The Fifty Nine Icosahedra

These are still in existence, and in excellent preservation.

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Author: H. S. M. Coxeter

Publisher: Springer Science & Business Media

ISBN: 9781461382164

Category: Mathematics

Page: 47

View: 343

The Fifty-Nine Icosahedra was originally published in 1938 as No. 6 of "University of Toronto Studies (Mathematical Series)". Of the four authors, only Coxeter and myself are still alive, and we two are the authors of the whole text of the book, in which any signs of immaturity may perhaps be regarded leniently on noting that both of us were still in our twenties when it was written. N either of the others was a professional mathematician. Flather died about 1950, and Petrie, tragically, in a road accident in 1972. Petrie's part in the book consisted in the extremely difficult drawings which consti tute the left half of each of the plates (the much simpler ones on the right being mine). A brief biographical note on Petrie will be found on p. 32 of Coxeter's Regular Polytopes (3rd. ed. , Dover, New York, 1973); and it may be added that he was still a schoolboy when he discovered the regular skew polygons that are named after him, and are the occasion for the note on him in Coxeter's book. (Coxeter also was a schoolboy when some of the results for which he will be most remembered were obtained; he and Petrie were schoolboy friends and used to work together on polyhedron and polytope theory. ) Flather's part in the book consisted in making a very beautiful set of miniature models of all the fifty-nine figures. These are still in existence, and in excellent preservation.

Polyhedral Stellation

Excerpt: This table contains an indexed list of the Uniform and stellated polyhedra from the book Polyhedron Models, by Magnus Wenninger. The book was written as a guide book to building polyhedra as physical models.

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Author: LLC Books

Publisher: General Books

ISBN: 1156027675

Category: Mathematics

Page: 68

View: 452

Chapters: List of Wenninger polyhedron models, The Fifty Nine Icosahedra, Final stellation of the icosahedron, Small stellated dodecahedron, Compound of five tetrahedra, Great stellated dodecahedron, Great icosahedron, Great dodecahedron, Small triambic icosahedron, Compound of five cubes, Compound of five octahedra, Stellated octahedron, Compound of ten tetrahedra, Compound of great icosahedron and great stellated dodecahedron, Compound of cube and octahedron, Compound of dodecahedron and icosahedron, . Source: Wikipedia. Pages: 62. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: This table contains an indexed list of the Uniform and stellated polyhedra from the book Polyhedron Models, by Magnus Wenninger. The book was written as a guide book to building polyhedra as physical models. It includes templates of face elements for construction and helpful hints in building, and also brief descriptions on the theory behind these shapes. It contains the 75 nonprismatic uniform polyhedra, as well as 44 stellated forms of the convex regular and semiregular polyhedra. This list was written to honor this early polyhedral work from Wenninger, and to provide a detailed reference to the 119 numbered models in his book. Models listed here can be cited as "Wenninger Model Number N," or WN for brevity. The polyhedra are grouped below in 5 tables: Regular (1-5), Semiregular (6-18), regular star polyhedra (20-22,41), Stellations and compounds (19-66), and uniform star polyhedra (67-119). The four regular star polyhedra are listed twice because they belong to both the uniform polyhedra and stellation groupings. M. Wenninger, Polyhedron Models, Errata: known errors in the various editions. ...More: http: //booksllc.net/?id=2915428

CRC Concise Encyclopedia of Mathematics

http://www.physics.orst.edu/~bulatov/polyhedra/icosahedron/. Coxeter, H. S. M.;
Du Val, P.; Flather, H. T.; and Petrie, J. F. The Fifty-Nine Icosahedra. Stradbroke,
England: Tarquin Publications, 1999. Hart, G. "59 Stellations of the Icosahedron.

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Author: Eric W. Weisstein

Publisher: CRC Press

ISBN: 9781420035223

Category: Mathematics

Page: 3252

View: 292

Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d

The Best Writing on Mathematics 2011

... take up recreational mathematics as a hobby. I began my addiction to
recreational mathematics in high school published in 1938 by the University of
Toronto Press with. with the fifty-nine icosahedra. The Fifty-Nine Icosahedra is a
little book.

