Small cellipenteractitriacontaditeron

The small cellipenteractitriacontaditeron or small cellated penteract, short name scant, also called the stericated 5-cube, is a convex uniform polyteron. It consists of 32 regular pentachora, 80 tetrahedral prisms, 80 triangular-square duoprisms, and 10+40 tesseracts. 1 pentachoron, 4 tetrahedral prisms, 6 triangular-square duoprisms, and 1+4 tesseracts join at each vertex. It can be formed by expanding the facets of either the penteract or its dual triacontaditeron outward.

The small cellated penteract contains the vertices of a small disprismatotesseractihexadecachoric prism, square-small rhombicuboctahedral duoprism, and octagonal-cubic duoprism.

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

Representations
A small cellipenteractitriacontaditeron has the following Coxeter diagrams:


 * x4o3o3o3x (full symmetry)
 * xxxx4oooo3oooo3oxxo&#xt (BC4 axial, tesseract-first)
 * wx xx4oo3oo3ox&#zx (BC4×A1 symmetry)
 * xx4ox xx4oo3xo&#zx (BC3×BC2 symmetry)

Related polytopes
The small cellipenteractitriacontaditeron is the colonel of aregiment that contains a total of 15 members.