Home > Gallery > My Models > Stewart Toroids > Prism-Expanded Dissected Cuboctahedron
Prev (Drilled Truncated Dodecahedron) Next (Rotunda-Drilled Truncated Icosidodecahedron)

Prism-Expanded Dissected Cuboctahedron

Like or comment on facebook
Stewart investigated various criteria for finding interesting toroids. Of the models which satisfied all his criteria, almost all of them had a convex hull with all regular faces. He eventually found a counter-example, but it had some excavations which did not increase the genus of the model, so it did not strictly satisfy all of his criteria.

It seems Stewart was unaware of this model however, which Alex Doskey discovered more recently. It satisfies all of his criteria perfectly, but its convex hull has some rhombic faces. It has a genus of 11. See also my genus-41 toroid.

It's also interesting to note that aside from 8 equilateral triangles, the other 78 faces are all squares. It's somehow surprising that squares alone can form intricate surfaces like this. In fact, an infinite lattice can be made based on this shape, by building on the triangles, leaving nothing but square faces.

Start by putting together the inner section. Then glue the outer parts around it.
Close-up view of finished model.

Home > Gallery > My Models > Stewart Toroids > Prism-Expanded Dissected Cuboctahedron
Prev (Drilled Truncated Dodecahedron) Next (Rotunda-Drilled Truncated Icosidodecahedron)

Copyright © 2001-2017, Robert Webb.