The focus of this work is the study of global properties of various kinds of colorings and maps of simplicial complexes. In addition to the usual sorts of coloring, the author studies colorings determined by groups, colorings based on regular polyhedra, and continuous colorings in finitely and infinitely many colors. The emphasis is on how all the colorings fit together, rather than on the existence of colorings or the number of colorings. Beginning with some fundamental properties of simplicial complexes and colorings, the author shows how colorings relate to various aspects of group theory, geometry, graph theory, and topology.
Properties of the combinatorial category The symmetric group complex $S n$ Complexes arising from geometry Graphs Complexes with a structure group Reflexive and self dual complexes Continuous colorings Coloring with arbitrary complexes.