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Prof. H.S.M. Coxeter, Professor Emeritus at the University of Toronto, has been called, "this century's preeminent classical geometer and mathematician of polyhedra" and "the world's best known geometer".
In his masterpiece 'Regular Polytopes', Professor Coxeter sets out the fulfilment of 24 years' work, introducing the reader to the dazzling beauty of his subject and relating it at every turn to other branches of mathematics such as graph theory, topology and the theory of groups.
The first six chapters deal with polygons and solid polyhedra and the remaining eight chapters deal with polytopes in higher space (a polytope is a geometrical figure bounded by portions of lines, planes or hyperplanes). The book is copiously illustrated with plates and line drawings and includes extensive tables and bibliography.
This book is a joy to read and will be of interest to students of mathematics and also to physicists now that polyhedra in higher dimensions are beginning to have important applications to modern string theory.
The book enumerates all n-dimensional polytopes and aids in visualizing multidimensional space.
The book could be improved with computer graphics of the polytopes, but otherwise it is perfect.
The following free MATLAB program implements many of the n-dimensional polytopes.
http://www.mathworks.com/matlabcentral/fileexchange/18523
There is similar information available from Mathematica
http://mathworld.wolfram.com/topics/Polytopes.html
P. S. Abrams and W. M. McKeeman. Computer display of the derived polytopes. CEGOS, June 1970
The Derived Polytopes in Euclidian N-Space, William Marshall McKeeman, Master of Science Thesis, July 7, 1961.
/s/ Bill McKeeman
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