Regular polyhedra in the $3$-torus
Date:
Contributed talk in the 5th Workshop Symmetries in Graphs Maps and Polytopes (SIGMAP)
ELIM Conference Centre
West Malvern, U.K.
Abstract: Since Grünbaum's paper about regular polyhedra in ordinary $3$-space in the 70's, there has been a lot of work towards a classification symmetric polyhedra-like structures in several spaces. Coxeter, Schulte, McMullen and many other authors have studied symmetric tessellations of the $n$-dimensional torus. J. Bracho, in joint work with other authors found the regular polyhedra with planar faces in the projective space; a couple of years after, McMullen completed the list of regular projective polyhedra. In this talk we'll discuss the problem of classifying regular polyhedra in the $3$-dimensional torus.