Hexagonal cupola

The hexagonal cupola, or hicu, is a cupola with a hexagonal base. It consists of 6 triangles, 6 squares, 1 hexagon, and 1 dodecagon. The CRF version is flat.

It is the hexagon-first cap of the small rhombitrihexagonal tiling.

Vertex coordinates
A hexagonal cupola of edge length 1 has vertices given by the following coordinates:


 * $$\left(±1,\,0,\,0\right),$$
 * $$\left(±\frac{1}{2},\,±\frac{\sqrt{3}}{2},\,0\right),$$
 * $$\left(±\frac{2+\sqrt{3}}{2},\,±\frac{1}{2},\,0\right),$$
 * $$\left(±\frac{1+\sqrt{3}}{2},\,±\frac{1+\sqrt{3}}{2},\,0\right),$$
 * $$\left(±\frac{1}{2},\,±\frac{2+\sqrt{3}}{2},\,0\right).$$

These are obtained by placing a hexagon and a dodecagon in the same plane.

Representations
A hexagonal cupola has the following Coxeter diagrams:


 * ox6xx&#x
 * so12ox&#x