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 faces and vertices of any known regular faced toroid, with 12 of each. However is not a Stewart toroid as it self-intersects. The record for the fewest faces of a Stewart toroid is 21, with the tunnelled elongated triangular cupola and the record for the fewest vertices is 15, with the tortuous tunnel.

Vertex coordinates
Its vertex coordinates are the same as those of the icosahedron.