Mathematical Model – Reciprocal Polyhedra

Coxeter Collection · Mathematics

Accession Number: 2016.mat.6

Instrument Name:

Mathematical Model – Reciprocal Polyhedra


A blue and brown paper model depicting a chiral compound of 5 tetrahedra “with 20 vertices of the dodecahedron and 20 face-planes of an icosahedron.”

Alternative Name: Chiral Compound of 5 Tetrahedra

Primary Materials: Cardboard


This model is marked with the number “36″

Dimensions (cm): Longest dimension = 12 cm

Function: Pedagogical math model.

Condition: Excellent

Manufacturer: Unknown

Date of Manufacture: c. 1960


These models existed at the Dept. of Mathematics during the tenure of Dr. H.S.M. Coxeter, who provided the comments below.

Additional Information and References:

“Here you see a blue dodecahedron and a brown icosahedron, with their edges crossing one another. Each blue edge crosses a brown edge at right angles. If you could cut off all those pyramids, what’s left is a figure with triangles and pentagons for faces, that’s what’s called an icosa-dodecahedron, a combination of the two. This goes back to Archimedes, and is related to the cube and the octahedron – the cube-octahedron. It has squares and triangles for faces. If you can imagine a cube and an octahedron put together in this sort of fashion and then, if you were to cut the pyramids off, you would see this.” – H.S.M.Coxeter, March 10, 2000.

Donated to UTSIC: No