Geodesic triangulations exist for cusped Platonic manifolds
arXiv:1705.04247
Abstract
We show that if a cusped hyperbolic manifold is Platonic, i.e., can be decomposed into isometric Platonic solids, it can also be decomposed into geodesic ideal tetrahedra.
4 pages, 4 figures; in version 2, the second half of the proof was rewritten to address concerns by the referee