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Author: Mircea Pitici

Publisher: Princeton University Press

ISBN: 9780691153155

Category: Mathematics

Page: 383

View: 640

This anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2011 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Ian Hacking discusses the salient features that distinguish mathematics from other disciplines of the mind; Doris Schattschneider identifies some of the mathematical inspirations of M. C. Escher's art; Jordan Ellenberg describes compressed sensing, a mathematical field that is reshaping the way people use large sets of data; Erica Klarreich reports on the use of algorithms in the job market for doctors; and much, much more. In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a foreword by esteemed physicist and mathematician Freeman Dyson. This book belongs on the shelf of anyone interested in where math has taken us--and where it is headed.

Polyhedron Models

... nets by consulting The fifty - nine icosahedra , by Coxeter , Flather , Du Val and
Petrie . In this booklet all the cases are illustrated with excellent drawings of both
the solids and their facial planes . Each one presents its own challenge and will ...

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Author: Magnus J. Wenninger

Publisher: Cambridge University Press

ISBN: 0521098599

Category: Mathematics

Page: 228

View: 500

An explicit guide to the geometric principles, design, and construction of complex polyhedral figures

Regular Polytopes

The nine regular solids. Proceedings of the First Canadian Mathematical
Congress (Toronto, 1946), pp. 252264. ... The Fiftynine Icosahedra. University of
Toronto Studies (Mathematical Series), 6 (1938), pp. 126. Curjel 1. Notes on the
regular ...

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Author: H. S. M. Coxeter

Publisher: Courier Corporation

ISBN: 9780486141589

Category: Mathematics

Page: 368

View: 584

Foremost book available on polytopes, incorporating ancient Greek and most modern work. Discusses polygons, polyhedrons, and multi-dimensional polytopes. Definitions of symbols. Includes 8 tables plus many diagrams and examples. 1963 edition.

International mathematical news

H . S . M . et al : The Fifty - Nine Icosahedra . Springer - Verlag , Berlin , 1982 , VII
+ 47 S . , DM 35 , - . Dieses Büchlein , ein Reprint einer „ Jugendarbeit “ der vier
Autoren H . S . M . Coxeter , P . Du Val , H . T . Flather , J . F . Petrie aus dem Jahr
 ...

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Author:

Publisher:

ISBN: UCAL:B3689242

Category: Mathematics

Page:

View: 966

University of Toronto Studies

... contact along edges ) . 4 . NOTES ON THE PLATES PLATE I . The Icosahedron
A needs no comment . B is obtained by erecting low triangular pyramids ( b ) on
each face of A , and is thus what we may call ( The FIFTY - NINE ICOSAHEDRA.

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Author:

Publisher:

ISBN: UOM:39015053962406

Category: Mathematics

Page:

View: 516

Mathematics and Culture V

After the War , Flather made another set , this time complete , of the fifty - nine
stellations ( kept at Trinity College , Cambridge ) . The manuscript of the “ Fifty -
nine Icosahedra ” was completed once Coxeter was in Toronto and it was
submitted ...

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Author: Michele Emmer

Publisher: Springer Verlag

ISBN: UOM:39015079211523

Category: Mathematics

Page: 269

View: 596

This volume of the "Mathematics and Culture" series is dedicated to Italian artist Armando Pizzicato. The work of Pollock is also discussed, thanks to the collaboration of the Venice Guggenheim Collection. Mathematics creates beauty in architecture, from topology to the projects of Gehry and Piano to the muqarnas of Islam. The fourth dimension is made visible in these pages. But mathematics can save lives as well. Mathematical models can fight against cancer and AIDS, prevent their spread and intervene in their cure. Mathematics can also be used to protect the environment. In the wake of the devastation caused by Hurricane Katrina, the discussion of the use of mathematical models in meteorology and the prediction of storms is particularly timely. This volume wouldn't be complete without Venice and its glass, the fantastic collection of murrine of Giovanni Sarpellon. There is even a bit of magic, thanks to Bustric. And finally, an homage to a great mathematician: H.S.M. "Donald" Coxeter.

