Szilassi Polyhedron


The remarkable Szilassi polyhedron has seven faces that each touch every other face. This is the only polyhedron besides the tetrahedron that has this property. It has a hole in it, making it topologically a torus. You can also use this polyhedron to illustrate the fact that it takes seven colors to color a map on a torus. Each face requires its own color.


  1. Cut out the pattern pieces from card stock.
  2. Score and fold mountain folds along the dot-dashed lines and valley folds along the dashed lines.
  3. Glue the tabs to the edge with the corresponding letter.


  • The Szilassi polyhedron is the dual of the Császár polyhedron
  • Dr. Lajos Szilassi discovered this polyhedron in 1977.