Cake pan

The cake pan is a quasi-convex Stewart toroid. It is a tunnelling of a elongated triangular cupola by a triangular cupola and a triangular prism.

It has the fewest faces of any known Stewart toroid with 21 faces.

Vertex coordinates
A cake pan with edge length 1 has the following vertex coordinates:
 * $$\left(\pm\frac{1}{2},\,-\frac{\sqrt{3}}{6},\,\frac{\sqrt{6}}{3}\pm\frac{1}{2}\right)$$,
 * $$\left(0,\,\frac{\sqrt{3}}{3},\,\frac{\sqrt{6}}{3}\pm\frac{1}{2}\right)$$,
 * $$\left(\pm\frac{1}{2},\,\pm\frac{\sqrt{3}}{2},\,\pm\frac{1}{2}\right)$$,
 * $$\left(0,\,\pm1,\,\pm\frac{1}{2}\right)$$.