HAROLD SCOTT MACDONALD "DONALD" COXETER, FRS, FRSC, CC (February 9,
1907 – March 31, 2003) was a British-born Canadian geometer.
Coxeter is regarded as one of the greatest geometers of the 20th
century. He was born in
**London**

London but spent most of his adult life in
**Canada**

Canada . He was always called Donald, from his third name MacDonald.

CONTENTS

* 1 Biography
* 2 Awards
* 3 Works
* 4 See also
* 5 References
* 6 Further reading
* 7 External links

BIOGRAPHY

In his youth, Coxeter composed music and was an accomplished pianist
at the age of 10. He felt that mathematics and music were intimately
related, outlining his ideas in a 1962 article on "Mathematics and
Music" in the Canadian Music Journal.

Coxeter went up to Trinity College , Cambridge in 1926 to read
mathematics. There he earned his BA (as
**Senior Wrangler**

Senior Wrangler ) in 1928, and
his doctorate in 1931. In 1932 he went to
**Princeton University**

Princeton University for a
year as a
**Rockefeller Fellow**

Rockefeller Fellow , where he worked with
**Hermann Weyl**

Hermann Weyl ,
**Oswald Veblen**

Oswald Veblen , and
**Solomon Lefschetz**

Solomon Lefschetz . Returning to Trinity for a
year, he attended
**Ludwig Wittgenstein**

Ludwig Wittgenstein 's seminars on the philosophy of
mathematics . In 1934 he spent a further year at Princeton as a
Procter Fellow.

In 1936 Coxeter moved to the University of Toronto. In 1938 he and P.
Du Val , H.T. Flather, and
**John Flinders Petrie** published The
Fifty-Nine Icosahedra with
**University of Toronto**

University of Toronto Press . In 1940
Coxeter edited the eleventh edition of Mathematical Recreations and
Essays, originally published by
**W. W. Rouse Ball**

W. W. Rouse Ball in 1892. He was
elevated to professor in 1948. Coxeter was elected a Fellow of the
Royal Society of
**Canada**

Canada in 1948 and a
**Fellow of the Royal Society**

Fellow of the Royal Society in
1950. He met Maurits Escher in 1954 and the two became lifelong
friends; his work on geometric figures helped inspire some of Escher's
works, particularly the Circle Limit series based on hyperbolic
tessellations . He also inspired some of the innovations of
**Buckminster Fuller**

Buckminster Fuller . Coxeter,
**M. S. Longuet-Higgins** and J. C. P.
Miller were the first to publish the full list of uniform polyhedra
(1954).

He worked for 60 years at the
**University of Toronto**

University of Toronto and published
twelve books . He was most noted for his work on regular polytopes and
higher-dimensional geometries. He was a champion of the classical
approach to geometry, in a period when the tendency was to approach
geometry more and more via algebra.

AWARDS

Since 1978, the
**Canadian Mathematical Society** have awarded the
**Coxeter–James Prize** in his honor.

He was made a
**Fellow of the Royal Society**

Fellow of the Royal Society in 1950 and in 1997 he was
awarded their
**Sylvester Medal**

Sylvester Medal . In 1990, he became a Foreign Member
of the
**American Academy of Arts and Sciences**

American Academy of Arts and Sciences and in 1997 was made a
Companion of the
**Order of Canada**

Order of Canada .

In 1973 he received the
**Jeffery–Williams Prize** .

WORKS

* 1940: Regular and Semi-Regular Polytopes I, Mathematische
Zeitschrift 46: 380-407, MR 2,10 doi :10.1007/BF01181449
* 1942: Non-Euclidean
**Geometry**

Geometry (1st edition), (2nd ed, 1947), (3rd
ed, 1957), (4th ed, 1961), (5th ed, 1965),
**University of Toronto**

University of Toronto Press
(6th ed, 1998), MAA .
* 1954: (with
**Michael S. Longuet-Higgins** and
**J. C. P. Miller** )
"Uniform Polyhedra", Philosophical Transactions of the Royal Society A
246: 401–50 doi :10.1098/rsta.1954.0003
* 1949: The Real Projective Plane
* 1957: (with W.O.J. Moser) Generators and Relations for Discrete
Groups 1980: Second edition, Springer-Verlag ISBN 0-387-09212-9
* 1961: Introduction to
**Geometry**

Geometry
* 1963: Regular Polytopes (2nd edition), Macmillan Company
* 1967: (with
**S. L. Greitzer** )
**Geometry**

Geometry Revisited
* 1970: Twisted honeycombs (American Mathematical Society, 1970,
Regional conference series in mathematics Number 4, ISBN 0-8218-1653-5
)
* 1973: Regular Polytopes , (3rd edition), Dover edition, ISBN
0-486-61480-8
* 1974: Projective
**Geometry**

Geometry (2nd edition)
* 1974: Regular Complex Polytopes,
**Cambridge University Press**

Cambridge University Press
* 1981: (with R. Frucht and D. L. Powers), Zero-Symmetric Graphs,
**Academic Press** .
* 1985: Regular and Semi-Regular Polytopes II, Mathematische
Zeitschrift 188: 559-591
* 1987 Projective
**Geometry**

Geometry (1987) ISBN 978-0-387-40623-7
* 1988: Regular and Semi-Regular Polytopes III, Mathematische
Zeitschrift 200: 3-45
* 1995: F. Arthur Sherk, Peter McMullen, Anthony C. Thompson and
Asia Ivić Weiss, editors: Kaleidoscopes — Selected Writings of
H.S.M. Coxeter.
**John Wiley and Sons** ISBN 0-471-01003-0
* 1999: The Beauty of Geometry: Twelve Essays, Dover Publications,
LCCN 99-35678, ISBN 0-486-40919-8

SEE ALSO

*
**Boerdijk–Coxeter helix**

Boerdijk–Coxeter helix
*
**Coxeter functor**
*
**Coxeter group**
*
**Coxeter number**
*
**Coxeter–Dynkin diagram**
*
**Coxeter–James Prize**
*
**Coxeter matroid**
*
**Coxeter–Todd lattice**
* Coxeter\'s loxodromic sequence of tangent circles
*
**LCF notation**
*
**Todd–Coxeter algorithm**
*
**Tutte–Coxeter graph**

REFERENCES

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