and died. His two short periods in Trento coincided with the first two sessions of the Council of Trent, 1546–48 and 1551–53. On both occasions Moroni painted a number of religious works (including the altarpiece of the Doctors of the Church for the church of Santa Maria Maggiore, Bergamo) as well as the series of portraits for which he is remembered.

During his stay in Trento he also made contact with Titian and the Count-Bishop, Cristoforo Madruzzo, whose own portrait is by Titian, but for whom Moroni painted portraits of Madruzzo's sons. There were nineteenth-century claims that he was trained by Titian at Trento, however, it is improbable that he ever ventured to the Venetian's studio for long, if at all. Moroni's period as the fashionable portraitist of Bergamo, nowhere documented but in the inscribed dates of his portraits, is unexpectedly condensed, spanning only the years ca. 1557–62, after which Bergamo was convulsed in internecine strife and Moroni retired permanently to Albino, (Rossi, Gregori et al.) where, in his provincial isolation, he was entirely overlooked by Giorgio Vasari. His output at Bergamo, influenced in part by study of the realism of Savoldo, produced in the few years a long series of portraits that, while not quite heroic, are full of dignified humanity and grounded in everyday life. The subjects are not drawn exclusively from the Bergamasque aristocracy, but from the newly self-aware class of scholars, professionals, and exemplary government bureaucrats, with a few soldiers, presented in detached and wary attitudes with Moroni's meticulous passages of still life and closer attention to textiles and clothing than to psychological penetration.

His output of religious paintings, destined for a less sophisticated audience in the local sub-Alpine valleys, was smaller and less successful than his portraits: "the exact truth of parts nowhere added up, in his altar pictures, even to the semblance of credibility", S. J. Freedberg has observed of their diagrammatic schemes borrowed from Moretto, Savoldo, and others. for example, he painted a Last Supper for the parish at Romano in Lombardy; Coronation of the Virgin in Sant'Alessandro della Croce, Bergamo; also for the cathedral of Verona, SS Peter and Paul, and in the Brera of Milan, the Assumption of the Virgin. Moroni was engaged upon a Last Judgment in the church of Gorlago, when he died. Overall, his style in these paintings shows influences of his master, Lorenzo Lotto, and Girolamo Savoldo. Giovanni Paolo Cavagna was an undistinguished pupil of Moroni, however, it is said that in following generations, his insightful portraiture influenced Fra' Galgario and Pietro Longhi.

Freedberg notes that while his religious canvases are "archaic", recalling the additive compositions of the late Quattrocento and show stilted unemotive saints, his portraits are remarkable for their sophisticated psychological insight, dignified air, fluent control, and exquisite silvery tonality. Patrons for religious art were not interested in an individualized, expressive "Madonna", they desired numinous archetypal saints. On the other hand, patrons were interested in the animated portraiture.

Public collections with works by Moroni
The National Gallery (London) has one of the best collections of his work, including the celebrated portrait known as Il sarto (The Tailor). Other portraits are found in the Uffizi (the Nobleman Pointing to Flame inscribed, "Et quid volo nisi ut ardeat?"), Berlin Gallery, the Canon Ludovico de' Terzi and Moroni's self-portrait; and in the National Gallery, Washington, D.C., A Gentleman in Adoration Before the Madonna, the full-length portrait of Gian Federico Madruzzo, and the seated half-figure of the Jesuit Ercole Tasso, traditionally called, "Titian's Schoolmaster", although there is no real connection with Titian.

Among the public collections holding works by Giovanni Battista Moroni are, the Accademia Carrara (Bergamo) (Portrait of an old man), Ashmolean Museum (University of Oxford), Brooks Museum of Art (Memphis, Tennessee), Detroit Institute of Arts, the Fine Arts Museums of San Francisco, the Hermitage Museum, the Honolulu Museum of Art, Kunsthistorisches Museum (Vienna), the Liechtenstein Museum (Vienna), the Musée du Louvre, Musée Condé Chantilly (Chantilly, France), Museo Poldi Pezzoli (Milan), the Museum of Fine Arts, Boston, National Galleries of Scotland, the National Gallery of Art (Washington, D.C.), The Metropolitan Museum of Art (New York), the Art Gallery of New South Wales, the National Gallery of Canada (Portrait of a Man), the National Gallery, London, the Norton Simon Museum (Pasadena, California), Pinacoteca Ambrosiana (Milan), Pinacoteca di Brera (Milan), Rijksmuseum, the John and Mable Ringling Museum of Art (Sarasota, Florida), Studio Esseci (Padua, Italy), University of Arizona Museum of Art, Virginia Museum of Fine Arts, National Gallery of Ireland (Portrait of a Gentleman and his two Children), the Uffizi (Portrait of Giovanni Antonio Pantera), the Prado (A Soldier), and the Worcester Art Museum (Portrait of a Man).

In 2016, "Portrait of a Man", attributed to the workshop of Giovanni Battista Moroni, was restituted to the heirs of Dr. August Liebmann Mayer. The painting had been looted by the Nazis, returned to France and in storage at the Louvre Museum in Paris since 1951.

title: Giovanni Battista Moroni


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5-cell

In geometry, the 5-cell is the convex 4-polytope with Schläfli symbol {3,3,3}. It is a 5-vertex four-dimensional object bounded by five tetrahedral cells. It is also known as a C5, pentachoron, pentatope, pentahedroid, or tetrahedral pyramid. It is the 4-simplex (Coxeter's $$\alpha_4$$ polytope), the simplest possible convex 4-polytope, and is analogous to the tetrahedron in three dimensions and the triangle in two dimensions. The 5-cell is a 4-dimensional pyramid with a tetrahedral base and four tetrahedral sides.

The regular 5-cell is bounded by five regular tetrahedra, and is one of the six regular convex 4-polytopes (the four-dimensional analogues of the Platonic solids). A regular 5-cell can be constructed from a regular tetrahedron by adding a fifth vertex one edge length distant from all the vertices of the tetrahedron. This cannot be done in 3-dimensional space. The regular 5-cell is a solution to the problem: Make 10 equilateral triangles, all of the same size, using 10 matchsticks, where each side of every triangle is exactly one matchstick, and none of the triangles and matchsticks intersect one another. No solution exists in three dimensions.

Alternative names

 * Pentachoron (5-point 4-polytope)
 * Hypertetrahedron (4-dimensional analogue of the tetrahedron)
 * 4-simplex (4-dimensional simplex)
 * Tetrahedral pyramid (4-dimensional hyperpyramid with a tetrahedral base)
 * Pentatope
 * Pentahedroid (Henry Parker Manning)
 * Pen (Jonathan Bowers: for pentachoron)

Geometry
The 5-cell is the 4-dimensional simplex, the simplest possible 4-polytope. As such it is the first in the sequence of 6 convex regular 4-polytopes (in order of size and complexity).

A 5-cell is formed by any five points which are not all in the same hyperplane (as a tetrahedron is formed by any four points which are not all in the same plane, and a triangle is formed by any three points which are not all in the same line). Any such five points constitute a 5-cell, though not usually a regular 5-cell. The regular 5-cell is not found within any of the other regular convex 4-polytopes except one: the 600-vertex 120-cell is a compound of 120 regular 5-cells.

Structure
When a net of five tetrahedra is folded up in 4-dimensional space such that each tetrahedron is face bonded to the other four, the resulting 5-cell has a total of 5 vertices, 10 edges and 10 faces. Four edges meet at each vertex, and three tetrahedral cells meet at each edge.

The 5-cell is self-dual (as are all simplexes), and its vertex figure is the tetrahedron. Its maximal intersection with 3-dimensional space is the triangular prism. Its dihedral angle is cos−1($1⁄4$), or approximately 75.52°.

The convex hull of two 5-cells in dual configuration is the disphenoidal 30-cell, dual of the bitruncated 5-cell.

As a configuration
This configuration matrix represents the 5-cell. The rows and columns correspond to vertices, edges, faces, and cells. The diagonal numbers say how many of each element occur in the whole 5-cell. The nondiagonal numbers say how many of the column's element occur in or at the row's element. This self-dual polytope's matrix is identical to its 180 degree rotation. The k-faces can be read as rows left of the diagonal, while the k-figures are read as rows after the diagonal. All these elements of the 5-cell are enumerated in Branko Grünbaum's Venn diagram of 5 points, which is literally an illustration of the regular 5-cell in projection to the plane.

