Dodecagonal antiprism

The dodecagonal antiprism, or twap, is a prismatic uniform polyhedron. It consists of 24 triangles and 2 dodecagons. Each vertex joins one dodecagon and three triangles. It is an antiprism based on a dodecagon.

Vertex coordinates
A dodecagonal antiprism of edge length 1 has vertex coordinates given by:
 * $$\left(±\frac12,\,±\frac{2+\sqrt3}{2},\,H\right),$$
 * $$\left(±\frac{2+\sqrt3}{2},\,±\frac12,\,H\right),$$
 * $$\left(±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,H\right),$$
 * $$\left(0,\,±\frac{\sqrt2+\sqrt6}{2},\,-H\right),$$
 * $$\left(±\frac{\sqrt2+\sqrt6}{2},\,0,\,-H\right),$$
 * $$\left(±\frac{\sqrt2+\sqrt6}{4},\,±\frac{3\sqrt2+\sqrt6}{4},\,-H\right),$$
 * $$\left(±\frac{3\sqrt2+\sqrt6}{4},\,±\frac{\sqrt2+\sqrt6}{4},\,-H\right),$$

where $$H=\sqrt{\frac{-6+3\sqrt6+\sqrt{98-40\sqrt6}}{8}}$$ is the distance between the antiprism's center and the center of one of its bases.

Representations
A dodecagonal antiprism has the following Coxeter diagrams:


 * s2s24o (alternated icositetragonal prism)
 * s2s12s (alternated didodecagonal prism)
 * xo12ox&#x (bases considered separately)