Title: The volume of a compact hyperbolic antiprism
Speaker: Nikolay Abrosimov, Novosibirsk State University
Time: 16:00-17:00, 8 November, Place: Room 522, Gewu Building
Abstract:
We consider a compact hyperbolic antiprism. It is a convex polyhedron with 2n vertices in the hyperbolic space ℍ3. This polyhedron has a symmetry group 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 polyhedra in ℍ3. Then we find relations between their dihedral angles and edge lengths in the form of a cosine rule. Finally, we obtain exact integral formulas expressing the volume of a hyperbolic antiprism in terms of the edge lengths. arXiv:1807.08297 [math.MG]
