Harold Scott MacDonald Coxeter

Coxeter was born in Kensington, England, to Harold Samuel Coxeter and Lucy (). 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 felt that mathematics and music were intimately related, outlining his ideas in a 1962 article on "Music and Mathematics" in the Canadian Music Journal. 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. In 1934 he spent a further year at Princeton as a Procter Fellow. originally published by W. W. Rouse Ball in 1892. He was elevated to professor in 1948. He was elected a Fellow of the Royal Society of Canada in 1948 and a Fellow of the Royal Society in 1950. He met M. C. 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. He worked for 60 years at the University of Toronto and published twelve books. ==Personal life==

Coxeter was a vegetarian. He attributed his longevity to his vegetarian diet, daily exercise such as fifty press-ups and standing on his head for fifteen minutes each morning, and consuming a nightly cocktail made from Kahlúa (a coffee liqueur), peach schnapps, and soy milk. ==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. and in 1997 was made a Companion of the Order of Canada. In 1973 he received the Jeffery–Williams Prize. A second such volume, The Coxeter Legacy, was published in 2006 based on a Toronto Coxeter symposium held in 2004. ==Works==

Books • 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, . • 1949: The Real Projective Plane • 1961: Introduction to Geometry, (2nd paperback edition 1989, .) • 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, ) • 1973: Regular Polytopes, (3rd edition), Dover edition, • 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, . • 1987 Projective Geometry (1987) • 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, . • 1999: The Beauty of Geometry: Twelve Essays, Dover Publications, , • 2011: The Fifty-Nine Icosahedra, Tarquin Group, Selected Papers • 1940: "Regular and Semi-Regular Polytopes I", Mathematische Zeitschrift 46: 380–407, MR 2,10 • 1954: (with Michael S. Longuet-Higgins and J. C. P. Miller) "Uniform Polyhedra", Philosophical Transactions of the Royal Society A 246: 401–50 • 1957: (with W. O. J. Moser) Generators and Relations for Discrete Groups 1980: Second edition, Springer-Verlag • • 1985: "Regular and Semi-Regular Polytopes II", Mathematische Zeitschrift 188: 559–591 • 1988: "Regular and Semi-Regular Polytopes III", Mathematische Zeitschrift 200: 3–45 ==See also==