Semiregular Gosset polytopes

Valerii Nikolaevich Berestovskii; Берестовский Валерий Николаевич; Yurii Gennadyevich Nikonorov; Никоноров Юрий Геннадьевич

doi:10.4213/im9169

Semiregular Gosset polytopes

Authors: Berestovskii V.N.¹, Nikonorov Y.G.²
Affiliations:
1. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
2. Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences
Issue: Vol 86, No 4 (2022)
Pages: 51-84
Section: Articles
URL: https://journals.rcsi.science/1607-0046/article/view/133873
DOI: https://doi.org/10.4213/im9169
ID: 133873

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Abstract

The paper is devoted to the study of metric properties of semiregular polytopesin Euclidean spaces

R^{n}

for

n ⩾ 4

(Gosset polytopes). Theresults obtained here enable us to complete the classification of regular andsemiregular polytopes in Euclidean spaces whose sets of vertices form normalhomogeneous or Clifford–Wolf homogeneous metric spaces.

Keywords

finite normal homogeneous metric space, finite homogeneous metric space, finiteClifford–Wolf homogeneous metric space, Gosset polytope, semiregular polytope, regular polytope

About the authors

Valerii Nikolaevich Berestovskii

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Email: berestov@ofim.oscsbras.ru
Doctor of physico-mathematical sciences, Professor

Yurii Gennadyevich Nikonorov

Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences

Email: nikonorov2006@mail.ru
Doctor of physico-mathematical sciences, Professor

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