Prism-Expanded Dissected Cuboctahedron
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
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
Start by putting together the inner section. Then glue the outer parts
Close-up view of finished model.