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. Polygons And Polyhedra -- Regular And Quasi-regular Solids -- Rotation Groups -- Tessellations And Honeycombs -- Kaleidoscope -- Star-polyhedra -- Ordinary Polytopes In Higher Space -- Truncation -- Poincare's Proof Of Euler's Formula -- Forms, Vectors, And Coordinates -- Generalized Kaleidoscope -- Generalized Petrie Polygon -- Sections And Projections -- Star-polytopes [by] H. S. M. Coxeter. Bibliography: P. 306-314.

Regular Polytopes: 3rd Edition

Coxeter, H. S. M. (Harold Scott Macdonald), 1907-2003

[by] H. S. M. Coxeter

New York, Dover Publications

Athenaeum of Philadelphia

Macmillan

Dover books on intermediate and advanced mathematics, Third edition, New York, 1973

3rd ed., unabridged and corr. repr. of the 2nd ed, New York, 1973

United States, United States of America

3d ed., New York, New York State, 1973

3rd ed., New York, United States, 1973

2d ed, New York, ©1963

Bibliography: p. 306-314.

Reprint of the 2nded., New York: Macmillan, 1963.

Foremost book available on polytopes, incorporating ancient Greek and most modern work done on them. Beginning with polygons and polyhedrons, the book moves on to multi-dimensional polytopes in a way that anyone with a basic knowledge of geometry and trigonometry can easily understand. Definitions of symbols. Eight tables plus many diagrams and examples. 1963 edition.

Polygongs and Polyhedra
Regular Polygons
Polyhedra
The five Platonic Solids
Graphs and Maps
"A voyage round the world"
Euler's Formula
Regular Maps
Configurations
Historical remarks
Regular and Quasi-Regular Solids
Regular Polyhedra
Reciprocation
Quasi-regular polyhedra
Radii and angles
Descartes' Formula

xiii, 321 p. 22 cm
Bibliography: p. 306-314

2024-07-01