Harold Scott MacDonald Coxeter 1907 - 2003 The Man Who Saved Geometry

King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry By Siobhan Roberts "Roberts' book really soars in its description of Coxeter's work and his ability to visualize space, to communicate the poetry of geometry and to inspire other mathematicians, physicists and artists.” —Nathan L. Harshman, Chicago Tribune

Many areas of Coxeter's work involved the study of symmetry Many areas of Coxeter's work involved the study of symmetry. Perhaps his best-known legacy is his work on the mathematics of kaleidoscopes, including those operating in higher dimensions. He described the Coxeter groups as "the algebraic expression of how many images of an object may be seen in a kaleidoscope". http://plus.maths.org/issue25/news/coxeter/index.html

In 1926, at the age of 19, Coxeter discovered a new regular polyhedron, having six hexagonal faces at each vertex. He went on to study the mathematics of kaleidoscopes and, by 1933, had enumerated the n-dimensional kaleidoscopes. His algebraic equations expressing how many images of an object may be seen in a kaleidoscope are now known as Coxeter groups. http://www.daviddarling.info/encyclopedia/C/Coxeter.html

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Fundamental Chamber in a Cube: One type of Kadeidoscope The FUNDAMENTAL CHAMBER is a pyramid whose vertices are at: The center of the solid (A) The center of a face (B) The midpoint of an edge (C) A vertex of the solid (D)

Fundamental Chamber in a Cube: Reflections of a Triangle

Fundamental Chamber in a Tetrahedron

Fundamental Chamber in an Octahedron

Fundamental Chamber in a Dodecahedron

Two Places to Start…

Donald Coxeter (died 04/02/03)…was regarded as the greatest classical geometer of his generation. He was guided by a profound and almost artistic appreciation of the beauty of symmetry and his work inspired many people outside the field of mathematics. http://www.telegraph.co.uk/news/main.jhtml?xml=/news/2003/04/03/db0301.xml