Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, CC (February 9,
1907 – March 31, 2003)[2] 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. He was always called Donald, from his third name MacDonald.[3]
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.[4]

Contents

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

Biography[edit]
In his youth, Coxeter composed music and was an accomplished pianist
at the age of 10.[5] 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.[5]
Coxeter went up to
**Trinity College, Cambridge**

Trinity College, Cambridge in 1926 to read
mathematics. There he earned his BA (as Senior Wrangler) in 1928, and
his doctorate in 1931.[5][3] In 1932 he went to Princeton University
for a year as a Rockefeller Fellow, where he worked with Hermann Weyl,
Oswald Veblen, and Solomon Lefschetz.[3] Returning to Trinity for a
year, he attended Ludwig Wittgenstein's seminars on the philosophy of
mathematics.[5] In 1934 he spent a further year at Princeton as a
Procter Fellow.[3]
In 1936 Coxeter moved to the University of Toronto. In 1938 he and P.
Du Val, H.T. Flather, and
**John Flinders Petrie**

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,[6] 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.[3] Coxeter,
**M. S. Longuet-Higgins** and
**J. C. P. Miller** were the
first to publish the full list of uniform polyhedra (1954).[7]
He worked for 60 years at the
**University of Toronto**

University of Toronto and published
twelve books.
Awards[edit]
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.[3] In 1990, he became a Foreign Member
of the American Academy of Arts and Sciences[8] and in 1997 was made a
Companion of the Order of Canada.[9]
In 1973 he received the Jeffery–Williams Prize.[3]
Works[edit]

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),[10] (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**

Philosophical Transactions of the Royal Society A 246:
401–50 doi:10.1098/rsta.1954.0003
1949: The Real Projective Plane[11]
1957: (with W.O.J. Moser) Generators and Relations for Discrete
Groups[12] 1980: Second edition, Springer-Verlag
ISBN 0-387-09212-9
1961: Introduction to Geometry[13][14]
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
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**

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[edit]

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
Goldberg–Coxeter construction
LCF notation
Todd–Coxeter algorithm
Tutte–Coxeter graph

References[edit]

^
**Harold Scott MacDonald Coxeter**

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**

The Boston Globe (September 10, 2006) "Review: The Man Who Saved
**Geometry**

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 & Company, 2006,
ISBN 0-8027-1499-4
^ Frame, J. S. (1940). "Review: Mathematical Recreations and Essays,
11th edition, by W. W. Rouse Ball; 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
& Sciences
^ Office of the Governor General of Canada.
**Order of Canada**

Order of Canada citation.
Queen's Printer for Canada. Retrieved 26 May 2010
^ Blumenthal, L. M. (1943). "Review: Non-euclidean geometry by H. S.
M. Coxeter" (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**

Geometry by H. S. M.
Coxeter". The Journal of Philosophy. 60 (1): 19–21.
doi:10.2307/2023059. JSTOR 2023059.

Further reading[edit]

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[edit]

Archival papers held at
**University of Toronto**

University of Toronto Archives and Records
Management Services
**Harold Scott MacDonald Coxeter**

Harold Scott MacDonald Coxeter at the Mathematics Genealogy Project
H. S. M. Coxeter (1907–2003), Erich W. Ellers, Branko Grünbaum,
Peter McMullen, Asia Ivic Weiss Notices of the AMS: Volume 50, Number
10.
www.donaldcoxeter.com www.math.yorku.ca/dcoxeter webpages dedicated to
him (in development)
Jaron's World: Shapes in Other Dimensions, Discover mag., Apr 2007
The Mathematics in the Art of M.C. Escher video of a lecture by H.S.M.
Coxeter, April 28, 2000.

Authority control

WorldCat Identities
VIAF: 95255476
LCCN: n81019969
ISNI: 0000 0001 0859 4550
GND: 118522507
SELIBR: 182370
SUDOC: 028881907
BNF: cb12062548j (data)
MGP: 12555
NDL: 00