Coordinates
The simplest set of Cartesian coordinates is: (2,0,0,0), (0,2,0,0), (0,0,2,0), (0,0,0,2), (𝜙,𝜙,𝜙,𝜙), with edge length 2√2, where 𝜙 is the golden ratio. While these coordinates are not origin-centered, subtracting $$(1,1,1,1)/(2-\tfrac{1}{\phi})$$ from each translates the 4-polytope's circumcenter to the origin with radius $$2(\phi-1/(2-\tfrac{1}{\phi})) =\sqrt{\tfrac{16}{5}}\approx 1.7888$$, with the following coordinates:

 * $$\left(\tfrac{2}{\phi}-3, 1, 1, 1\right)/(\tfrac{1}{\phi}-2)$$
 * $$\left(1,\tfrac{2}{\phi}-3,1,1 \right)/(\tfrac{1}{\phi}-2)$$
 * $$\left(1,1,\tfrac{2}{\phi}-3,1 \right)/(\tfrac{1}{\phi}-2)$$
 * $$\left(1,1,1,\tfrac{2}{\phi}-3 \right)/(\tfrac{1}{\phi}-2)$$
 * $$\left(\tfrac{2}{\phi},\tfrac{2}{\phi},\tfrac{2}{\phi},\tfrac{2}{\phi} \right)/(\tfrac{1}{\phi}-2)$$

The following set of origin-centered coordinates with the same radius and edge length as above can be seen as a hyperpyramid with a regular tetrahedral base in 3-space:

 * $$\left( 1, 1, 1, \frac{-1}\sqrt{5}\right)$$
 * $$\left( 1,-1,-1,\frac{-1}\sqrt{5} \right)$$
 * $$\left(-1, 1,-1,\frac{-1}\sqrt{5} \right)$$
 * $$\left(-1,-1, 1,\frac{-1}\sqrt{5} \right)$$
 * $$\left( 0, 0, 0,\frac{4}\sqrt{5} \right)$$

Scaling these or the previous set of coordinates by $$\tfrac{\sqrt{5}}{4}$$ give unit-radius origin-centered regular 5-cells with edge lengths $$\sqrt{\tfrac{5}{2}}$$. The hyperpyramid has coordinates:

 * $$\left( \sqrt{5}, \sqrt{5}, \sqrt{5}, -1 \right)/4$$
 * $$\left( \sqrt{5},-\sqrt{5},-\sqrt{5}, -1 \right)/4$$
 * $$\left(-\sqrt{5}, \sqrt{5},-\sqrt{5}, -1 \right)/4$$
 * $$\left(-\sqrt{5},-\sqrt{5}, \sqrt{5}, -1 \right)/4$$
 * $$\left( 0, 0, 0, 1 \right)$$

Coordinates for the vertices of another origin-centered regular 5-cell with edge length 2 and radius $$\sqrt{\tfrac{8}{5}}\approx 1.265$$ are:

 * $$\left( \frac{1}{\sqrt{10}},\ \frac{1}{\sqrt{6}},\  \frac{1}{\sqrt{3}},\  \pm1\right)$$
 * $$\left( \frac{1}{\sqrt{10}},\ \frac{1}{\sqrt{6}},\  \frac{-2}{\sqrt{3}},\ 0   \right)$$
 * $$\left( \frac{1}{\sqrt{10}},\ -\sqrt{\frac{3}{2}},\ 0,\                   0   \right)$$
 * $$\left( -2\sqrt{\frac{2}{5}},\ 0,\                  0,\                   0   \right)$$

Scaling these by $$\sqrt{\tfrac{5}{8}}$$ to unit-radius and edge length $$\sqrt{\tfrac{5}{2}}$$ gives:
 * $$\left(\sqrt{3}, \sqrt{5}, \sqrt{10},\pm\sqrt{30} \right)/(4\sqrt{3})$$
 * $$\left(\sqrt{3}, \sqrt{5}, -\sqrt{40},0\right)/(4\sqrt{3})$$
 * $$\left(\sqrt{3},-\sqrt{45},0,0\right)/(4\sqrt{3})$$
 * $$\left(-1, 0, 0, 0 \right)$$

The vertices of a 4-simplex (with edge $\sqrt{2}$ and radius 1) can be more simply constructed on a hyperplane in 5-space, as (distinct) permutations of (0,0,0,0,1) or (0,1,1,1,1); in these positions it is a facet of, respectively, the 5-orthoplex or the rectified penteract.

Geodesics and rotations
The 5-cell has only digon central planes through vertices. It has 10 digon central planes, where each vertex pair is an edge, not an axis, of the 5-cell. Each digon plane is orthogonal to 3 others, but completely orthogonal to none of them. The characteristic isoclinic rotation of the 5-cell has, as pairs of invariant planes, those 10 digon planes and their completely orthogonal central planes, which are 0-gon planes which intersect no 5-cell vertices.

There are only two ways to make a circuit of the 5-cell through all 5 vertices along 5 edges, so there are two discrete Hopf fibrations of the great digons of the 5-cell. Each of the two fibrations corresponds to a left-right pair of isoclinic rotations which each rotate all 5 vertices in a circuit of period 5. The 5-cell has only two distinct period 5 isoclines (those circles through all 5 vertices), each of which acts as the single isocline of a right rotation and the single isocline of a left rotation in two different fibrations.

Below, a spinning 5-cell is visualized with the fourth dimension squashed and displayed as colour. The Clifford torus is depicted in its rectangular (wrapping) form.

Boerdijk–Coxeter helix
A 5-cell can be constructed as a Boerdijk–Coxeter helix of five chained tetrahedra, folded into a 4-dimensional ring. The 10 triangle faces can be seen in a 2D net within a triangular tiling, with 6 triangles around every vertex, although folding into 4-dimensions causes edges to coincide. The purple edges form a regular pentagon which is the Petrie polygon of the 5-cell. The blue edges connect every second vertex, forming a pentagram which is the Clifford polygon of the 5-cell. The pentagram's blue edges are the chords of the 5-cell's isocline, the circular rotational path its vertices take during an isoclinic rotation, also known as a Clifford displacement.
 * 5-cell 5-ring net.png

Projections

The A4 Coxeter plane projects the 5-cell into a regular pentagon and pentagram. The A3 Coxeter plane projection of the 5-cell is that of a square pyramid. The A2 Coxeter plane projection of the regular 5-cell is that of a triangular bipyramid (two tetrahedra joined face-to-face) with the two opposite vertices centered.

Irregular 5-cells
In the case of simplexes such as the 5-cell, certain irregular forms are in some sense more fundamental than the regular form. Although regular 5-cells cannot fill 4-space or the regular 4-polytopes, there are irregular 5-cells which do. These characteristic 5-cells are the fundamental domains of the different symmetry groups which give rise to the various 4-polytopes.

Orthoschemes
A 4-orthoscheme is a 5-cell where all 10 faces are right triangles. An orthoscheme is an irregular simplex that is the convex hull of a tree in which all edges are mutually perpendicular. In a 4-dimensional orthoscheme, the tree consists of four perpendicular edges connecting all five vertices in a linear path that makes three right-angled turns. The elements of an orthoscheme are also orthoschemes (just as the elements of a regular simplex are also regular simplexes). Each tetrahedral cell of a 4-orthoscheme is a 3-orthoscheme, and each triangular face is a 2-orthoscheme (a right triangle).

Orthoschemes are the characteristic simplexes of the regular polytopes, because each regular polytope is generated by reflections in the bounding facets of its particular characteristic orthoscheme. For example, the special case of the 4-orthoscheme with equal-length perpendicular edges is the characteristic orthoscheme of the 4-cube (also called the tesseract or 8-cell), the 4-dimensional analogue of the 3-dimensional cube. If the three perpendicular edges of the 4-orthoscheme are of unit length, then all its edges are of length $\sqrt{1}$, $\sqrt{2}$, $\sqrt{3}$, or $\sqrt{4}$, precisely the chord lengths of the unit 4-cube (the lengths of the 4-cube's edges and its various diagonals). Therefore this 4-orthoscheme fits within the 4-cube, and the 4-cube (like every regular convex polytope) can be dissected into instances of its characteristic orthoscheme.

