Theory of Polyhedra-Mathematics Monograph Series 9

This monograph is for a unified theory of surfaces, embeddings and maps all considered as polyhedra via the joint tree modal which was initiated from the author’s articles in the seventies of last century and has been basically developed in recent decades. Complete invariants for each classification are topologically, combinatorially or isomorphically extracted. A number of counting polynomials including handle and crosscap polynomials are presented. In particular, an appendix serves as the exhaustive counting super maps (rooted and nonrooted) including these polynomials with under graphs of small size for the reader’s digests.

Chapter I Preliminaries
Chapter II Surfaces
Chapter III Embeddings of Graphs
Chapter IV Mathematical Maps
Chapter V Duality on Surfaces
Chapter VI Invariants on Basic Class
Chapter VII Asymmetrization
Chapter VIII Asymmetrized Census
Chapter IX Petal Bundles
Chapter X Super Maps of Genus Zero
Chapter XI Symmetric Census
Chapter XII Cycle Oriented Maps
Chapter XIII Census by Genus
Chapter XIV Classic Applications