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Mathematical Model – A pair of Mobius Tetrahedra

Coxeter · Mathematics

A pair of cardboard tetrahedra are joined at their vertices by strings. They touch each other at the centre of one edge. The shape of the model forms a cube.

Accession Number: 2016.mat.20

Alternative Name:

Primary Materials: Cardboard


The model is marked with the number “14” in black felt marker.

Dimensions (cm): Cube: 10 cm per side.

Function: Pedagogical mathematical model.

Condition: Excellent

Associated Instruments:


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:

”Each of those two tetrahedra is a special kind of tetrahedra called an orthoscheme. Two orthoschemes together have the vertices of the cube. With the orthoscheme, each face is a right-angled triangle. It’s associated with projective geometry in three dimensions. It is of interest that you can have two tetrahedra so that the face planes of each contain the vertices of the other. Made by Eric Moorehouse, a graduate student here. “ H.S.M. Coxeter. March 10, 2000.

Historical Notes: