Finite Homogeneous Subspaces of Euclidean Spaces

Autor:	V. N. Berestovskiĭ, Yu. G. Nikonorov
Rok vydání:	2021
Předmět:	Convex hull General Mathematics Archimedean solid Combinatorics symbols.namesake Polyhedron Metric space symbols Tetrahedron Mathematics::Metric Geometry Cube Isometry group Mathematics Regular polytope
Zdroj:	Siberian Advances in Mathematics. 31:155-176
ISSN:	1934-8126 1055-1344
Popis:	The paper is devoted to the study of the metric properties of regular and semiregular polyhedra in Euclidean spaces. In the first part, we prove that every regular polytope of dimension 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–Wolf homogeneous finite metric space. The second part of the paper is devoted to the study of special properties of Archimedean solids. In particular, for each Archimedean solid, its description is given as the convex hull of the orbit of a suitable point of a regular tetrahedron, cube or dodecahedron under the action of the corresponding isometry group.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::85cc68408f5467db605e732763a53455 https://doi.org/10.1134/s1055134421030019 Zobrazit plný text záznamu Full text from SpringerLink