Small rhombated triacontaditeron

The small rhombated triacontaditeron, or sart, also called the cantellated 5-orthoplex, is a convex uniform polyteron. It consists of 40 octahedral prisms, 32 small rhombated pentachora, and 10 icositetrachora. One icositetrachoron, 2 octahedral prisms, and 4 small rhombated pentachora join at each vertex. As the name suggests, it is the cantellation of the triacontaditeron.

The small rhombated triacontaditeron contains the vertices of a square-truncated octahedral duoprism.

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

Representations
A small rhombated triacontaditeron has the following Coxeter diagrams:


 * o4o3x3o3x (full symmetry)
 * o3x3o *b3o3x (D5 symmetry)
 * ooooo4ooxoo3xxoxx3oxxxo&#xt (BC4 axial, icositetrachoron-first)
 * ooxoo3xxoxx3ooxoo *b3oxxxo&#xt (D4 axial, icositetrachoron-first)

Related polytopes
The small rhombated triacontaditeron is the colonel of a regiment that contains 92 members and one fissary. Of these, 28, plus the fissary, have full symmetry, while the rest have only D5 symmetry. This makes it the third-largest regiment of non-prismatic uniform polytera.