Mathematical Model – Regular Sponge

Coxeter Collection · Mathematics

Accession Number: 2016.mat.25


A wooden model consisting of four elements formed into a regular sponge. The model is stained a deep brown. Certain faces are painted a dark grey or black.

Primary Materials: Wood

Dimensions (cm): height = 14 cm

Function: Pedagogical mathematical model.

Condition: Excellent

Manufacturer: Unknown

Additional Information and References:

“This is one of the regular sponges, a skew polyhedra, that has at each vertex four hexagons, at various angles of one another. You have to think of the black squares as the holes, they are not part of the polyhedron. The polyhedron consists of hexagons, four at each vertex, and, therefore, in the notation you call this 6:4. As you can see, it continues all over space, one could go on putting these things together indefinitely. It’s space-filling, or a regular sponge. It was discovered by Petrie, son of the Egyptologist Petrie. We were schoolmates together, and he thought of this in 1926. I think the model was made by a carpenter. So you could reciprocate this 6:4 with a 4:6. Which is six squares per vertex.” H.S.M. Coxeter, March 10, 2000