Volumes of ideal hyperbolic drums

Abstract

Milnor computed the volumes of ideal hyperbolic prisms as part of an effort to construct 3-manifolds whose volumes are finite rational sums of the Lobachevsky function evaluated at rational multiples of pi. Motivated by these results and with an eye to related applications, we prove a volume formula for arbitrary ideal hyperbolic antiprisms, also called drums.

6 pages, 4 figures