• Corpus ID: 239768572

The volume of a spherical antiprism

@inproceedings{Abrosimov2021TheVO,
  title={The volume of a spherical antiprism},
  author={Nikolay V. Abrosimov and Bao Quoc Vuong},
  year={2021}
}
We consider a spherical antiprism. It is a convex polyhedron with 2n vertices in the spherical space S. This polyhedron has a group of symmetries S2n 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 . Then we find relations between its dihedral angles and edge lengths in the form of cosine rules through a property of a spherical isosceles… 

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References

SHOWING 1-10 OF 10 REFERENCES
The volume of a compact hyperbolic antiprism
We consider a compact hyperbolic antiprism. It is a convex polyhedron with [Formula: see text] vertices in the hyperbolic space [Formula: see text]. This polyhedron has a symmetry group [Formula: see
Hyperbolic volumes of Fibonacci manifolds
A. Yu. Vesnin and A. D. Mednykh UDC 515.16 + 512.817.7 This article is devoted to the study of three-dimensional compact orientable hyperbolic manifolds connected with the Fibonacci groups. The
On the volume of a hyperbolic octahedron with $$\bar 3$$-symmetry
We consider hyperbolic octahedra with $$\bar 3$$-symmetry. For these octahedra, we find existence conditions, establish relations between the edge lengths and dihedral angles, and obtain exact
Geometry of Spaces of Constant Curvature
TLDR
This paper develops elementary geometry in a way very similar to that used to create the geometry the authors learned at school, but since its basic notions can be interpreted in different ways, this geometry can be applied to objects other than the conventional physical space.
The geometry and topology of 3-manifolds
On Volumes of some hyperbolic 3-manifolds
Mednykh, On the volume of a hyperbolic octahedron with 3-symmetry
  • Proceedings of the Steklov Institute of Mathematics,
  • 2015
Solodovnikov, Geometry of spaces of constant curvature, in Geometry II: Spaces of Constant Curvature
  • Encyclopedia of Mathematical Sciences
  • 1993
The volume of a hyperbolic tetrahedron with symmetry group S4
  • Trudy Instituta Matematiki i Mekhaniki UrO RAN,
  • 2017
Mednykh, Hyperbolic volumes of Fibonacci manifolds
  • Siberian Mathematical Journal,
  • 1995