Hexagonal antifastegium

The hexagonal antifastegium, or haf, is a CRF segmentochoron (designated K-4.46 on Richard Klitzing's list). It consists of 1 hexagonal prism, 2 hexagonal antiprisms, 6 tetrahedra, and 6 square pyramids. It is a member of the infinite family of polygonal antifastegiums.

It is a segmentochoron between a hexagon and a hexagonal antiprism or between a hexagon and a gyro hexagonal prism.

Vertex coordinates
The vertices of a hexagonal antifastegium of edge length 1 are given by:
 * $$\left(±\frac12,\,±\frac{\sqrt3}2,\,±\frac12,\,0\right),$$
 * $$\left(±1,\,0,\,±\frac12,\,0\right),$$
 * $$\left(±\frac{\sqrt3}2,\,±\frac12,\,0,\,\frac{\sqrt{4\sqrt3-5}}2\right),$$
 * $$\left(0,\,±1,\,0,\,\frac{\sqrt{4\sqrt3-5}}2\right).$$

Representations
The hexagonal antifastegium can be represented by the following Coxeter diagram s:


 * ox xo6ox&#x
 * xoo6oxx&#x