He worked for 60 years at the University of Toronto and published twelve books. He was most noted for his work on regular polytopes and hyperdimensional geometries. He met Maurits Escher and his work on geometric figures helped inspire some of Escher's works. He also inspired some of the innovations of Buckminster Fuller.
He studied the philosophy of mathematics under Ludwig Wittgenstein at Trinity College, Cambridge. He remained at Cambridge following his doctorate, then did postgraduate studies at Princeton University. In 1936 he moved to the University of Toronto, becoming a professor in 1948. He was elected a Fellow of the Royal Society in 1950.