Small disprismatotesseractihexadecachoron

The small disprismatotesseractihexadecachoron, square duoexpandoprism, or sidpith, also commonly called the runcinated tesseract, is a convex uniform polychoron that consists of 16 regular tetrahedra, 32 triangular prisms, and 8+24 cubes. 1 tetrahedron, 3 triangular prisms, and 1+3 cubes join at each vertex. It is the result of expanding the cells of either a tesseract or a hexadecachoron outwards, and thus could also be called the runcinated 16-cell.

It is the second in the series of duoexpandoprisms formed as the convex hull of a compound of two perpendicular 4-8 duoprisms and the only uniform one. Blending it with these duoprisms produces the inverted quasiprismatodishexadecachoron.

Vertex coordinates
Coordinates for the vertices of a small disprismatotesseractihexadecachoron with edge length 1 are given by all permutations of:
 * (±(1+$\sqrt{2}$)/2, ±1/2, ±1/2, ±1/2).

Representations
A small disprismatotesseractihexadecachoron has the following Coxeter diagrams:


 * x4o3o3x (full symmetry)
 * xxxx4oooo3oxxo&#xt (BC3 axial, cube-first)
 * xxxowoqo3ooqooqoo3oqowoxxx&#xt (A3 axial, tetrahedron-first)
 * xowqwox xxxxxxx4oxoxoxo&#xt (BC2×A1 symmetry, cube-first)
 * qo3oo3oq *b3xx&#zx (D4 symmetry)
 * wx xx4oo3ox&#zx (BC3×A1 symmetry)
 * xo4xx ox4xx&#zx (BC3×BC2 symmetry, square duoexpandoprism)
 * wxxx xwxx xxwx xxxw&#zx (A1×A1×A1×A1 symmetry)

Representations
A small disprismatotesseractihexadecachoron can be constructed from a small rhombicuboctahedral prism by attaching cube atop small rhombicuboctahedron segmentochora to its bases.