Regular Complex Polytopes [Hardcover]

H. S. M. Coxeter (Author)

Book Description

ISBN-10: 0521394902 | ISBN-13: 978-0521394901 | Publication Date: April 26, 1991 | Edition: 2

The properties of regular solids exercise a fascination which often appeals strongly to the mathematically inclined, whether they are professionals, students or amateurs. In this classic book Professor Coxeter explores these properties in easy stages, introducing the reader to complex polyhedra (a beautiful generalization of regular solids derived from complex numbers) and unexpected relationships with concepts from various branches of mathematics: magic squares, frieze patterns, kaleidoscopes, Cayley diagrams, Clifford surfaces, crystallographic and non-crystallographic groups, kinematics, spherical trigonometry, and algebraic geometry. In the latter half of the book, these preliminary ideas are put together to describe a natural generalization of the Five Platonic Solids. This updated second edition contains a new chapter on Almost Regular Polytopes, with beautiful 'abstract art' drawings. New exercises and discussions have been added throughout the book, including an introduction to Hopf fibration and real representations for two complex polyhedra.

Editorial Reviews

Review

The properties of polytopes, the four-dimensional analog of polyhedra, exercise an intellectual fascination that appeals strongly to the mathematically inclined, whether they are professionals, students or amateurs. In this classic book, Professor Coxeter explores these properties in easy stages introducing the reader to complex polytopes (a beautiful generalization of regular solids derived from complex numbers) and the unexpected relationships that complex polytopes have with concepts from various branches of mathematics. In the first half of the book the author discusses magic squares, frieze patterns, kaleidoscopes, Cayley diagrams, Clifford surfaces, non-crystallographic groups, kinematics, spherical trigonometry, and algebraic geometry. Later these ideas are assembled to describe a natural generalization of the Five Platonic Solids. The fully updated second edition contains a new chapter on "Almost Regular Polytopes" and beautiful abstract art drawings. In addition, new exercises and discussions, including an introduction to Hopf fibration and real representations for two complex polyhedra, supplement the text. -- Book Description

Product Details

• Hardcover: 224 pages
• Publisher: Cambridge University Press; 2 edition (April 26, 1991)
• Language: English
• ISBN-10: 0521394902
• ISBN-13: 978-0521394901
• Product Dimensions: 11.1 x 10.1 x 0.8 inches
• Shipping Weight: 2.4 pounds
• Average Customer Review: 4.5 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,156,569 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

2 of 2 people found the following review helpful:

4.0 out of 5 stars Regular Complex Polytopes, October 18, 2007

By 

J. A. De Wet (Plettenberg Bay,South Africa) - See all my reviews
(REAL NAME)   

This review is from: Regular Complex Polytopes (Hardcover)

Coxeter's book covers a wide field of finite group representations including the groups of quaternions which unfortunately he does not relate to the Exceptional Lie algebras E6,E7 and E8, that are of growing interest to particle physicists, by utilising the Mackay correspondence.There are good short sections on E6 and E8 in Ch 12 (called the Hessian and Witting polyhedra) but I found that too much depended on other references.I would also liked to have found a closer link between the Coxeter diagrams and those of Dynkin which are now classics.

1 of 2 people found the following review helpful:

5.0 out of 5 stars there is a reason they want $128 for this used..., March 17, 2009

By 

R. Bagula "Roger L. Bagula" (Lakeside, Ca United States) - See all my reviews
(VINE VOICE)    (REAL NAME)   

This review is from: Regular Complex Polytopes (Hardcover)

It is said that H.S.M. Coxeter reinvented geometry for the 20th century.
This book is the reference they give for E_8 circle connection diagrams.
I have it checked out for two weeks,
two years is a more likely estimate.
There is a cheap substitute in "Regular Polytropes" from Dover:Regular Polytopes,
but it probably isn't the same...