A 3-orthoscheme is easily illustrated, but a 4-orthoscheme is more difficult to visualize. A 4-orthoscheme is a tetrahedral pyramid with a 3-orthoscheme as its base. It has four more edges than the 3-orthoscheme, joining the four vertices of the base to its apex (the fifth vertex of the 5-cell). Pick out any one of the 3-orthoschemes of the six shown in the 3-cube illustration. Notice that it touches four of the cube's eight vertices, and those four vertices are linked by a 3-edge path that makes two right-angled turns. Imagine that this 3-orthoscheme is the base of a 4-orthoscheme, so that from each of those four vertices, an unseen 4-orthoscheme edge connects to a fifth apex vertex (which is outside the 3-cube and does not appear in the illustration at all). Although the four additional edges all reach the same apex vertex, they will all be of different lengths. The first of them, at one end of the 3-edge orthogonal path, extends that path with a fourth orthogonal $\sqrt{1}$ edge by making a third 90 degree turn and reaching perpendicularly into the fourth dimension to the apex. The second of the four additional edges is a $\sqrt{2}$ diagonal of a cube face (not of the illustrated 3-cube, but of another of the tesseract's eight 3-cubes). The third additional edge is a $\sqrt{3}$ diagonal of a 3-cube (again, not the original illustrated 3-cube). The fourth additional edge (at the other end of the orthogonal path) is a long diameter of the tesseract itself, of length $\sqrt{4}$. It reaches through the exact center of the tesseract to the antipodal vertex (a vertex of the opposing 3-cube), which is the apex. Thus the characteristic 5-cell of the 4-cube has four $\sqrt{1}$ edges, three $\sqrt{2}$ edges, two $\sqrt{3}$ edges, and one $\sqrt{4}$ edge.

The 4-cube can be dissected into 24 such 4-orthoschemes  eight different ways, with six 4-orthoschemes surrounding each of four orthogonal $\sqrt{4}$ tesseract long diameters. The 4-cube can also be dissected into 384 smaller instances of this same characteristic 4-orthoscheme, just one way, by all of its symmetry hyperplanes at once, which divide it into 384 4-orthoschemes that all meet at the center of the 4-cube.

More generally, any regular polytope can be dissected into g instances of its characteristic orthoscheme that all meet at the regular polytope's center. The number g is the order of the polytope, the number of reflected instances of its characteristic orthoscheme that comprise the polytope when a single mirror-surfaced orthoscheme instance is reflected in its own facets. More generally still, characteristic simplexes are able to fill uniform polytopes because they possess all the requisite elements of the polytope. They also possess all the requisite angles between elements (from 90 degrees on down). The characteristic simplexes are the genetic codes of polytopes: like a Swiss Army knife, they contain one of everything needed to construct the polytope by replication.

Every regular polytope, including the regular 5-cell, has its characteristic orthoscheme. There is a 4-orthoscheme which is the characteristic 5-cell of the regular 5-cell. It is a tetrahedral pyramid based on the characteristic tetrahedron of the regular tetrahedron. The regular 5-cell can be dissected into 120 instances of this characteristic 4-orthoscheme  just one way, by all of its symmetry hyperplanes at once, which divide it into 120 4-orthoschemes that all meet at the center of the regular 5-cell.

The characteristic 5-cell (4-orthoscheme) of the regular 5-cell has four more edges than its base characteristic tetrahedron (3-orthoscheme), which join the four vertices of the base to its apex (the fifth vertex of the 4-orthoscheme, at the center of the regular 5-cell). If the regular 5-cell has unit radius and edge length $$\sqrt{\tfrac{5}{2}}$$, its characteristic 5-cell's ten edges have lengths $$\sqrt{\tfrac{1}{10}}$$ , $$\sqrt{\tfrac{1}{30}}$$ , $$\sqrt{\tfrac{2}{15}}$$ around its exterior right-triangle face (the edges opposite the characteristic angles 𝟀, 𝝉, 𝟁), plus $$\sqrt{\tfrac{3}{20}}$$ , $$\sqrt{\tfrac{1}{20}}$$ , $$\sqrt{\tfrac{1}{60}}$$ (the other three edges of the exterior 3-orthoscheme facet the characteristic tetrahedron, which are the characteristic radii of the regular tetrahedron), plus $$\sqrt{1}$$ , $$\sqrt{\tfrac{3}{8}}$$ , $$\sqrt{\tfrac{1}{6}}$$ , $$\sqrt{\tfrac{1}{16}}$$ (edges which are the characteristic radii of the regular 5-cell). The 4-edge path along orthogonal edges of the orthoscheme is $$\sqrt{\tfrac{1}{30}}$$, $$\sqrt{\tfrac{2}{15}}$$ , $$\sqrt{\tfrac{1}{60}}$$ , $$\sqrt{\tfrac{1}{16}}$$ , first from a regular 5-cell vertex to a regular 5-cell edge center, then turning 90° to a regular 5-cell face center, then turning 90° to a regular 5-cell tetrahedral cell center, then turning 90° to the regular 5-cell center.

Isometries
There are many lower symmetry forms of the 5-cell, including these found as uniform polytope vertex figures:

The tetrahedral pyramid is a special case of a 5-cell, a polyhedral pyramid, constructed as a regular tetrahedron base in a 3-space hyperplane, and an apex point above the hyperplane. The four sides of the pyramid are made of triangular pyramid cells.

Many uniform 5-polytopes have tetrahedral pyramid vertex figures with Schläfli symbols ∨{3,3}.

Other uniform 5-polytopes have irregular 5-cell vertex figures. The symmetry of a vertex figure of a uniform polytope is represented by removing the ringed nodes of the Coxeter diagram.

Compound
The compound of two 5-cells in dual configurations can be seen in this A5 Coxeter plane projection, with a red and blue 5-cell vertices and edges. This compound has 3,3,3 symmetry, order 240. The intersection of these two 5-cells is a uniform bitruncated 5-cell. = ∩.
 * Compound_dual_5-cells_A5_coxeter_plane.png

This compound can be seen as the 4D analogue of the 2D hexagram {$6⁄2$} and the 3D compound of two tetrahedra.

Related polytopes and honeycombs
The pentachoron (5-cell) is the simplest of 9 uniform polychora constructed from the [3,3,3] Coxeter group.

It is in the {p,3,3} sequence of regular polychora with a tetrahedral vertex figure: the tesseract {4,3,3} and 120-cell {5,3,3} of Euclidean 4-space, and the hexagonal tiling honeycomb {6,3,3} of hyperbolic space.

It is one of three {3,3,p} regular 4-polytopes with tetrahedral cells, along with the 16-cell {3,3,4} and 600-cell {3,3,5}. The order-6 tetrahedral honeycomb {3,3,6} of hyperbolic space also has tetrahedral cells.

It is self-dual like the 24-cell {3,4,3}, having a palindromic {3,p,3} Schläfli symbol.

title: 5-cell


text:
Mittelbau-Dora concentration camp

Mittelbau-Dora (also Dora-Mittelbau and Nordhausen-Dora) was a Nazi concentration camp located near Nordhausen in Thuringia, Germany. It was established in late summer 1943 as a subcamp of Buchenwald concentration camp, supplying slave labour from many Eastern countries occupied by Germany (including evacuated survivors of eastern extermination camps), for extending the nearby tunnels in the Kohnstein and for manufacturing the V-2 rocket and the V-1 flying bomb. In the summer of 1944, Mittelbau became an independent concentration camp with numerous subcamps of its own. In 1945, most of the surviving inmates were sent on death marches or crammed in trains of box-cars by the SS. On 11 April 1945, US troops freed the remaining prisoners.

The inmates at Dora-Mittelbau were treated in a brutal and inhumane manner, working 14-hour days and being denied access to basic hygiene, beds, and adequate rations. Around one in three of the roughly 60,000 prisoners who were sent to Dora-Mittelbau died.

Today, the site hosts a memorial and museum.

