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Nikolay Abrosimov-The volume of a compact hyperbolic antiprism
发布人:吴劲松  发布时间:2018-11-02   浏览次数:16

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


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]