Toroidal icosahedron faceting

The toroidal icoasahedron faceting or toif is a orbiform toroid. As its name suggests, it is a faceting of the icosahedron.

It has 12 faces, giving it the fewest known faces of any regular faced toroid. 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.