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**About this book :- **

**Regular Polytopes ** written by
** H.S.M. Coxeter **.

A POLYTOPE is a geometrical figure bounded by portions of lines, planes, or hyperplanes ?? e.g., in two dimensions it is a polygon, in three a polyhedron. The word polytope seems to have been coined by Hoppe in 1????2, and introduced into English by Mrs. Stott about twenty years later. But the concept, under the name polyscheme, goes back to Schläfli, who completed his great monograph in 1??52.

However, there is a law of symmetry (4•32) which prohibits the inanimate occurrence of any pentagonal figure, such as the regular dodecahedron. Thus the chief reason for studying regular polyhedra is still the same as in the time of the Pythagoreans, namely, that their symmetrical shapes appeal to one’s artistic sense. (To be sure, there is a little more to it than that ?? Klein’s Lectures on the Icosahedron2 cast fresh light on the general quintic equation. But if Klein had not been an artist he might have expressed his results in purely algebraic terms.)

**Book Detail :- **
** Title: ** Regular Polytopes
** Edition: **
** Author(s): ** H.S.M. Coxeter
** Publisher: ** Dover Publications
** Series: **
** Year: ** 2012
** Pages: ** 562
** Type: ** PDF
** Language: ** English
** ISBN: ** 9780486141589
** Country: ** Canada

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**About Author :- **

The author **Harold Scott MacDonald "Donald" Coxeter **, CC, FRS, FRSC (1907–2003) British-born Canadian geometer. He is regarded as one of the greatest geometers of the 20th century.

Coxeter was born in Kensington to Harold Samuel Coxeter and Lucy (née Gee). His father had taken over the family business of Coxeter & Son, manufacturers of surgical instruments and compressed gases (including a mechanism for anaesthetising surgical patients with nitrous oxide), but was able to retire early and focus on sculpting and baritone singing; Lucy Coxeter was a portrait and landscape painter who had attended the Royal Academy of Arts. A maternal cousin was the architect Sir Giles Gilbert Scott. He worked for 60 years at the University of Toronto and published twelve books.

Since 1978, the Canadian Mathematical Society have awarded the Coxeter–James Prize in his honor. He was made a Fellow of the Royal Society in 1950 and in 1997 he was awarded their Sylvester Medal. In 1990, he became a Foreign Member of the American Academy of Arts and Sciences and in 1997 was made a Companion of the Order of Canada. In 1973 he received the Jeffery–Williams Prize. A festschrift in his honour, The Geometric Vein, was published in 1982. It contained 41 essays on geometry, based on a symposium for Coxeter held at Toronto in 1979.

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**Book Contents :- **
**Regular Polytopes ** written by
** H.S.M. Coxeter **
cover the following topics.

1. POLYGONS AND POLYHEDRA

2. REGULAR AND QUASI-REGULAR SOLIDS

3. ROTATION GROUPS

4. TESSELLATIONS AND HONEYCOMBS

5. THE KALEIDOSCOPE

6. STAR-POLYHEDRA

7. ORDINARY POLYTOPES IN HIGHER SPACE

8. TRUNCATION

9. POINCARÉ’S PROOF OF EULER’S FORMULA

10. FORMS, VECTORS, AND COORDINATES

11. THE GENERALIZED KALEIDOSCOPE

12. THE GENERALIZED PETRIE POLYGON

13. SECTIONS AND PROJECTIONS

14. STAR-POLYTOPES

EPILOGUE

DEFINITIO NS OF SYMBOLS USED IN THE FOLLOWING

TABLES

BIBLIOG RAPHY

INDEX

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