The volume of a spherical antiprism with $S_{2n}$ symmetry Full article
| Journal |
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304 |
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| Output data | Year: 2021, Volume: 18, Number: 2, Pages: 1165-1179 Pages count : 15 DOI: 10.33048/semi.2021.18.088 | ||||||
| Tags | Rotation followed by reflection; Spherical antiprism; Spherical isosceles trapezoid; Spherical volume; Symmetry group s2n | ||||||
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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 sucient 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.
Cite:
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
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
Dates:
| Published online: | Nov 9, 2021 |
Identifiers:
| Web of science: | WOS:000734395000008 |
| Scopus: | 2-s2.0-85124160291 |
| OpenAlex: | W4205351345 |
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