Аннотация
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.
Язык оригинала | английский |
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Номер статьи | 1842010 |
Число страниц | 12 |
Журнал | Journal of Knot Theory and its Ramifications |
Том | 27 |
Номер выпуска | 13 |
DOI | |
Состояние | Опубликовано - ноя 2018 |