Penteractitriacontaditeron

The penteractitriacontaditeron, or nit, also called the birectified 5-cube, is a convex uniform polyteron. It consists of 10 icositetrachora and 32 rectified pentachora. 3 icositetrachora and 4 rectified pentachora join at each triangular-square duoprismatic vertex. It is the middle stage in the series of truncations between a regular penteract and its dual triacontaditeron. It is also the rectified demipenteract.

The penteractitriacontaditeron contains the vertices of a square-cuboctahedral duoprism.

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

Representations
A penteractitriacontaditeron has the following Coxeter diagrams:


 * o4o3x3o3o (full symmetry)
 * o3x3o *b3o3o (D5 symmetry, rectified demipenteract)
 * ooo4oxo3xox3ooo&#xt (BC4 axial, icositetrachoron-first)
 * oxo3xox3oxo *b3ooo&#xt (D4 axial, icositetrachoron-first)
 * oxoo3xoxo3oxox3ooxo&#xt (A4 axial, rectified pentachoron-first)
 * ox(uoo)xo3xo(xox)ox3ox(oou)xo ox(ouo)xo&#xt (A3×A1 axial)
 * qoo4oxo3oox oxo4ooq&#zx (BC2×BC2 symmetry)
 * ox(ou)x(xo)oo3oo(xo)x(ou)xo ox(oo)x(oo)xo4oo(qo)o(qo)oo&#xt (BC3×A2 axial, vertex-first)

Related polytopes
The penteractitriacontaditeron is the colonel of the largest known regiment of nonprismatic uniform polytera. Its regiment includes 149 main members, 138 fissaries, and one compound. Of these, 24 main members, 10 fissaries, and the compound have full symmetry, the rest have D5 symmetry only.