Background
In early summer 1943, mass production of the A4 (later better known as V-2, V standing for Vergeltung or retribution) ballistic rocket started at the Heeresanstalt Peenemünde on the Baltic island of Usedom as well as at the Raxwerke in Wiener Neustadt, Austria and at the Zeppelin works in Friedrichshafen on Lake Constance.

On 18 August 1943, a bombing raid by the Royal Air Force on Peenemünde ("Operation Hydra") seriously damaged the facilities and ended construction of V-2s there. Other air raids had damaged the other two sites in June and August. As a result, the Nazi leadership accelerated plans to move military construction to areas less threatened by Allied bombers. On 22 August 1943, Adolf Hitler ordered SS leader Heinrich Himmler to use concentration camp workers in future A4/V-2 production. One of the sites selected was at the mountain known as Kohnstein, near Nordhausen in Thuringia. Since 1936, the Wirtschaftliche Forschungsgesellschaft (WIFO) (Economic Research Company) had been building a subterranean fuel depot for the Wehrmacht there. By late summer 1943, this was almost finished.

To oversee the creation and operation of the new construction facility, Albert Speer, Himmler and Karl Saur agreed on the foundation of  (the name referring to the works' location in Mitteldeutschland). Its board consisted of Hans Kammler, who was head of Amtsgruppe C at the SS-Wirtschafts-Verwaltungshauptamt (WVHA) and two of Speer's armaments managers, and, the former seconded from Commerzbank. To actually run the plant,, who had earlier been in charge of producing the "Tiger I" tank at Henschel, was appointed. Operational security for the project was overseen by SS-Oberstürmbannfuhrer Helmut Bischoff, a former Gestapo official and a member of Kammler's staff. The initial contract for Mittelwerk was for 12,000 rockets, valued at 750 million Reichsmark for a standard price per unit, once production reached 5,000 units, of 50,000 Reichsmark per rocket.

Especially for Kammler, this became a prestige project.

Establishment
Only ten days after the raid on Peenemünde, on 28 August 1943, the first 107 concentration camp inmates from Buchenwald arrived with their SS guards at the Kohnstein. The official name of the new subcamp of Buchenwald was Arbeitslager Dora. Another 1,223 Buchenwald prisoners followed on 2 September and workers from Peenemünde came in mid-October. Over the next months, many more prisoners were brought to the area in almost daily transports from Buchenwald. By late September, the number of workers had risen to over 3,000, by late October to 6,800 and by Christmas 1943 to more than 10,500. Since there were initially no huts, the prisoners were housed inside the tunnels – in specially designated Schlafstollen with four levels of beds stacked over each other.

There were no sanitary facilities except for barrels that served as latrines. Inmates (the majority of them from the Soviet Union, Poland or France) died from hunger, thirst, cold and overwork. During the first months, most of the work done was heavy construction and transport. Only in January 1944, when production of the A4/V-2 began, were the first prisoners moved to the new above-ground camp on the south side of the mountain. Many had to sleep in the tunnels until May 1944.

In these initial months, from October 1943 to March 1944, out of a total of 17,500 slave labourers, almost 2,900 died at Dora. Another 3,000 who were very ill or dying were sent to Lublin-Majdanek and Bergen-Belsen concentration camps. Few of them survived. At the end of 1943, the Dora work squads had "the highest death rate in the entire concentration camp system".

By late 1943, production had started. On 10 December, Albert Speer and his staff visited the tunnels, observing the terrible conditions and finding them littered with corpses. Some members of Speer's staff were so shocked that they had to take an extra period of leave. A week later, Speer wrote to Kammler, congratulating him on his success "in transforming the underground installation ... from its raw condition two months ago into a factory, which has no equal in Europe and which is unsurpassed even when measured against American standards. I take this opportunity to express my appreciation for this really unique achievement and to ask you also in future to support Herr Degenkolb in this wonderful way."

Prisoners
Inmates came from almost all countries of Europe; many of them had been arrested for political reasons. After May 1944, Jews were also brought to Mittelbau. With the dissolution of the so-called Zigeuner-Familienlager (Gypsy family camp) at Auschwitz-Birkenau, the SS transported many Roma and Sinti to Mittelbau between April and August 1944.

The prisoners were subject to extreme cruelty. As a result, they often suffered injuries, including permanent disability and disfigurement, and death. Severe beatings were routine, as was deliberate starvation, torture and summary executions.

In total, around 60,000 prisoners passed through the Mittelbau camps between August 1943 and March 1945. The precise number of people killed is impossible to determine. The SS files counted around 12,000 dead. In addition, an unknown number of unregistered prisoners died or were murdered in the camps. Around 5,000 sick and dying were sent in early 1944 and in March 1945 to Lublin and Bergen-Belsen.

Of those killed, around 350 were hanged (including 200 for sabotage). The rate of executions notably accelerated after the personnel from Auschwitz arrived: in February and March 1945, the SS on some days hanged 30, on one occasion even 50 prisoners.

Rocket production
On 1 January 1944, the Mittelwerk delivered its first three rockets, all of which suffered from serious production defects. The SS considered those prisoners who had expanded the tunnels in autumn and winter of 1943/44 as unusable in actual production work, because they were either too weakened or not qualified for work on the assembly lines. As a result, new prisoners were brought in from other concentration camps. From March 1944, the others were moved to newly created subcamps in the area around Nordhausen where they continued to be used for digging new tunnels or working at construction sites above ground.

By late January, 56 rockets had been produced. By May, monthly output was 400 units. There were still defects, resulting in launch-pad and mid-air explosions. Output was still far below the goal of 1,000 units per month. Wernher von Braun visited the Nordhausen plant on 25 January 1944 and again on 6 May 1944, when he met Walter Dornberger, Arthur Rudolph and Albin Sawatzki, discussing the need to enslave another 1,800 skilled French workers.

On 8 September 1944, the first V-2 built at Mittelbau was successfully launched at London. That month, production hit 600 units, a pace that was kept up until February 1945.

Construction and subcamps
On 31 December 1943, construction of the above-ground camp, less than a kilometre from the tunnel B entrance was sufficiently completed for the workers to move in. The underground detainee accommodations (Schlafstollen or "sleeping tunnels") were dismantled in May 1944.

Besides the main camp Dora, housing an average of 15,000 prisoners, the main subcamps were Lager Ellrich (established 2 May 1944, averaging around 8,000 prisoners), Lager Harzungen (1 April 1944, 4,000 prisoners), Lager Rottleberode (13 March 1944, 1,000 prisoners) and the SS construction units III and IV (totaling around 3,000 prisoners, distributed among several small camps along a newly constructed railway line between Nordhausen and Herzberg am Harz. More subcamps were added once Mittelbau was officially independent. By spring 1945, the number of inmates totaled over 40,000 in around 40 camps.

From spring/summer 1944, the camp became the centre of a subcamp system of its own. Originally, these still were part of the Buchenwald system. With the creation of the Jägerstab (Fighter Staff), led by Speer, as an institution to oversee a boost to fighter plane production and the move of military production underground, facilities for the production of fighter planes for the Junkers company were to be created around Nordhausen – along with the necessary infrastructure. In addition, after the creation of the Geilenbergstab (named after Edmund Geilenberg), over the summer of 1944 more underground construction was requested for the German petroleum industry. Demand for workers for these projects was satisfied with concentration camp prisoners, but also with foreign forced labourers, POWs and drafted Germans.

The SS administration separated Mittelbau-Dora from Buchenwald at the end of September 1944 and Dora became the center of it. In effect, the new camp became officially operational on 1 November 1944 with 32,471 prisoners.

Decline
By the time Dora became operational in November 1944, the decline of Mittelbau-Dora was already beginning. With the subcamps overcrowded and the weather turning colder, conditions in all camps deteriorated and the death rate rose significantly. After peaking in March 1944 at 750, this had declined to 100 to 150 per month by the summer. From November it picked up and in December 1944 the official tally was 570, of whom 500 died at Lager Ellrich.

