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3 21 polytope — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/3_21_polytope
License (as archived): CC-BY-SA-4.0
Archived: 2026-11-06T15:13:53.480Z
SHA-256 of the archived text: 5c79f0c425098aee6c46fec4018ad59b518647793a55b63f20036eaf4e09b383
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3 21 polytope — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/3_21_polytope (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_f33914aa4ec7 (Metraipolis archive dc_f33914aa4ec7, sha256 5c79f0c425098aee6c46fec4018ad59b518647793a55b63f20036eaf4e09b383)

BibTeX

@misc{dcf33914aa4ec7,
  title = {3 21 polytope — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/3_21_polytope},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_f33914aa4ec7; sha256 5c79f0c425098aee6c46fec4018ad59b518647793a55b63f20036eaf4e09b383},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/3_21_polytope. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In 7-dimensional geometry, the 321 polytope is a uniform 7-polytope, constructed within the symmetry of the E7 group. It was discovered by Thorold Gosset, published in his 1900 paper. He called it a 7-ic semi-regular figure. Its Coxeter symbol is 321, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of one of the 3-node sequences. The rectified 321 is constructed by points at the mid-edges of the 321. The birectified 321 is constructed by points at the triangle face centers of the 321. The trirectified 321 is constructed by points at the tetrahedral centers of the 321, and is the same as the rectified 132. These polytopes are part of a family of 127 (27−1) convex uniform polytopes in 7 dimensions, made of uniform 6-polytope facets and vertex figures, defined by all permutations of rings in this Coxeter-Dynkin diagram: .

Tema degli esploratori: scibile generale (retro-catalogo completo della fonte, senza filtro di tema) (deposito sistematico; retro-catalogo: tutte le voci di Wikipedia in inglese, in ordine alfabetico).
Fonte: Wikipedia in inglese, voce «3 21 polytope» — https://en.wikipedia.org/wiki/3_21_polytope
Wikidata Q4636457: «uniform 7-polytope» (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q4636457
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/3_21_polytope?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1371079497, consultata il 2026-11-06T15:10:25.017Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: f80659308920de7cedcadd82d90af4e03b68ede9a2e729f820ac20950afa8769