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.
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.

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** for a
year as a
**Rockefeller Fellow** , where he worked with
**Hermann Weyl** ,
**Oswald Veblen**

Oswald Veblen , and
**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** Press . In 1940
Coxeter edited the eleventh edition of Mathematical Recreations and
Essays, originally published by
**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** 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** and published
twelve books .

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** 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**

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** (1st edition), (2nd ed, 1947), (3rd
ed, 1957), (4th ed, 1961), (5th ed, 1965),
**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**
* 1963: Regular Polytopes (2nd edition), Macmillan Company
* 1967: (with
**S. L. Greitzer** )
**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** (2nd edition)
* 1974: Regular Complex Polytopes,
**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** (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–Dynkin diagram
*
**Coxeter–James Prize**
*
**Coxeter matroid**
*
**Coxeter–Todd lattice**
* Coxeter\'s loxodromic sequence of tangent circles
*
**LCF notation**

LCF notation
*
**Todd–Coxeter algorithm**
*
**Tutte–Coxeter graph**

REFERENCES

* ^
**Harold Scott MacDonald Coxeter** at the Mathematics Genealogy
Project
* ^ Roberts, S.; Ivic Weiss, A. (2006). "Harold Scott MacDonald
Coxeter. 9 February 1907 -- 31 March 2003: Elected FRS 1950".
**Biographical Memoirs of Fellows of the Royal Society** . 52: 45–66.
doi :10.1098/rsbm.2006.0004 .
* ^ A B C D E F G O\'Connor, John J. ; Robertson, Edmund F. ,
"Harold Scott MacDonald Coxeter", MacTutor History of Mathematics
archive ,
**University of St Andrews** .
* ^
**The Boston Globe** (September 10, 2006) "Review: The Man Who
Saved
**Geometry** by Siobhan Roberts. "Crying `Death to Triangles!' a
generation of mathematicians tried to eliminate geometry in favor of
algebra. Were it not for Donald Coxeter, they might have succeeded"
* ^ A B C D Roberts, Siobhan, King of Infinite Space: Donald
Coxeter, The Man Who Saved Geometry, Walker revised by H. S. M.
Coxeter" (PDF). Bull. Amer. Math. Soc. 45 (3): 211–213. doi
:10.1090/S0002-9904-1940-07170-8 .
* ^ Coxeter 1954
* ^ Foreign Honorary Member elected 1990 2016 American Academy of
Arts ">(PDF). Bull. Amer. Math. Soc. 49 (9): 679–680. doi
:10.1090/s0002-9904-1943-07977-3 .
* ^ DuVal, Patrick (1950). "Review: The real projective plane by H.
S. M. Coxeter" (PDF). Bull. Amer. Math. Soc. 56 (4): 376–378. doi
:10.1090/s0002-9904-1950-09414-2 .
* ^ Hall Jr., Marshall (1958). "Review: Generators and relations
for discrete groups by H. S. M. Coxeter and W. O. J. Moser" (PDF).
**Bulletin of the American Mathematical Society** . 64, Part 1 (3):
106–108. doi :10.1090/S0002-9904-1958-10178-0 .
* ^ Freudenthal, H. (1962). "Review: Introduction to geometry by H.
S. M. Coxeter" (PDF). Bull. Amer. Math. Soc. 68 (2): 55–59. doi
:10.1090/s0002-9904-1962-10714-9 .
* ^ Levi, H. (1963). "Review: Introduction to
**Geometry** by H. S. M.
Coxeter". The Journal of Philosophy. 60 (1): 19–21. doi
:10.2307/2023059 .
**JSTOR** 2023059 .

FURTHER READING

* Davis, Chandler ; Ellers, Erich W, eds. (2006). The Coxeter
Legacy: Reflections and Projections. Providence, R.I.: American
Mathematical Society. ISBN 978-0-8218-3722-1 .
**OCLC** 62282754 .
* Roberts, Siobhan (2006). King of Infinite Space: Donald Coxeter,
the Man Who Saved Geometry. New York: Walker & Company. ISBN
978-0-8027-1499-2 .
**OCLC** 71436884 .

EXTERNAL LINKS

* Archival papers