"It has been known for some
time that the minimal polyhedral subdivision of the surface of the p=1
toroid has seven hexagonal regions, each contiguous with the other six
and that a minimal triangulation of this surface has fourteen triangular
faces." (*Adventures Among the Toroids)* ISBN 0-686-119 36-3, Professor
B.M. Stewart

The former polyhedron with seven hexagonal regions mentioned and shown above is known as the Szilassi polyhedron (discovered in 1977).

It is also possible to colour
a number of Stewart Toroids such that all faces
of the same colour are contiguous and each of the seven colours is contiguous
with the other six. The image below links to an example VRML model
of a **K3 / Q3T3** coloured in such a fashion.

__Császár Polyhedron__

The triangulated polyhedron mentioned in the opening paragraph is known as the Császár polyhedron (discovered in 1949).

The form of the Császár polyhedron is not obvious from
a completed model. It's generation can be seen from this series of
models with:

(i) The first six triangles (note the deep
valley through the centre)

(ii) The first eight triangles (the valley
is now covered)

(iii) The completed polyhedron

Vertices of both polyhedra
courtesy Stewart (*p245*).

**Next: Simple
Stewart Toroids**
**Back: To Toroids**

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