Rectified triacontaditeron

The rectified triacontaditeron, or rat, also called the rectified 5-orthoplex, is a convex uniform polyteron. It consists of 10 hexadecachora and 32 rectified pentachora. Two hexadecachora and 8 rectified pentachora join at each octahedral prismatic vertex. As the name suggests, it is the rectification of the triacontaditeron.

The rectified triacontaditeron contains the vertices of a square-octahedral duoprism.

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

Representations
A rectified triacontaditeron has the following Coxeter diagrams:


 * o4o3o3x3o (full symmetry)
 * o3o3o *b3x3o (D5 symmetry)
 * ooo4ooo3oxo3xox&#xt (BC4 axial, hexadecachoronfirst)
 * ooo3oxo3ooo *b3xox&#xt (D4 axial, hexadecachoron-first)
 * oxo3xoo3oox3oxo&#xt (A4 axial, rectified pentachoron-first)
 * qo oo4oo3ox3xo&#zx (BC4×A1 symmetry)
 * qoo4oxo ooo4oox3oxo#zx (BC3×BC2 symmetry)
 * ox(ou)xo oo(oo)oo4oo(xo)oo3ox(oo)oo&#xt (BC3×A1 axial, vertex-first)
 * ox(ou)xo oo(xo)oo3ox(oo)xo3oo(xo)oo&#xt (A3×A1 symmetry, vertex-first)

Related polytopes
The rectified triacontaditeron is the colonel of a regiment that includes a total of 44 uniform members, plus one compound. Of the 44 members, 19 have full BC5 symmetry, while the other 25 have D5 symmetry only.