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The volume of a spherical antiprism with S-2n symmetry. / Abrosimov, N.; Vuong, B.

In: Сибирские электронные математические известия, Vol. 18, No. 2, 24, 09.11.2021, p. 1165-1179.

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

Harvard

Abrosimov, N & Vuong, B 2021, 'The volume of a spherical antiprism with S-2n symmetry', Сибирские электронные математические известия, vol. 18, no. 2, 24, pp. 1165-1179. https://doi.org/10.33048/SEMI.2021.18.088

APA

Abrosimov, N., & Vuong, B. (2021). The volume of a spherical antiprism with S-2n symmetry. Сибирские электронные математические известия, 18(2), 1165-1179. [24]. https://doi.org/10.33048/SEMI.2021.18.088

Vancouver

Abrosimov N, Vuong B. The volume of a spherical antiprism with S-2n symmetry. Сибирские электронные математические известия. 2021 Nov 9;18(2):1165-1179. 24. doi: 10.33048/SEMI.2021.18.088

Author

Abrosimov, N. ; Vuong, B. / The volume of a spherical antiprism with S-2n symmetry. In: Сибирские электронные математические известия. 2021 ; Vol. 18, No. 2. pp. 1165-1179.

BibTeX

@article{7e74ea4977614bbbbc901489baffa396,
title = "The volume of a spherical antiprism with S-2n symmetry",
abstract = "We consider a spherical antiprism. It is a convex polyhedron,with 2n vertices in the spherical space S 3. This polyhedron has a group,of symmetries S 2n generated by a mirror-rotational symmetry of order,2n, i.e. rotation to the angle π/n followed by a reflection. We establish,necessary and sufficient conditions for the existence of such polyhedron in,S 3. Then we find relations between its dihedral angles and edge lengths,in the form of cosine rules through a property of a spherical isosceles,trapezoid. Finally, we obtain an explicit integral formula for the volume,of a spherical antiprism in terms of the edge lengths ",
keywords = "spherical antiprism, spherical volume, symmetry group S-2n, rotation followed by reflection, spherical isosceles trapezoid, Spherical isosceles trapezoid, Symmetry group s, Spherical antiprism, Rotation followed by reflection, Spherical volume",
author = "N. Abrosimov and B. Vuong",
note = "Funding Information: Abrosimov, N.V., Vuong, B., The volume of a spherical antiprism with S2n symmetry. {\textcopyright} 2021 Abrosimov N.V., Vuong B. This work was supported by the Ministry of Science and Higher Education of Russia (agreement No. 075-02-2021-1392). Received October, 17, 2021, published November, 9, 2021. Publisher Copyright: {\textcopyright} 2021 Abrosimov N.V., Vuong B",
year = "2021",
month = nov,
day = "9",
doi = "10.33048/SEMI.2021.18.088",
language = "English",
volume = "18",
pages = "1165--1179",
journal = "Сибирские электронные математические известия",
issn = "1813-3304",
publisher = "Sobolev Institute of Mathematics",
number = "2",

}

RIS

TY - JOUR

T1 - The volume of a spherical antiprism with S-2n symmetry

AU - Abrosimov, N.

AU - Vuong, B.

N1 - Funding Information: Abrosimov, N.V., Vuong, B., The volume of a spherical antiprism with S2n symmetry. © 2021 Abrosimov N.V., Vuong B. This work was supported by the Ministry of Science and Higher Education of Russia (agreement No. 075-02-2021-1392). Received October, 17, 2021, published November, 9, 2021. Publisher Copyright: © 2021 Abrosimov N.V., Vuong B

PY - 2021/11/9

Y1 - 2021/11/9

N2 - We consider a spherical antiprism. It is a convex polyhedron,with 2n vertices in the spherical space S 3. This polyhedron has a group,of symmetries S 2n generated by a mirror-rotational symmetry of order,2n, i.e. rotation to the angle π/n followed by a reflection. We establish,necessary and sufficient conditions for the existence of such polyhedron in,S 3. Then we find relations between its dihedral angles and edge lengths,in the form of cosine rules through a property of a spherical isosceles,trapezoid. Finally, we obtain an explicit integral formula for the volume,of a spherical antiprism in terms of the edge lengths

AB - We consider a spherical antiprism. It is a convex polyhedron,with 2n vertices in the spherical space S 3. This polyhedron has a group,of symmetries S 2n generated by a mirror-rotational symmetry of order,2n, i.e. rotation to the angle π/n followed by a reflection. We establish,necessary and sufficient conditions for the existence of such polyhedron in,S 3. Then we find relations between its dihedral angles and edge lengths,in the form of cosine rules through a property of a spherical isosceles,trapezoid. Finally, we obtain an explicit integral formula for the volume,of a spherical antiprism in terms of the edge lengths

KW - spherical antiprism

KW - spherical volume

KW - symmetry group S-2n

KW - rotation followed by reflection

KW - spherical isosceles trapezoid

KW - Spherical isosceles trapezoid

KW - Symmetry group s

KW - Spherical antiprism

KW - Rotation followed by reflection

KW - Spherical volume

UR - http://www.scopus.com/inward/record.url?scp=85124160291&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=47669563

U2 - 10.33048/SEMI.2021.18.088

DO - 10.33048/SEMI.2021.18.088

M3 - Article

VL - 18

SP - 1165

EP - 1179

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

IS - 2

M1 - 24

ER -

ID: 35217249