Abstract

In the 70´s Coxeter considered the 4-dimensional regular polytopes and used the so-called Petrie Polygons to obtain quotients of the polytopes that, while having all possible rotational symmetry, lack reflectional symmetry. He called these objects Twisted Honeycombs. Nowadays, objects with such symmetry properties are often called chiral. In this talk I will review Coxeter´s twisted honeycombs and explore a natural way to extend Coxeter´s work to polytope-like structures, in particular, we shall see some properties and examples of so-called chiral skeletal polyhedra, and an application of them.