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:
 * (±$\sqrt{6}$/2, ±$\sqrt{2}$/2, ±$\sqrt{5}$/2, 0, 0).

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)