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Mathematical Model – Four Platonic Solids

Coxeter · Mathematics

Four cardboard shapes representing several Platonic solids.

2016.mat.1a – Tetrahedron
2016.mat.1b – Pentagon
2016.mat.1c – Icosahedron
2016.mat.1d – Octahedron

Accession Number: 2016.mat.1

Alternative Name:

Primary Materials: Paper/ Cardboard


“2015.mat.1a – Tetrahedron” is marked with the number “10” and has white likes drawn on its faces.
“2015.mat.1b – Pentagon” is marked with the number “3”
“2015.mat.1c – Icosahedron” is marked with the number “11” and has pencil lines on its faces.
“2015.mat.1d – Octahedron” is marked with the number “4” and has pencil lines on its vertices

Dimensions (cm):

2015.mat.1a = 11cm longest dimension; 2015.mat.1b = 11cm longest dimension; 2015.mat.1c = 10cm longest dimension; 2015.mat.1d = 10cm longest dimension

Function: Sculpture, Pedagogical


Good-all models have subtle blemishes and markings on their surfaces.

Associated Instruments:

Manufacturer: Unknown

Date of Manufacture: Unknown


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

When this set was first catalogued in 1999, it included a cube. This earlier set is shown in the final photo below. This cube was among a collection passed to Dr. Asia Ivić Weiss of York University following Dr. Coxeter’s death in 2003 and is now in the collection of the Canada Science and Technology Museum in Ottawa.

Additional Information and References:

“The smallest is the cube-octahedron, called cube-octahedron because it has six square faces like the cube, and eight triangular faces like the octahedron. The vertices of the cube-octahedron are the mid points of the edges of the cube or the midpoints of the edges of the octahedron. Cube-octahedron, a name given to it by Kepler – very à propos. The next smallest one is called the truncated octahedron. You get that by cutting the corners off the octahedron which is particularly interesting because you have an unlimited number of them and you can fit them together in space that’s cubed. The next one is a truncated icosahedron, it has twenty hexagonal faces and corresponds to twenty triangular faces of the icosoles. It also has twelve pentagonal faces corresponding to the twelve pentagonal faces of the *hedron. This is particularly interesting because it was used within the last twenty years or so as the typical shape for a football. So the same shape as the lamp hanging in the front hall of this house (see, and concocted by a chemist who found that one of the crystalline forms of carbon c60 which has one atom of carbon at each vertex of the truncated icosahedron. And when the chemists first discovered this they had never heard of Archimedes, didn’t know that Kepler had called this the truncated icosahedron. So the chemists called it Buckminster Fullerene, and then they regarded this as a whole series of shapes they called Fullerenes.” H.S.M. Coxeter. Dec. 23, 1999

Historical Notes: