Truncated cubic prism

The truncated cubic prism or ticcup, is a pprismatic uniform polychoron that consists of 2 truncated cubes, 6 octagonal prisms, and 8 triangular prisms. Each vertex joins 1 truncated cube, 1 octagonal prism, and 2 triangular prisms. As the name suggests, it is a prism based on the truncated cube. As such it is also a convex segmentochoron (designated K-4.99 on Richard Klitzing's list).

The truncated cubic prism can be obtained from a small rhombated tesseract by removing two small rhombicuboctahedron atop truncated cube segmentochora. This diminishing cuts the lateral small rhombicuboctahedra into their equatorial octagonal prisms only. It is also a central segment of the small prismatotetracontoctachoron.

Vertex coordinates
The vertices of a truncated cubic prism of edge length 1 are given by all permutations of the first three coordinates of:
 * (±(1+$\sqrt{2+√2}$)/2, ±(1+)/2, ±1/2, ±1/2).

Representations
The truncated cubic prism has the following Coxeter diagrams:


 * x x4x3o (full symmetry)
 * xx4xx3oo&#x (bases considered separately)
 * xxxx xwwx4xoox&#xt (BC2×A1 axial, octagonal prism-first)