models appeared in a number of Coxeter’s books, including Regular Polytopes. Donchian was a rug salesman by trade, but his obsession with hyperspace and making models to depict it, consumed so much of his time that his rug business struggled financially. Donchian exhibited his hyperspace models at Chicago’s World Fair in 1934, where Coxeter first encountered him. One newspaper headline read: “Paul S. Donchian Opens Door To a Fairyland of Pure Science, His Wire and Cardboard Models Explain Highest Mathematics,” while another noted: “Einstein Was Barred From Exhibit Lest Crowds Crush Both Him and Models.”

ROE GOODMAN on "Alice Through Looking-Glass after Looking- Glass — The Mathematics of Kaleidoscopes" Goodman, a professor of mathematics at Rutgers University, in New Brunswick, New Jersey, will speak about Coxeter’s very visual approach to geometry, using kaleidoscopes to investigate the symmetries of solids and shapes. As a student at Cambridge, Coxeter carried with him at all times his portable kaleidoscopes, protected in felt pouches sewn by his mother. Goodman constructed a similar set of kaleidoscopes to help his students understand reflection groups in the theory of Lie algebras. He will display these kaleidoscopes and explore their mechanics by drawing an analogy to Alice’s adventures in Wonderland, imagining Alice’s trip through a peculiar cone- shaped arrangement of three looking glasses. “Alice wonders how many different ways the mirrors could be arranged so that she could have other trips through the looking glasses and still return the same day for tea,” Goodman wrote in a paper on the subject. “Alice’s problem was solved (for all dimensions) by H.S.M. Coxeter, who classified all possible systems of n mirrors in n-dimensional Euclidean space whose reflections generate a finite group of orthogonal matrices.”

J.R. GOTT III on “Regular Skew Polyhedra and the Sponge-Like Topology of the Large Scale Structure in the Universe.” Gott, a professor of astrophysics at Princeton, first became acquainted with the regular skew polyhedra almost forty years after Coxeter discovered these new geometric solids as a teenager with his friend John Petrie. Gott was a teenager himself when he rediscovered the same figures. “The first one I found was hexagons-four-around-a-point,” he said. “I noticed four hexagons could join in a saddle-shaped surface and this could be continued to make a repeating sponge-like structure.” Gott will discuss this Coxeterian intersection of