Cellirhombipenteractitriacontaditeron

The cellirhombipenteractitriacontaditeron or cellirhombated penteractitriacontaditeron, short name 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 cellirhombipenteractitriacontaditeron contains the vertices of a prismatorhombated hexadecachoric prism and octagonal-great rhombicuboctahedral duoprism.

Vertex coordinates
The vertices of a cellirhombipenteractitriacontaditeron of edge length 1 are given by all permutations of:
 * $$\left(±\frac{1+2\sqrt2}{2},\,±\frac{1+\sqrt2}{2},\,±\frac{1+\sqrt2}{2},\,±\frac12,\,±\frac12\right).$$

Representations
A cellirhombipenteractitriacontaditeron has the following Coxeter diagrams:


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

Related polytopes
The cellirhombipenteractitriacontaditeron is the colonel of a regiment of 27 members.