Donald Coxeter: How to Visualize Four-Dimensional Polyhedra

Donald Coxeter 1907–2003

Donald Scott MacDonald Coxeter was born on February 9, 1907 in Kensington UK. At an early age, he displayed an interest in mathematics and music, becoming an accomplished pianist at age 10. Eventually choosing mathematics as his life’s work, he enrolled in 1925, at Cambridge University. By 1928, he had become Senior Wrangler and within four years, earned his doctorate in mathematics. In 1936, he moved to the University of Toronto where he worked for the next 60 years of his life, until his death on March 31, 2003, at the age of 96. 

Donald Coxeter, described as “the greatest classical geometer of the 20th century,” once described how his subconcious mind worked on problems as he slept:

I had long been trying to extend to four dimensions the familiar construction for the snub cube…So, I went to bed and soon slept soundly. About 3 a.m. I awoke with the idea of using a symmetrical “isosceles” tetrahedron; … I could thus choose a point on the axis of symmetry and adjust its height so as to equate the distances of the two types of neighboring point. I switched on the light and went into my living room to write it down, lest I might find the next morning that it had passed away like any ordinary dream. When morning came, there it was, ready for all the details to be filled in. 

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