Small birhombipenteractitriacontaditeron

The small birhombated penteract, also called the small birhombipenteractitriacontaditeron, or sibrant, also called the bicantellated 5-cube, is a convex uniform polyteron. It consists of 80 triangular-square duoprisms, 32 small rhombated pentachora, and 10 rectified icositetrachora. 2 triangular-square duoprisms, 2 small rhombated pentachora, and 2 rectified icositetrachora join at each vertex. As the name suggests, it is the bicantellation of the penteract, or equivalenty of its dual triacontaditeron.

Vertex coordinates
The vertices of a small birhombated penteract of edge length 1 are given by all permutations of:
 * $$\left(±\sqrt2,\,±\sqrt2,\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0\right).$$

Representations
A small birhombated penteract has the following Coxeter diagrams:


 * o4x3o3x3o (full symmetry)
 * x3o3x *b3x3o (D5 symmetry, as cantellated demipenteract)
 * s4x3o3x3o (D5 symmetry, as alternated faceting)
 * ooqoo4xxoxx3oxxxo3xooox&#xt (BC4 axial, rectified icositetrachoron-first)