New Technical Books

The fifty-nine icosahedra. NY: Springer-Verlag, 1982. 26 p. $12, paper. 82-10582
. ISBN 0-387-90770-X. Contents: Complete enumeration of stellated icosahedra,
by considering the possible faces. An alternative enumeration, by considering ...

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Author: New York Public Library

Publisher:

ISBN: UOM:39015036923285

Category: Engineering

Page:

View: 682

The Mathematical Gazette

Şee H . S . M . Coxeter , P . du Val , H . T . Flather and J . F . Petrie , The Fifty -
nine Icosahedra ( University of Toronto Press , 1938 ) . H . MARTYN CUNDY .
1617 . Approximate method of inscribing a regular polygon in a circle . The
following ...

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Author:

Publisher:

ISBN: IND:30000089590982

Category: Mathematics

Page:

View: 643

The Publishers Trade List Annual

1961. xiv + 320 pages. 6 x 9. $6.95 E. Coxeter, H. S. M. Non-Euclidean Geometry
. 4th ed., revised & enl., 1957. xvi + 310 pages. 5% x 8%. ME II. $5.50 E. Coxeter,
H. S. M. The Fifty-nine Icosahedra. By H. S. M. Coxeter, P. Du Val, H. T. Flather, ...

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Author:

Publisher:

ISBN: STANFORD:36105124470811

Category: American literature

Page:

View: 109

Convex Polyhedra with Regularity Conditions and Hilbert s Third Problem

Interested readers may look up their book The Fifty nine Icosahedra [5]. Semi-
regular polyhedra may also be stellated to give a variety of very attractive non-
convex solids. Interested readers may look up M.J. Wenninger's book (25).
Finally ...

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Author: A. R. Rajwade

Publisher: Hindustan Book Agency and Indian National Science Academy

ISBN: UCSC:32106016557735

Category: Mathematics

Page: 194

View: 957

Since antiquity, people knew that there are only five regular solids, i.e. polyhedra whose all faces are regular polygons and all solid angles are also regular. These solids are, of course, the tetrahedron, the octahedron, the cube, the icosahedron, and the dodecahedron. Later, much attention was drawn to the question of how to describe polyhedra with other types of regularity conditions. The author puts together many facts known in this direction. He formulates four regularity conditions (two for faces and two for solid angles) and for any combination of their conditions lists all the corresponding polyhedra. In this way, he obtains such very interesting classes of solids as 13 semiregular solids, or 8 deltahedra, or 92 regularly faces polyhedra, etc. In later chapters the author presents some related topics of geometry of solids, like star polyhedra and plane tessellations. In the concluding chapter, a complete solution of the Hilbert 3rd problem is given. Supplied with many figures, the book can be easily read by anyone interested in this beautiful classical geometry.

Booklist

OREGON STATE COLLEGE LIBRARY - 6 - BOOKLIST no.9, Oct. 1, 1954 QA276.
5 QA300 QA305 QA303 QA308 QA531 QA343 QA35l QA372 QA40l QA40l
QA406 QA431 QA433 QA445 QA453 ... Coxeter, H. S. M. The fifty-nine
icosahedra.

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Author: Oregon State University. Library

Publisher:

ISBN: UIUC:30112071097106

Category: Library science

Page:

View: 261

The Australian Mathematics Teacher

... Fifty - nine Icosahedra The Mathematical Experience Illustrated Maths
Dictionary for Australian Schools Teaching Problem Solving Strategies AA - WW
Elementary Mathematics – Selected Topics and Problem Solving Motivated
Mathematics ...

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Author:

Publisher:

ISBN: UOM:39015085215294

Category: Mathematics

Page:

View: 947

American Book Publishing Record

COXETER , H. S. M. 1907516'.15 ( Harold Scott Macdonald ) , The fifty - nine
icosahedra / by H.S.M. Coxeter and P. Du Val . New York : Springer - Verlag ,
c1982 . p . cm . Originally published : Toronto : University of Toronto Press , 1938.

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Author:

Publisher:

ISBN: MINN:31951000694715S

Category: American literature

Page:

View: 219