Scissors Congruence, the Golden Ratio and Volumes in Hyperbolic 5-Space
By different scissors congruence techniques a number of dissection identities are presented between certain quasi-Coxeter polytopes, whose parameters are related to the golden section, and an ideal regular simplex in hyperbolic 5-space. As a consequence, several hyperbolic polyhedral 5-volumes can be computed explicitly in terms of Apery's constan zeta(3) and the trilogarithmic value pi(3)(pi/5).
scissors congruence hyperbolic 5-space quasi-coxeter polytopes trilogarithms zeta values