Transfers from Auschwitz
At the end of 1944, the SS began to evacuate the inmates of Auschwitz and Gross-Rosen before the advancing Red Army. Many of them were transported to the Mittelbau. Through March 1945, up to 16,000 prisoners arrived, including women and children. Although many died in transit, this raised the number of Jews at Mittelbau. Those who survived were often extremely weak or sick. Once again, the death rate rose: Between January and early April 1945, around 6,000 inmates died, around 3,000 of them at the Boelcke-Kaserne (a former Luftwaffe barracks) at Nordhausen, which had been used by the SS after January 1945 as the main Sterbelager (camp for the dying) for the Mittelbau system. Also from January to April 1945, at least 1,700 V-2 and over 6,000 V-1 rockets were built.

Along with the inmates from Auschwitz arrived several hundred SS guards who joined the staff at Mittelbau, including Richard Baer, who succeeded Otto Förschner as overall Mittelbau commandant on 1 February 1945. Baer replaced most senior personnel with people from Auschwitz. Franz Hössler became commandant of the Häftlinglager Dora. Eduard Wirths became the new Standortarzt. became head of the Arbeitseinsatz-Dienststelle which coordinated the use of forced labour. became head of the Politische Abteilung (the local Gestapo office).

Allied attacks
On 3 and 4 April 1945, Nordhausen was attacked in two waves by several hundred Lancasters and Mosquitos of Nos 1 and 8 Groups of the Royal Air Force Bomber Command. Around 75% of the town was destroyed, the medieval old town was hit particularly hard. Out of 40,000 inhabitants, roughly 8,800 people died, 20,000 lost their homes. Among the dead were also an estimated 1,300-1,500 Mittelbau prisoners, who were confined at the Boelcke-Kaserne at the time.

Evacuation
In early April 1945, as US troops were advancing towards the Harz, the SS decided to evacuate most of the Mittelbau camps. In great haste and with considerable brutality, the inmates were forced to board box cars. Several trains, each with thousands of prisoners, left the area through 6 April for Bergen-Belsen, Sachsenhausen and Ravensbrück. Others were forced to walk through the Harz hills towards the northeast. Those unable to keep up with these death marches were summarily shot by the guards.

The worst atrocity occurred at Gardelegen, known as the Gardelegen massacre. More than 1,000 prisoners from Mittelbau and Neuengamme subcamps were murdered in a barn that was set on fire. Those who were not burned alive were shot by SS, Wehrmacht and men of the Volkssturm.

Overall, although no reliable statistics on the number of deaths on these transports exist, estimates put the number of prisoners killed at up to 8,000.

Liberation
As most of the camps of the Mittelbau system were completely evacuated, there were not many prisoners left to be liberated by the Allies. The SS also left several hundred sick prisoners at Dora and in the Boelcke-Kaserne. They were freed when US troops (consisting of the 3rd Armored Division, the 104th Infantry Division, and the 9th Infantry Division) reached Nordhausen on 11 April 1945. There were also around 1,300 dead prisoners at the barracks.

War correspondents took pictures and made films of the dead and dying prisoners at Dora. Like the documentation of Nazi atrocities at Bergen-Belsen, these were published around the globe and became some of the best-known testimonies of Nazi crimes.

Most of those inmates who survived the transports were freed in mid-April at Bergen-Belsen or at other camps. Some, however, remained prisoners until early May and were freed in Mecklenburg or Austria.

In total, even conservative estimates put the number of people who did not survive being sent to Mittelbau-Dora at over 20,000. Thus, around one in three of those confined here did not survive.

Bergen-Belsen
Transports from Mittelbau arrived at Bergen-Belsen between 8 and 11 April 1945. Several thousand men were housed in the so-called Kasernenlager around 2 km north of the main camp, which was already overflowing with prisoners. Of the approximately 15,000 prisoners from Mittelbau, about half were from the Soviet Union and Poland. Although not in good health, these men were much healthier than most of the prisoners in the Belsen main camp. When the British Army liberated Belsen on 15 April, many of the inmates turned on their former overseers at Mittelbau. About 170 of these "Kapos" were killed that day.

Belsen Trial
Some of the SS personnel who had come from Auschwitz with the evacuation trains went on to Bergen-Belsen when Mittelbau was itself evacuated. A few of them, notably Franz Hössler, were prosecuted by the British military authorities at the Belsen trial in Lüneburg in September 1945. However, charges at this trial related only to crimes committed either at Auschwitz or at Bergen-Belsen, not at Mittelbau. Hössler was among those found guilty and executed on 13 December 1945.

Dora Trial
Following the June 1945 Fedden Mission investigation of conditions at Dora, the trial "The United States of America versus Arthur Kurt Andrae et al." trial commenced on 7 August 1947 at the Dachau internment camp against 19 defendants. Otto Förschner was not a defendant in the Dora Trial, since he had already been executed after being convicted in the Dachau camp trial.

The court convicted 15 Dora SS guards and Kapos (one of them was executed), four defendants were acquitted. The trial also addressed the question of liability of the engineers and scientists — former Generaldirektor of Mittelwerk Georg Rickhey was acquitted. Arthur Rudolph (recruited in 1945 under Operation Paperclip and later exiled from the US in 1984) was not even charged. A related trial was also held 1959–1961 in Essen.

Research continuity
Immediately after taking control of the area, US specialists began to inspect the rocket works and seized materials, parts and documents. They were later joined by British experts. Eventually the Soviets took over.

Apart from Rickhey, Rudolph, and von Braun, several dozen former Mittelwerk engineers and scientists quickly hired on with the US government. They first constructed rocket weapons or jet planes and then mostly went on to join the American space program. The Soviets also hired some of the engineers.

Like the rocket engineers, many construction engineers at Mittelwerk were able to continue with their careers. Very few were charged in connection with their role in the Nazi slave labour program.

DP-camp
After liberation, the US forces and the United Nations Relief and Rehabilitation Administration (UNRRA) turned Dora and Harzungen camps into accommodations for displaced persons (DPs). In mid-May 1945, there were around 14,000 people living at Dora, several hundred liberated concentration camp inmates and many POWs as well as foreign civilian forced labourers. Repatriation was fairly quick for those from Western Europe, but many from Eastern Europe had to wait months before they were able to return home. In early July, Thuringia passed from American to Soviet control. The Red Army now used Dora as a repatriation camp for former Polish and Soviet slave labourers. The Soviet authorities treated their citizens who had been forced to work for the Germans with suspicion, blaming them for collaborating with the enemy. These men were subject to debriefing by the Soviet secret service and some of them were imprisoned once more and sent to the Gulag.

Umsiedlerlager
Once the last forced labourers had left, Dora camp was used from December 1945 by German authorities as a holding camp for Germans expelled from Czechoslovakia. They were then distributed among various municipalities in northern Thuringia. The number of expelled housed in the camp averaged about 5,000. The camp was dissolved in July 1946.

Demolition
After that, the town of Nordhausen had the huts at Dora dismantled and re-erected at other locations in the district as emergency housing for the homeless. Only the camp's crematorium, the fire station and the camp prison remained. Nature reclaimed the area of the camp. The Soviets briefly continued to use parts of the tunnel network for manufacturing rockets. In 1947, the entrances and some internal parts were blown up in accordance with the Allied agreement to destroy military facilities in Germany.

Similar to what happened at Dora, most of the subcamps were soon dismantled and the wood used for heating or new construction. Local authorities decided in 1952 to demolish the Dora camp prison – in the face of protests by former detainees.

German Democratic Republic
By the early 1950s, most of the traces of the central Dora camp had disappeared. Whilst the prison was being demolished, some people from Nordhausen began to turn the area around the crematorium into a memorial and cemetery. In 1964, the local district SED created the Mahn- und Gedenkstätte Dora and had a sculpture by the artist Jürgen von Woyski erected in front of the crematorium. In 1966, a permanent exhibition opened inside the building under the title Die Blutspur führt nach Bonn ("the blood trail leads to Bonn"), implying a historical continuity between the Nazi concentration camp and the government of West Germany.

By contrast with Buchenwald, Sachsenhausen and Ravensbrück, the communist government of the GDR never raised Dora to the status of Nationale Mahn- und Gedenkstätte (national memorial). In the early 1970s, the local authorities turned the completely overgrown muster ground into an Ehrenplatz der Nationen with a rostrum, flag poles and an eternal fire. In 1988, an attempt was made to access one of the tunnels inside Kohnstein, but it was abandoned due to a lack of funds that same year.

