Cellirhombipenteractitriacontaditeron

The cellirhombated penteractitriacontaditeron, or carnit, also called the stericantellated 5-cube, is a convex uniform polyteron. It consists of 80 triangular-square duoprisms, 80 cuboctahedral prisms, 40 small rhombicuboctahedral prisms, 32 small rhombated pentachora, and 10 small rhombated tesseracts. 1 triangular-square duoprism, 1 small rhombated tesseract, 1 small rhombated pentachoron, 2 small rhombicuboctahedral prisms, and 2 cuboctahedral prisms join at each vertex. As the name suggests, it is the stericantellation of the penteract or its dual triacontaditeron.

The cellirhombated penteractitriacontaditeron contains the vertices of a prismatorhombated hexadecachoric prism and octagonal-great rhombicuboctahedral duoprism.

Vertex coordinates
The vertices of a cellirhombated penteractitriacontaditeron of edge length 1 are given by all permutations of:
 * (±(1+2$\sqrt{2}$)/2, ±(1+$\sqrt{17+8√2}$)/2, ±(1+$\sqrt{2}$)/2, ±1/2, ±1/2)

Representations
A cellirhombated penteractitriacontaditeron has the following Coxeter diagrams:


 * x4o3x3o3x (full symmetry)
 * xxooxx4ooxxoo3xxooxx3oxxxxo&#xt (BC4 axial, small rhombated tesseract-first)