15 Mar
2007
15 Mar
'07
2:06 p.m.
Not sure if I'd ever heard of the Szilassi polyhedron before, but (for those in the same boat) it has 7 (nonconvex) polygonal faces each of meets the other 6, is topologically a torus, and it embeds in 3-space. My favorite torus polyhedron has 7 regular hexagons as faces, any two of which meet each other along an edge.* This embeds isometrically in R^6 (so that its 84 symmetries are all in the orthogonal group O(6)). Does anyone know for sure whether 6 is the lowest possible dimension for this? --Dan _______________________________________________________ * Which is of course the nicest way to 7-color a torus.