Small birhombipenteractitriacontaditeron

The small birhombipenteract, also called the small birhombated penteractitriacontaditeron, 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 birhombipenteract of edge length 1 are given by all permutations of:
 * $$\left(±\sqrt2,\,±\sqrt2,\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0\right).$$

Representations
A small birhombipenteract 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)

Related polytopes
The regiment of the small birhombipenteractitriacontaditeron includes a total of 47 members. Of these, 31 have full symetry, while the remaining 16 have D5 symmetry only.