Regular Polytopes Dover Books on Mathematics 3rd Edition by H S M Coxeter ISBN 0486614808 9780486614809

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Product details:

ISBN 10: 0486614808

ISBN 13: 9780486614809

Author: H. S. M. Coxeter 

Polytopes are geometrical figures bounded by portions of lines, planes, or hyperplanes. In plane (two dimensional) geometry, they are known as polygons and comprise such figures as triangles, squares, pentagons, etc. In solid (three dimensional) geometry they are known as polyhedra and include such figures as tetrahedra (a type of pyramid), cubes, icosahedra, and many more; the possibilities, in fact, are infinite! H. S. M. Coxeter’s book is the foremost book available on regular polyhedra, incorporating not only the ancient Greek work on the subject, but also the vast amount of information that has been accumulated on them since, especially in the last hundred years. The author, professor of Mathematics, University of Toronto, has contributed much valuable work himself on polytopes and is a well-known authority on them.
Professor Coxeter begins with the fundamental concepts of plane and solid geometry and then moves on to multi-dimensionality. Among the many subjects covered are Euler’s formula, rotation groups, star-polyhedra, truncation, forms, vectors, coordinates, kaleidoscopes, Petrie polygons, sections and projections, and star-polytopes. Each chapter ends with a historical summary showing when and how the information contained therein was discovered. Numerous figures and examples and the author’s lucid explanations also help to make the text readily comprehensible. Although the study of polytopes does have some practical applications to mineralogy, architecture, linear programming, and other areas, most people enjoy contemplating these figures simply because their symmetrical shapes have an aesthetic appeal. But whatever the reasons, anyone with an elementary knowledge of geometry and trigonometry will find this one of the best source books available on this fascinating study.

Table of contents:

CHAPTER I – POLYGONS AND POLYHEDRA
CHAPTER II – REGULAR AND QUASI-REGULAR SOLIDS
CHAPTER III – ROTATION GROUPS
CHAPTER IV – TESSELLATIONS AND HONEYCOMBS
CHAPTER V – THE KALEIDOSCOPE
CHAPTER VI – STAR-POLYHEDRA
CHAPTER VII – ORDINARY POLYTOPES IN HIGHER SPACE
CHAPTER VIII – TRUNCATION
CHAPTER IX – POINCARÉ’S PROOF OF EULER’S FORMULA
CHAPTER X – FORMS, VECTORS, AND COORDINATES
CHAPTER XI – THE GENERALIZED KALEIDOSCOPE
CHAPTER XII – THE GENERALIZED PETRIE POLYGON
CHAPTER XIII – SECTIONS AND PROJECTIONS
CHAPTER XIV – STAR-POLYTOPES

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Tags: H S M Coxeter, Regular Polytopes, Dover Books, Mathematics