Great rhombated triacontaditeron

The great rhombated triacontaditeron, or gart, also called the cantitruncated 5-orthoplex, is a convex uniform polyteron. It consists of 40 octahedral prisms, 32 great rhombated pentachora, and 10 truncated hexadecachora. One truncated hexadecachoron, 1 octahedral prism, and 4 great rhombated pentachora join at each vertex. As the name suggests, it is the cantitruncation of the triacontaditeron.

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

Representations
A great rhombated triacontaditeron has the following Coxeter diagrams:


 * o4o3x3x3 (full symmetry)
 * o3x3o *b3x3x (D5 symmetry)

Related polytopes
The great rhombated triacontaditeron is the colonel of a two-member regiment that also includes the great rhombated hexadecahemidecateron.