Cellirhombidodecateron

The cellirhombidodecateron, or card, also called the cellirhombated hexateron or stericantellated 5-simplex, is a convex uniform polyteron. It consists of 20 triangular duoprisms, 30 cuboctahedral prisms, and 12 small rhombated pentachora. 1 triangular duoprism, 2 small rhombated pentachora, and 4 cuboctahedral prisms join at each vertex. As the name suggests, it is the stericantellation of the hexateron.

Vertex coordinates
The vertices of a cellirhombated dodecateron of edge length 1 can be given in 6 dimensions as all permutations of:
 * $$\left(\frac{3\sqrt2}{2},\,\sqrt2,\,\sqrt2,\,\frac{\sqrt2}{2},\,\frac{\sqrt2}{2},\,0\right).$$

Representations
A cellirhombated dodecateron has the following Coxeter diagrams:


 * x3o3x3o3x (full symmetry)
 * xxxo3xxoo3ooxx3oxxx&#xt (A4 axial, small rhombated pentachoron-first)
 * x(uo)(xd)(uo)x x(xx)(xo)(ou)x3o(xo)(xx)(xo)o3x(ou)(xo)(xx)x&#xt (A3×A1 axial, cuboctahedral prism-first)

Related polytopes
The cellirhombidodecateron is the colonel of a regiment of 18 members. Of these, 9 have full symmetry, while the other 9 have single A5 symmetry only.