Small rhombated tesseract

The small rhombated tesseract, or srit, also commonly called the cantellated tesseract, is a convex uniform polychoron that consists of 16 regular octahedra, 32 triangular prisms, and 8 small rhombicuboctahedra. 1 octahedron, 2 triangular prisms, and 2 small rhombicuboctahedra join at each vertex. As one of its names suggests, it can be obtained by cantellating the tesseract.

The small rhombated tesseract can be vertex-inscribed into a small prismatotetracontoctachoron and contains the vertices of an octagonal duoprism and the truncated cubic prism.

Vertex coordinates
The vertices of a small rhombated tesseract of edge length 1 are given by all permutations of:
 * (±(1+$\sqrt{2}$)/2, ±(1+$\sqrt{2+√2}$)/2, ±1/2, ±1/2).

Representations
The small rhombated tesseract has the following Coxeter diagrams:


 * x4o3x3o (full symmetry)
 * xxxx4oxxo3xoox&#xt (BC3 axial, small rhombicuboctahedron-first)
 * oqowxxooo3xxwoqowxx3oooxxwoqo&#xt (A3 axial, octahedron-first)
 * qo3xx3oq *b3oo&#zx (D4 symmetry)
 * wx xx4ox3xo&#zx (BC3×A1 symmetry)
 * oxo4xxw oxo4wxx&#zxt (BC2×BC2 symmetry)

Related polychora
The small rhombated tesseract can be seen as a truncated cubic prism with the bases augmented by small rhombicuboctahedron atop truncated cube segmentochora. The octagonal prisms of the central prism will combine with the square cupolas of the segmentochoral caps to produce small rhombicuboctahedral cells.

The small rhombicuboctahedra of the small rhombated tesseract can be augmented by octahedron atop small rhombicuboctahedron segmentochora. If all eight are augmented, the result is the small prismatotetracontoctachoron.

Another cap of the small rhombated tesseract is the square pucofastegium. In fact, 8 of these caps, in 2 sets of 4, can be chopped off to give an inscribed octagonal duoprism, wieh the octagonal prisms formed alternatingly either from middle segments of small rhombicuboctahedra or bases of the removed caps.