Abstract
The problem of calculating volumes of non-Euclidean polytopes was already studied by Lobachevsky and Schlafli and is of actual interest, in particular, in connection with the structure of volume spectra of hyperbolic space forms. A brief summary of these results and an introduction to the volume problem for hyperbolic polytopes are given. The covolumes of some hyperbolic five-dimensional manifolds are computed; these are built upon hyperbolic crystals of simple combinatorial metrical type, and their volumes are all commensurable with Riemann’s zeta function at three.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.