Great birhombipenteractitriacontaditeron

The great birhombated penteract, also called the great birhombated penteractitriacontaditeron, or gibrant, also called the bicantitruncated 5-cube, is a convex uniform polyteron. It consists of 80 triangular-square duoprisms, 32 great rhombated pentachora, and 10 truncated icositetrachora. 1 triangular-square duoprism, 2 great rhombated pentachora, and 2 truncated icositetrachora join at each vertex. As the name suggests, it is the bicantitruncation of the penteract, or equivalently of its dual triacontaditeron.

Vertex coordinates
The vertices of a great birhombated penteract of edge length 1 are given by all permutations of:
 * $$\left(±\frac{3\sqrt2}{2},\,±\frac{3\sqrt2}{2},\,±\sqrt2,\,±\frac{\sqrt2}{2},\,0\right).$$

Representations
A great birhombated penteract has the following Coxeter diagrams:


 * o4x3x3x3o (full symmetry)
 * x3x3x *b3x3o (D5 symmetry, as cantitruncate demipenteract)
 * s4x3x3x3o (D5 symmetry, as alternated faceting)