• Corpus ID: 239768572

The volume of a spherical antiprism

  title={The volume of a spherical antiprism},
  author={Nikolay V. Abrosimov and Bao Quoc Vuong},
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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