Hendecagonal-square antiprismatic duoprism

The hendecagonal-square antiprismatic duoprism or hensquap is a convex uniform duoprism that consists of 11 square antiprismatic prisms, 2 square-hendecagonal duoprisms, and 8 triangular-hendecagonal duoprisms. Each vertex joins 2 square antiprismatic prisms, 3 triangular-hendecagonal duoprisms, and 1 square-hendecagonal duoprism.

Vertex coordinates
The vertices of a hendecagonal-square antiprismatic duoprism of edge length 2sin(π/11) are given by: where j = 2, 4, 6, 8, 10.
 * $$\left(1,\,0,\,±\sin\frac\pi{11},\,±\sin\frac\pi{11},\,\frac{\sqrt[4]8\sin\frac\pi{11}}2\right),$$
 * $$\left(\cos\frac{j\pi}{11},\,±\sin\frac{j\pi}{11},\,±\sin\frac\pi{11},\,±\sin\frac\pi{11},\,\frac{\sqrt[4]8\sin\frac\pi{11}}2\right),$$
 * $$\left(1,\,0,\,0,\,±\sqrt2\sin\frac\pi{11},\,-\frac{\sqrt[4]8\sin\frac\pi{11}}2\right),$$
 * $$\left(\cos\frac{j\pi}{11},\,±\sin\frac{j\pi}{11},\,0,\,±\sqrt2\sin\frac\pi{11},\,-\frac{\sqrt[4]8\sin\frac\pi{11}}2\right),$$
 * $$\left(1,\,0,\,±\sqrt2\sin\frac\pi{11},\,0,\,-\frac{\sqrt[4]8\sin\frac\pi{11}}2\right),$$
 * $$\left(\cos\frac{j\pi}{11},\,±\sin\frac{j\pi}{11},\,±\sqrt2\sin\frac\pi{11},\,0,\,-\frac{\sqrt[4]8\sin\frac\pi{11}}2\right),$$

Representations
A hendecagonal-square antiprismatic duoprism has the following Coxeter diagrams:
 * x11o s2s8o (full symmetry; square antiprisms as alternated octagonal prisms)
 * x11o s2s4s (square antiprisms as alternated ditetragonal prisms)