New Research Results on the Regular Polytopes

This monograph examines the n-dimensional regular polytopes from various aspects through a series of papers, model pictures and data. These papers don't seem to have direct relations among them, but they, in fact, separately explored various aspects of the n-dimensional regular polytopes, such as structure, internal relationship, included angles and size scales, etc.. The mathematical knowledges involved includes group theory, combinatorial mathematics, disperse geometry, partial differential geometry and topology etc. They form the unique characteristics of this monograph: each paper has its own independent character, and all of the papers are inter-connected and related to the n-dimensional regular polytopes. What is more important is that the monograph contains many rarely known formulae, relative expressions and data. The main purpose of writing this monograph is that by digesting the research presented, people can understand that the reasoning ability of mankind can absolutely reach the n-dimensional space and calculate accurately the numerical values concerning the n-dimensional regular polytopes.