Regular Polytopes

An Introduction to the Geometry of N Dimensions which I have used well over the years seems be a good book to go with this one. It may takes me years to get the worth of this book, but I have already the first yield. The combination of group theory with higher dimensions in combinatorial topological terms has been a 20th century gold mine of new ideas and new groups. That some of the results have seeded the Engineering mathematics of error correcting codes should be noted. That Cosmology has recently been using both Coxeter and Cartan to see back toward the beginning of time shows that physics hasn't been blind to geometry.

References: 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

This book is a classic in the field and written by the man who revitalised the entire field of geometry. It is not intended as a step-by-step guide to making polyhedral models. But if you want a grasp on polytopes in n-dimensional space, this is the book for you. The cover and figures would benefit from a new edition but the mathematical content is concise and comprehensible.

I just wanted to counter the previous reviewer. This book isn't intended as something for beginners, and certainly could only be well taught as a graduate level math course. Still if you're able to take in bits at a time, there's lots of beautiful theory and history of higher dimensional polytopes. A book that takes a lifetime to write can take a lifetime to appreciate, and this is such a book.

Thi is an excellent text that I recommend to anyone seriously interested in geometry.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.