Toroidal icosahedron faceting

The toroidal icosahedron faceting or toif, also called the crazy tube, is an orbiform toroid. As its name suggests, it is a faceting of the icosahedron.

It has the fewest known faces and vertices of any regular faced toroid, with 12 of each. However is not a Stewart toroid as it self-intersects. The tunnelled elongated triangular cupola has the fewest faces of any known Stewart toroid with 21 faces.

Vertex coordinates
It's vertex coordinates are the same as those of the icosahedron.