Message #3273

From: Roice Nelson <>
Subject: Császár and Szilassi polyhedra
Date: Sat, 12 Dec 2015 17:14:50 -0600

Yesterday I learned about the Császár polyhedron
<> on

It is the only known polyhedron besides the tetrahedron that has no
diagonals - all 7 vertices connect to every other. With 21 edges and 14
faces, its genus is 1. You can think of it as the complete graph
<> K_7 embedded on the torus.
It also has a dual, the Szilassi polyhedron
<>. Both relate to
the Heawood
graph <>.

Turns out I already had the latter configured in MagicTile (the {6,3}
7-Color), but I didn’t have the former, so I just added it. Here are some
pictures of the tilings.

Both are in the Euclidean/Torus section of MagicTile.