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Regular Polytopes Paperback – June 1, 1973

ISBN-13: 978-0486614809 ISBN-10: 0486614808 Edition: 3rd

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Regular Polytopes + Shapes, Space, and Symmetry (Dover Books on Mathematics) + The Beauty of Geometry: Twelve Essays (Dover Books on Mathematics)
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Product Details

  • Paperback: 350 pages
  • Publisher: Dover Publications; 3rd edition (June 1, 1973)
  • Language: English
  • ISBN-10: 0486614808
  • ISBN-13: 978-0486614809
  • Product Dimensions: 8.5 x 5.4 x 0.7 inches
  • Shipping Weight: 13.6 ounces (View shipping rates and policies)
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (10 customer reviews)
  • Amazon Best Sellers Rank: #187,454 in Books (See Top 100 in Books)

Editorial Reviews

About the Author

H. S. M. Coxeter: Through the Looking Glass
Harold Scott MacDonald Coxeter (1907–2003) is one of the greatest geometers of the last century, or of any century, for that matter. Coxeter was associated with the University of Toronto for sixty years, the author of twelve books regarded as classics in their field, a student of Hermann Weyl in the 1930s, and a colleague of the intriguing Dutch artist and printmaker Maurits Escher in the 1950s.

In the Author's Own Words:
"I'm a Platonist — a follower of Plato — who believes that one didn't invent these sorts of things, that one discovers them. In a sense, all these mathematical facts are right there waiting to be discovered."

"In our times, geometers are still exploring those new Wonderlands, partly for the sake of their applications to cosmology and other branches of science, but much more for the sheer joy of passing through the looking glass into a land where the familiar lines, planes, triangles, circles, and spheres are seen to behave in strange but precisely determined ways."

"Geometry is perhaps the most elementary of the sciences that enable man, by purely intellectual processes, to make predictions (based on observation) about the physical world. The power of geometry, in the sense of accuracy and utility of these deductions, is impressive, and has been a powerful motivation for the study of logic in geometry."

"Let us revisit Euclid. Let us discover for ourselves a few of the newer results. Perhaps we may be able to recapture some of the wonder and awe that our first contact with geometry aroused." — H. S. M. Coxeter


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Customer Reviews

4.3 out of 5 stars
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Most Helpful Customer Reviews

24 of 24 people found the following review helpful By T. Ruen on April 17, 2007
Format: Paperback
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.
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29 of 33 people found the following review helpful By A Customer on February 16, 1999
Format: Paperback
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.
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8 of 8 people found the following review helpful By William McKeeman on December 8, 2008
Format: Paperback
References:
The following free MATLAB program implements many of the n-dimensional polytopes.
[...]
There is similar information available from Mathematica
[...]
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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5 of 5 people found the following review helpful By Dr Baz on March 19, 2008
Format: Paperback
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.
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1 of 1 people found the following review helpful By Roberto L Mazzarella on March 5, 2013
Format: Paperback Verified Purchase
Regular Polytopes is not Euclidian Geometry. It's an advanced good step to being able to imagine or visualize multiple dimensions. Without an advanced math background, I just slow down and contemplate what Coexeter says.
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