Random tilings of spherical 3-manifolds

A set of random tilings for the compact Euclidean 3-manifolds have been considered recently. In this paper, non-deterministic triangulations of spherical 3-manifolds based on recursive procedures are introduced. Simplicial structures for lens, prism and Poincaré spherical dodecahedron spaces are described. The configurational entropies for the random structures depend only on the information in 2D and are consistent with the Bekenstein–Hawking bound.