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Mathematical Model – Proof of Rotating Cube

Coxeter · Mathematics

A cardboard model consisting of four interlocking triangles. They are coloured red, blue, orange, and green respectively.

The Department of Mathematics display describes this model as follows:
“the vertices of the triangles in this sculpture by [George] Odom coincide with the vertices of a cuboctahedron”

Accession Number: 2016.mat.32

Alternative Name:

Primary Materials: Cardboard


The model is marked with the number “40”.

Dimensions (cm): Longest dimension = 25 cm

Function: Pedagogical mathematical model.


Good: The model has slight damage at its corners.

Associated Instruments:

Manufacturer: George Odom

Date of Manufacture: c. 1970


Additional Information and References:

“Made by George Odom. It is of interest, because it’s a very easy proof regarding the rotations of the cube or octahedron into itself. Let’s say the elements of the octahedron group are isomorphic to the symmetric group of degree four, which is the group of all permutations of four objects. In this case, the four objects are the four hollow triangles of different colours that make up this model. The hollow triangles being an equilateral triangle with a similar triangle cut out of the middle. And these triangles are fitted together so that every two of them are interlocked. By turning it around, I can bring these rotations around to itself, two or three or four different positions, to illustrate the four permutations or four rotations of the cube to itself. By just looking at this you can see the isomorphism between the permutations of four things and rotations of cube to itself.” H.S.M. Coxeter. March 10, 2000.

Historical Notes: