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Finite Homogeneous Subspaces of Euclidean Spaces Научная публикация

Журнал

Siberian Advances in Mathematics
ISSN: 1055-1344 , E-ISSN: 1934-8126

Вых. Данные

Год: 2021, Том: 31, Номер: 3, Страницы: 155-176 Страниц : 22 DOI: 10.1134/S1055134421030019

Ключевые слова

Archimedean solid; finite Clifford–Wolf homogeneous metric space; finite homogeneous metric space; finite normal homogeneous metric space; Platonic solid; regular polytope; semiregular polytope

Авторы

Berestovskiĭ V.N. ¹ , Nikonorov Y.G. ²

Организации

1	Sobolev Institute of Mathematics, Novosibirsk, 630090, Russian Federation
2	Southern Mathematical Institute of the Vladikavkaz Scientific Center ofRAS, Vladikavkaz, 362027, Russian Federation

Abstract: The paper is devoted to the study of the metric properties of regular and semiregularpolyhedra in Euclidean spaces. In the first part, we prove that every regular polytope ofdimension greater or equal than 4, and different from 120-cell in $$\mathbb {E}^4$$ is such that the set of its vertices is a Clifford–Wolfhomogeneous finite metric space. The second part of the paper is devoted to the study of specialproperties of Archimedean solids. In particular, for each Archimedean solid, its description isgiven as the convex hull of the orbit of a suitable point of a regular tetrahedron, cube ordodecahedron under the action of the corresponding isometry group. © 2021, Pleiades Publishing, Ltd.

Berestovskiĭ V.N. , Nikonorov Y.G.
Finite Homogeneous Subspaces of Euclidean Spaces
Siberian Advances in Mathematics. 2021. V.31. N3. P.155-176. DOI: 10.1134/S1055134421030019 Scopus OpenAlex

Scopus:	2-s2.0-85114728221
OpenAlex:	W3210103981

БД	Цитирований
Scopus	1
OpenAlex	7