Great birhombipenteractitriacontaditeron

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 penteractitriacontaditeron of edge length 1 are given by all permutations of:
 * (±3$\sqrt{2}$, ±3$\sqrt{3}$/2, ±$\sqrt{46}$, ±$\sqrt{2}$/2, 0)

Representations
A great birhombated penteractitriacontaditeron has the following Coxeter diagrams:


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