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The volume of a spherical antiprism with $S_{2n}$ symmetry Научная публикация

Журнал

Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304

Вых. Данные

Год: 2021, Том: 18, Номер: 2, Страницы: 1165-1179 Страниц : 15 DOI: 10.33048/semi.2021.18.088

Ключевые слова

Rotation followed by reflection; Spherical antiprism; Spherical isosceles trapezoid; Spherical volume; Symmetry group s2n

Авторы

Abrosimov N.V. ^1,2,3 , Vuong B. ^2,3

Организации

1	Sobolev Institute of Mathematics
2	Novosibirsk State University
3	Tomsk State University

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 su􏰅cient 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.

Abrosimov N.V. , Vuong B.
The volume of a spherical antiprism with $S_{2n}$ symmetry
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2021. V.18. N2. P.1165-1179. DOI: 10.33048/semi.2021.18.088 WOS Scopus OpenAlex

Опубликована online:

9 нояб. 2021 г.

Web of science:	WOS:000734395000008
Scopus:	2-s2.0-85124160291
OpenAlex:	W4205351345

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