Standard

Ideal right-angled polyhedra in Lobachevsky space. / Yurievich, Vesnin Andrei; Alexandrovich, Egorov Andrey.

In: Chebyshevskii Sbornik, Vol. 21, No. 2, 01.02.2020, p. 65-83.

Research output: Contribution to journal › Article › peer-review

Harvard

Yurievich, VA & Alexandrovich, EA 2020, 'Ideal right-angled polyhedra in Lobachevsky space', Chebyshevskii Sbornik, vol. 21, no. 2, pp. 65-83. https://doi.org/10.22405/2226-8383-2020-21-2-65-83

APA

Yurievich, V. A., & Alexandrovich, E. A. (2020). Ideal right-angled polyhedra in Lobachevsky space. Chebyshevskii Sbornik, 21(2), 65-83. https://doi.org/10.22405/2226-8383-2020-21-2-65-83

Vancouver

Yurievich VA, Alexandrovich EA. Ideal right-angled polyhedra in Lobachevsky space. Chebyshevskii Sbornik. 2020 Feb 1;21(2):65-83. doi: 10.22405/2226-8383-2020-21-2-65-83

Author

Yurievich, Vesnin Andrei ; Alexandrovich, Egorov Andrey. / Ideal right-angled polyhedra in Lobachevsky space. In: Chebyshevskii Sbornik. 2020 ; Vol. 21, No. 2. pp. 65-83.

BibTeX

@article{79cd2c5415d341f0a404b422aea75085,
title = "Ideal right-angled polyhedra in Lobachevsky space",
abstract = "In this paper we consider a class of right-angled polyhedra in three-dimensional Lobachevsky space, all vertices of which lie on the absolute. New upper bounds on volumes in terms the number of faces of the polyhedron are obtained. Volumes of polyhedra with at most 23 faces are computed. It is shown that the minimum volumes are realized on antiprisms and twisted antiprisms. The first 248 values of volumes of ideal right-angled polyhedra are presented. Moreover, the class of polyhedra with isolated triangles is introduces and there are obtained combinatorial bounds on their existence as well as minimal examples of such polyhedra are given.",
keywords = "Antiprism, Hyperbolic 3-space, Ideal polyhedron, Right-angled polyhedron",
author = "Yurievich, {Vesnin Andrei} and Alexandrovich, {Egorov Andrey}",
note = "Веснин А.Ю., Егоров А.А. Идеальные прямоугольные многогранники в пространстве Лобачевского // Чебышевский сборник. - 2020. - Т. 21. - № 2. - С. 65-83",
year = "2020",
month = feb,
day = "1",
doi = "10.22405/2226-8383-2020-21-2-65-83",
language = "English",
volume = "21",
pages = "65--83",
journal = "Chebyshevskii Sbornik",
issn = "2226-8383",
publisher = "State Lev Tolstoy Pedagogical University",
number = "2",

}

RIS

TY - JOUR

T1 - Ideal right-angled polyhedra in Lobachevsky space

AU - Yurievich, Vesnin Andrei

AU - Alexandrovich, Egorov Andrey

N1 - Веснин А.Ю., Егоров А.А. Идеальные прямоугольные многогранники в пространстве Лобачевского // Чебышевский сборник. - 2020. - Т. 21. - № 2. - С. 65-83

PY - 2020/2/1

Y1 - 2020/2/1

N2 - In this paper we consider a class of right-angled polyhedra in three-dimensional Lobachevsky space, all vertices of which lie on the absolute. New upper bounds on volumes in terms the number of faces of the polyhedron are obtained. Volumes of polyhedra with at most 23 faces are computed. It is shown that the minimum volumes are realized on antiprisms and twisted antiprisms. The first 248 values of volumes of ideal right-angled polyhedra are presented. Moreover, the class of polyhedra with isolated triangles is introduces and there are obtained combinatorial bounds on their existence as well as minimal examples of such polyhedra are given.

AB - In this paper we consider a class of right-angled polyhedra in three-dimensional Lobachevsky space, all vertices of which lie on the absolute. New upper bounds on volumes in terms the number of faces of the polyhedron are obtained. Volumes of polyhedra with at most 23 faces are computed. It is shown that the minimum volumes are realized on antiprisms and twisted antiprisms. The first 248 values of volumes of ideal right-angled polyhedra are presented. Moreover, the class of polyhedra with isolated triangles is introduces and there are obtained combinatorial bounds on their existence as well as minimal examples of such polyhedra are given.

KW - Antiprism

KW - Hyperbolic 3-space

KW - Ideal polyhedron

KW - Right-angled polyhedron

UR - http://www.scopus.com/inward/record.url?scp=85086128524&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=42773647

U2 - 10.22405/2226-8383-2020-21-2-65-83

DO - 10.22405/2226-8383-2020-21-2-65-83

M3 - Article

AN - SCOPUS:85086128524

VL - 21

SP - 65

EP - 83

JO - Chebyshevskii Sbornik

JF - Chebyshevskii Sbornik

SN - 2226-8383

IS - 2

ER -

ID: 24520770