My actual goal is understanding highly symmetric polytopes. For example, regular polytopes, archimedean solids, complex regular polytopes, regular abstract polytopes, etc.
I apologize that I don't know the general term including all of these concepts hence I use the term regular abstract polytopes.
I choose H.S.M. Coxeter, Regular Polytopes and Peter McMullen, Egon Schulte, Abstract Regular Polytopes to refer.
Are there any suggestions?
On
The two books you mention, Coxeter and McMullen & Schulte, are the standard texts on the subject. You can also add Coxeter's Regular Complex Polytopes.
However polytopes and high symmetries are distinct areas of study which do not overlap as cleanly as one might expect. For example a regular complex polytope has no bounding surface in the topological sense but is better understood as a configuration. An abstract polytope is a class of incidence complex having a "diamond condition" ensuring for example that faces meet in pairs along edges and so on, but each cell (subface of 3 or more dimensions) does not need to be a topological ball. These both fly in the face of the simplicial decomposition of a manifold in order to determine its homology class, which is derived from Euler's original polyhedron formula V − E + F = 2 and leads to the understanding of a polytope as a class of topological CW complex.
A simple and well-illustrated introduction to the symmetry aspect is provided by Conway, Burgiel and Goodman-Strauss in The Symmetries of Things, while a good account of the topological origins is given by David S. Richeson in Euler's Gem: The Polyhedron Formula and the Birth of Topology.
You can find my own embryonic attempt at resolving some of these inconsistencies at http://www.steelpillow.com/polyhedra/morphic/morphic.html
Two standard references:
Lectures on Polytopes by Ziegler.
Convex Polytopes by Grünbaum.