Reunified Germany
After reunification, the memorial was redesigned. A small portion of the original tunnel system was reopened and has been accessible to visitors since 1995. Since 2000, the Stiftung Gedenkstätten Buchenwald und Mittelbau-Dora runs the memorial, financed by the Thuringian state and the federal government. The GDR era memorial installations were left intact as a documentation of the way the Communist regime treated the Nazi past. A new permanent exhibition opened in a new museum building in 2006. Some work has also been done at the largest subcamp, Lager Ellrich-Juliushütte, that had been cut in half by the inner-German border.

title: Mittelbau-Dora concentration camp


text:
File:Arms-peterborough.jpg

Licensing
Armorial bearings of Peterborough City Council. From Civic Heraldry of England and Wales, with permission.

Use in the articles Peterborough and Peterborough City Council is believed to be fair, within the meaning of the Copyright, Designs and Patents Act 1988 s.30 (1988 cap.48) in the United Kingdom and the Copyright Act of 1976, 17 U.S.C. § 107 (Pub.L. 94-553) in the United States. The image is used to identify Peterborough City Council, a subject of public interest. Peterborough City Council redirects to the article at Peterborough local government.

The exhibition of low-resolution images of logos, to illustrate the subject in question on the English-language Wikipedia, hosted on servers in the United States by the non-profit Wikimedia Foundation qualifies as fair use under United States copyright law. It does not limit the copyright owner's rights to sell product or said image. No free equivalent is available or could be created that would serve the same encyclopedic purpose. The further use of this image on Wikipedia is not believed to disadvantage the copyright holder in any way.

Summary
Granted and assigned by Letters Patent sealed by Garter, Clarenceux and Norroy & Ulster Kings of Arms dated 06 September 1960. Azure two Keys in saltire Or enfiled by a Mural Crown Argent; the Shield ensigned with a Mural Crown of six Towers Gold. On either side a Lion Ermine winged Argent charged on the wing with three Estoiles Sable the interior paw resting on a Tree trunk fesswise proper. Motto Upon this rock.

Peterborough owes it origin to the foundation circa in AD 655 by Paeda, King of Mercia, of a monastery (from which the present fine Cathedral has derived) dedicated to the glory of Christ and the honour of Saint Peter. The Shield shows the keys, symbolic of those to the gates of Heaven given by Christ to St. Peter (Matthew 16 v.19). They are shown enfiled by the mural crown as a differentiation to the simple crossed keys which are the arms recorded for the See of Gloucester. The gold mural crown replacing a Crest above the shield is intended as a civic symbol and this is particularly emphasized by the towers, the whole suggesting the walls of a town. The lions are the ermine lions of the Marquess of Exeter, hereditary Lord Paramount of Peterborough, differenced by the wings of the eagle supporters of Mordaunt, first Earl of Peterborough, the estoiles or stars thereon coming from his arms. The tree trunks derive from a device of Earl Fitzwilliam, whose estate forms an important part of the area. The Compartment upon which the supporters stand is composed of rock from its traditional association with Peter (and Paeda) and the motto is similarly derived.

The earlier version, adopted on incorporation in 1874, impaled the coats of arms of the bishopric (cross keys) to the dexter with those of the dean and chapter (cross swords) to the sinister.

title: File:Arms-peterborough.jpg


text:
User:Hroefn

The victim hands were nailed to the cross bar. The nails iron or wooden pegs would be driven through the wrists, not the palms (hands), as the palm would not support the body weight. It would tear and the victim would fall off the Greek/Roman Cross. Many Greek scholars define the cross shaped like the Greek capital Tau (T).

By: Daniel C. High

Three types of crosses used in crucifying: \/ /\ Or ___ Or __|__ |      |        |       |

title: User:Hroefn


text:
Gulfstream IV

The Gulfstream IV (or G-IV or GIV) and derivatives are a family of twinjet aircraft, mainly for private or business use. They were designed and built by Gulfstream Aerospace, a General Dynamics company based in Savannah, Georgia, United States, from 1985 until 2018. Aircraft power is provided by two Rolls-Royce RB.183 Tay turbofans.

Upon delivery of the last G450, over 900 GIV/GIV-SP/G450 units had been produced. The last of the G450’s was delivered on 19 January 2018 after 365 deliveries over 12 years, ending a 30-year production run, to be replaced by the G500.

Development

Gulfstream, in collaboration with Grumman, began work on the Gulfstream IV in March 1983 as a re-engined, stretched fuselage derivative of the Gulfstream III. The first GIV made its maiden flight on September 19, 1985. The model received type certification from the FAA on April 22, 1987. The G-IV entered into service with serial number 1000 in 1987 and was upgraded to the special purpose GIV-SP version at serial number 1214 in 1993. It was later redesignated G400 at serial number 1500. A shorter range variant was created based on the GIV and given the G300 designation in 2002.

In 2001, Gulfstream began work on an improved version of the GIV-SP, originally designated GIV-X. It was later renamed G450. The G450 is lengthened 1 ft (0.305 m) over the G400 and shares the forward fuselage and larger cockpit of the G550. Following its first flight on 30 April 2003, production of the G450 began in October 2004, replacing the G400. The G450 has better performance and comes with the PlaneView cockpit with four 14-inch (355 mm) liquid crystal displays and a Head up display (HUD). The shorter range G350 version of the G450 was developed and received certification in 2004.

By 2018, 1990 to 1992 GIVs were for sale at $1.6-4.4 million, 1992 to 1999 GIVSPs were listed for $1.25-5.2 million, 15-year-old G300s and G400s were available for $4.5-7 million and 2006 to 2016 G450s at $9.95-23.75 million.

Design

Compared to the Gulfstream III, a decision to redesign the wing structure for weight reduction presented an opportunity for an aerodynamic redesign of the wing to reduce cruise drag and increase range. Wing contour modifications had to be restricted to the forward 65% of wing chord so that no redesign of the control surfaces would be necessary. Modification of the inboard wing would have entailed a redesign of the fuselage floor structure, consequently this region of the wing was not modified. Outboard wing modifications were aimed at reducing the peak subcritical pressure coefficient and moving it aft in an effort to reduce shock strength and increase shock sweep.

At 12,420 lbs, the Rolls-Royce Tay fanjet engines provided more thrust than the 11,400 lbs of the Gulfstream III. Speed, noise levels, emissions, fuel economy, range, and cargo capacity were also markedly improved over the earlier model.

The Gulfstream IV wing has a weaker, more swept outboard shock resulting in a lower cruise drag. Other benefits arising from this design are a lower root bending moment due to the more inboard center of pressure, a lower stall speed due to washout and a larger fuel volume due to increased chord. These aerodynamic improvements result in an increase in range of over 300 nautical miles. In addition to the wing redesign, the Gulfstream IV also became the first business jet to have an entire glass cockpit.

The G400 has a large cabin, long range of 4,350 nautical miles (8,060 km) and the same comfort and design that characterize the G series. Maximum cruise height and speed are 45,000 ft and Mach 0.85. Earlier models were fitted with Honeywell's SPZ 8000 Avionics package. The SPZ 8400 Avionics Package was an option, becoming standard on later models. Its second-hand price was below $15 million (~$ in ) in 2009. Gulfstream had also considered making a 5.5 m longer, 24-27 seat model for airline use.

Operational history

The National Oceanic and Atmospheric Administration (NOAA) operates a GIV-SP (N49RF) modified to fly scientists and crew members at 45,000 feet around tropical cyclones. The aircraft was modified to drop instruments called "dropsondes" to measure windspeed, barometric pressure, humidity, and temperature as they fall to the surface of the ocean. By sampling the cyclone with these dropsondes over a 4,000 mile track around the storm, the forecasters at NOAA's National Hurricane Center and Hurricane Research Division can better predict where the hurricane will be "steered" by the upper level winds. They also predict wind shear that will either increase or decrease a hurricane's strength. The GIV-SP is suited for this mission since it is fast, and can fly long distances with ample cabin space for the crew and instruments. In 2009, the NOAA GIV-SP was further modified by the addition of a side-scanning Doppler radar to the rear fuselage. This radar is used for storm cloud profiling.

In June 1987 a Gulfstream IV set 22 world records in its class in flying west around the world in 45 hr 25 min. The next year another GIV set 11 world records flying east around the world. In 1990, Gulfstream CEO Allen Paulson and a Gulfstream flight crew set 35 international records for around-the-world flight in a GIV.

C-20F/G/H/J military variants

The U.S. military variant of the IV, designated C-20F/G/H/J Gulfstream IV in Department of Defense service. The C-20F is a GIV model operated by the U.S. Army in a command/executive transport role.

The C-20G aircraft may be configured for cargo operations, 26 passenger operations or combinations of the two. With passengers seats removed, it may be configured as three pallets with no passengers or two pallets and eight passengers or one pallet and fourteen passengers. With full seating, the aircraft is capable of accommodating up to twenty-six passengers and a crew of four. A hydraulically operated cargo door is installed on the starboard side of the aircraft, and a ball roller cargo floor is capable of accommodating palletized cargo. The C-20G was operated by Fleet Logistics Support Squadron Four Eight (VR-48) at Naval Air Facility, Andrews Air Force Base, Maryland before its 2012 deactivation. It is operated by VMR Detachment Kaneohe Bay, Marine Corps Air Station Kaneohe Bay, Marine Corps Base Hawaii. The C-20G is also known as the "Grey Ghost"

The C-20H is a GIV-SP model operated by the U.S. Air Force in a command/executive transport role. The C-20J is a GIV-SP model operated by the U.S. Army in a command/executive transport role.

The United States Department of Defense C-20A/B/C/D/E aircraft are all Gulfstream III variants.

G350/G450

The G450 is a designation for the model GIV-X, approved by the FAA on August 12, 2004, as is the G350, which has a reduced fuel capacity. Compared to the Gulfstream IV, its fuselage is 12 inches longer and the main entry door relocated aft. The Rolls-Royce Tay 611 engines are replaced by 611-8Cs with FADEC, redesigned thrust reversers, nacelles and pylons which increases range and payload, coupled with aerodynamic improvements. Many Gulfstream V-SP improvements are used: the Honeywell advanced flight deck display suite, electrical power generation, cabin temperature control and pressurization, nose and nose landing gear. It also has an improved APU and flap/stab actuation system, redesigned main landing gear wheels and brakes, flight control system hard-over protection system.

By the end of the G450 production run, 365 aircraft were produced, with prices ranging from $15 million to $32 million.

Civil operators

The aircraft is operated by private individuals, companies and executive charter operators, and in fractional ownership programs.

Government and military operators

 * Sultan of Brunei
 * Chilean Air Force
 * Côte d'Ivoire Air Force
 * Japan Air Self-Defense Force
 * Sultan of Johor
 * Royal Netherlands Air Force
 * Pakistan Air Force
 * Royal Saudi Air Force
 * Swedish Air Force
 * 🇹🇿 Tanzania
 * Tanzania Air Force Command
 * United States Air Force
 * United States Army
 * United States Navy
 * United States Marine Corps
 * National Oceanic and Atmospheric Administration
 * Swedish Air Force
 * 🇹🇿 Tanzania
 * Tanzania Air Force Command
 * United States Air Force
 * United States Army
 * United States Navy
 * United States Marine Corps
 * National Oceanic and Atmospheric Administration
 * National Oceanic and Atmospheric Administration

Former military operators

 * The Irish Air Corps previously operated a G-IV as a government transport.
 * The Government of Uganda purchased one G-IV SP in December 2000 at a cost of US$31.5 million for Presidential flights. It was replaced in February 2009 by a G550.
 * The Government of Uganda purchased one G-IV SP in December 2000 at a cost of US$31.5 million for Presidential flights. It was replaced in February 2009 by a G550.
 * The Government of Uganda purchased one G-IV SP in December 2000 at a cost of US$31.5 million for Presidential flights. It was replaced in February 2009 by a G550.

title: Gulfstream IV


text:
Pangnirtung

Pangnirtung (or Pang, also Pangniqtuuq, in syllabics: ᐸᖕᓂᖅᑑᖅ ) is an Inuit hamlet, in the Qikiqtaaluk Region of the Canadian territory of Nunavut, located on Baffin Island. The community is located about 45 km south of the Arctic Circle, and about 2,700 km from the North Pole. Pangnirtung is situated on a coastal plain at the coast of Pangnirtung Fjord, a fjord which eventually merges with Cumberland Sound. As of January 2022, the mayor is Lynn Mike.

Name
There is some confusion about the village name. Residents say the real name is Pangniqtuuq, which means "the place of many bull caribou". Early in 2005 residents voted against officially changing the name of the village to the native one, as Pangnirtung has achieved an international reputation. Its residents have created high-quality traditional arts in sculpture, as well as adaptation of themes and design in printmaking and weaving.

Pangnirtung is nicknamed the Switzerland of the Arctic, or simply Pang.

History
The Inuit and their ancestors, Paleo-Eskimo, have inhabited the area for thousands of years, perhaps up to 4000 years. Their cultures became well-adapted to the climate and environment.

Contact with European Canadians has been limited to less than the last century. In 1921, the Hudson's Bay Company established a trading post in Pangnirtung. Two years later, the Royal Canadian Mounted Police erected a permanent office. The first government-appointed teacher arrived in 1956. The first administrative office was established in 1962.

Since then, numerous Inuit have achieved success with marketing their traditional arts. They transformed traditional drawing skills to produce lithographs and other forms of prints, allowing reproduction and wider distribution of their work. Other artists have made sculptures and carvings in local stone. Since the government established a weaving studio in 1970, many Inuit have learned to weave and are producing tapestries and other works that find an international market.

Demographics
In the 2021 Canadian census conducted by Statistics Canada, Pangnirtung had a population of 1,504 living in 396 of its 456 total private dwellings, a change of NaN% from its 2016 population of 1,481. With a land area of 7.98 km2, it had a population density of in 2021.

Economic development
The community operates a turbot fishery. In 2008, the federal government budgeted for the construction of a harbour. Pangnirtung Fisheries Limited operates a packing plant to process local turbot catches. Founded in 1992 during peak summer operations the company has over 40 employees during peak season.

Auyuittuq Lodge is the hamlet's only hotel, which comprises 25 rooms, shared facilities, a dining room, and a lounge.

Local services
Power is supplied to Pangnirtung via standalone diesel generators operated by Qulliq Energy.

Fuel is imported via tanker and stored in a tank farm near the Pangnirtung Airport. The purchase of diesel fuel is the responsibility of the government of Nunavut.

Water, sewage, and garbage services are provided by the municipality of Pangnirtung. Water trucks fill up at a reservoir adjacent to the hamlet and deliver seven days a week. Sewage is pumped out and treated at the municipal treatment plant. Garbage is picked up five days a week and transported to a landfill that slowly deteriorates due to Arctic temperatures.

For emergency services it is protected by the 14-member Pangnirtung Fire Department. The fire service uses one pumper with one older reserve from one station. Policing is provided by the Royal Canadian Mounted Police Pangnirtung Detachment attached to V Division.

Mini C, The North West Company (Northern Store), Pangnirtung Inuit Co-op and Co-op Express are the only local retailers and grocery options. KFC Express, Pizza Hut and Co-op Express are the only fast food restaurants in the hamlet. Perishable goods are shipped by air and all other items by sealift when waters are ice-free.

Banking is done through the Co-op or money orders

Gasoline for cars or snowmobiles is done at the Quickstop or the Co-op.

Education
There are two schools in Pangnirtung:
 * Alookie Elementary School - kindergarten to Grade 5
 * Attagoyuk Ilisavik High School - Grades 6 to 12

Post secondary-studies opportunities can be made through Nunavut Arctic College's Community Learning Centre.

Recreation
Aksayuk Arena is a sports and recreational centre.

Transportation
Like all Nunavut communities Pangnirtung is a fly-in community with no road access to the rest of Nunavut. Pangnirtung Airport provides the only viable means of access. There are gravel roads in the community and residents use SUV's, pickup trucks, 4-wheel ATV's and snowmobiles.

Places of worship
Two churches can be found in Pangnirtung:
 * St. Luke's Anglican Church
 * Full Gospel (Pentecostal) Church

Health
Basic medical services are available at the Health Centre. Four beds are available for assessment only, with advance care via medevac to Iqaluit.

Near Pangnirtung
Pangnirtung is the nearest town (1 hour by boat) to Auyuittuq National Park and the location of one of two park offices, the other is in Qikiqtarjuaq. Located near to the Parks Canada office is the Angmarlik Visitor Centre. Iglunga, now uninhabited, is an Inuit hamlet, just south of Iglunga Island, is about 65 km to the west.

Small craft harbour
In 2009, the then Canadian Prime Minister, Stephen Harper, proposed building a new modern harbour in Pangnirtung to support the region's turbot-fishing industry. Harper received a warm welcome with many residents gathered at the airport to greet him. The town's 1,500 residents listened as Harper announced that $17 million worth of harbour construction promised in the last two budgets would get under way in the fall of that year. Harper said the greatest potential for the hamlet's future lies in the inshore turbot fishery. The shortfalls of the previous harbour were a big problem for fishermen: When the tide ebbed, the harbour turned to mud.

The work on the harbour was completed in September 2013. The entire project ended up costing about $40.5 million. The improvements to the harbour include a fixed wharf, breakwater, marshalling area, sea lift ramp and a dredged channel and basin. The improvements will allow residents to unload their catches faster by allowing smaller crafts to dock easily and safely.

Broadband communications
The community has been served by the Qiniq network since 2005. Qiniq is a fixed wireless service to homes and businesses, connecting to the outside world via a satellite backbone. The Qiniq network is designed and operated by SSI Micro. In 2017, the network was upgraded to 4G LTE technology, and 2G-GSM for mobile voice.

In popular culture
The 2022 Canadian Inuit science fiction film Slash/Back was filmed in Pangnirtung. It was directed by Nyla Innuksuk in her feature debut, and starred largely local actors recruited for the film.

Notable residents

 * Elisapee Ishulutaq
 * Simeonie Keenainak
 * Ipeelee Kilabuk
 * Peter Kilabuk, Nunavut's first Minister of Education
 * Nakasuk
 * Paul Okalik, Nunavut's first premier
 * Stephen Osborne
 * Andrew Qappik
 * Riit

title: Pangnirtung


text:
Talk:Graham's number

The ten leftmost digits of Graham’s number
The ten rightmost digits of Graham’s number is 2464195387, but what are the ten leftmost digits of Graham’s number? I want to know them like 2402:7500:901:F4A7:B569:939A:AC71:FAC9 (talk) 01:36, 17 November 2022 (UTC)
 * Somebody please put a banner at the top of this talk page with a warning related to this question that I'm sure people will keep asking over and over again. Georgia guy (talk) 02:02, 17 November 2022 (UTC)
 * Sorry, but I think that this article can show the leftmost 1000 digits and the rightmost 1000 digits for the Graham’s number. 2402:7500:901:F4A7:B569:939A:AC71:FAC9 (talk) 02:05, 17 November 2022 (UTC)
 * No, they can't. This is currently too difficult a problem to calculate.  At least, it is too difficult in base 10.  In base 3 the answer is 1000000000... SpinningSpark 14:21, 17 November 2022 (UTC)

Reference 6
What does Iteror.org have to do with Graham's number? Chasrob (talk) 10:52, 10 October 2023 (UTC)
 * It is a part of the chain which lies on the path to Wayback machine's link to the Scientific American article. A part of the service the reader needs to read the reference. When one part of the chain is broken, the ref is broken, so we need the chain, to read the Martin Gardner article. --Ancheta Wis   (talk  | contribs) 13:09, 10 October 2023 (UTC)
 * I've reformatted the reference so now the link in the title points to the archived version rather than to the usurped / dead link. --JBL (talk) 21:42, 10 October 2023 (UTC)

64 vs 63
Christ this is stupid. The relevant edits are   from September, before    from the last two days. Pinging. --JBL (talk) 23:45, 3 November 2023 (UTC)

 * Graham's Number is g(64), not g(63), most of the mathematical youtubers can confirm that Graham's Number is g(64) Joajohball MSAE (talk) 23:56, 3 November 2023 (UTC)
 * When a brand new editor makes a change like that without citing a source, it might be legit, but I can't assess it myself. "Most of the mathematical youtubers" - point to one, please.
 * Also, is this just a "start at 0" vs "start at 1" thing? DS (talk) 00:32, 4 November 2023 (UTC)
 * Numberphile, Dr. Trefor Bazett, Travis Richardson, a brazilian youtuber called "Ciência Todo Dia" and more, most of the people don't actually mention a number g(0). Joajohball MSAE (talk) 04:19, 4 November 2023 (UTC)
 * The number is almost always defined as g(64) instead of g(63). Source — Panamitsu (talk) 00:42, 4 November 2023 (UTC)
 * I don't really care whether this article uses zero indexing or not, whether is starts with g0 or g1, or whether Graham's number is g63 or g64.
 * But it needs to be consistent, and hopefully consistent with the body of literature it is based on.
 * Right now, we have the following text that disagrees with the mathematical notation that precedes it:
 * In other words, G is calculated in 64 steps: the first step is to calculate g(0) with four up-arrows between 3s; the second step is to calculate g(1) with g(0) up-arrows between 3s; the third step is to calculate g(2) with g(1) up-arrows between 3s; and so on, until finally calculating G = g(63) with g(62) up-arrows between 3s.
 * Earlier, g(0) is defined as equal to four, so not need to "calculate" it. And the final step is computing g(64) not g(63). Could someone please fix the text? Or the formulae? I'm not sure I want to wade into the dispute at this juncture. Mr. Swordfish (talk) 01:43, 13 November 2023 (UTC)
 * Ok. Nobody else stepped up so I made this edit myself.
 * There are still some other places in the article where there is a similar discrepancy with the stated definition. I'll take a look at addressing that. Mr. Swordfish (talk) 15:22, 15 November 2023 (UTC)

I don't want to bother right now, but g64 (rather than g(64)) seems to be universal everywhere else. Looks like that got changed in the same revision that shifted the numbering convention by 1. Patallurgist (talk) 01:56, 7 November 2023 (UTC)
 * (Incidentally, neither Graham nor Gardner used this notation. Does anyone know where it came from?) Patallurgist (talk) 02:15, 7 November 2023 (UTC)
 * Really? I wonder why people use that notation then. Waylon111 (talk) 21:32, 16 November 2023 (UTC)
 * Because often early attempts at notation when the mathematician is still figuring it all out is cumbersome, and more elegant notation is developed later. For example, Newton's Method_of_Fluxions notation for calculus - Leibniz's notation is what we use today. Or the Ackerman function, to cite just two examples.
 * Anyway, we have a reliable source - that uses that notation, or rather it uses subscript notation gn instead of function notation g(n). I'll leave making that change to the article as an exercise for the reader. (c: Mr. Swordfish (talk) 14:37, 17 November 2023 (UTC)

I reverted the notation to the subscript (g64) notation used in the revision of 17 August 2023, which was stable and had no issues. If anyone wishes to argue for changing to function notation they are welcome to post here. Arcorann (talk) 06:04, 22 November 2023 (UTC)

Rightmost decimal digits
Edited the "Rightmost decimal digits" section, fixing some mistakes (i.e., the wrong assumption that any integer tetration of height d should have at least d-1 stable digits, which is false... consequently, I added the trivial example of the base 2 that has d-2 stable digits only, given the fact that 2^^2=4 is not congruent modulo 10 to 2^^3=16), explaining which is the exact number of stable digits of G (providing also proper peer-reviewed references) and improving the overall quality of the page. Please, let me know if something is not clear or needs further edits. P.S. Still trying to learn how to sign my comments properly. --Marcokrt (talk) 16:35, 5 January 2024 (UTC)

Feedback from New Page Review process
I left the following feedback for the creator/future reviewers while reviewing this article: Please remember to tag redirects that you create per WP:REDCAT.

voorts (talk/contributions) 20:07, 4 July 2024 (UTC)

title: Talk:Graham's number