Truncated tetrahedral prism

The truncated tetrahedral prism or tuttip is a prismatic uniform polychoron that consists of 2 truncated tetrahedra, 4 hexagonal prisms, and 4 triangular prisms. Each vertex joins 1 truncated tetrahedron, 1 triangular prism, and 2 hexagonal prisms. As the name suggests, it is a prism based on the truncated tetrahedron. As such it is also a convex segmentochoron (designated K-4.57 on Richard Klitzing's list).

Vertex coordinates
Coordinates for the vertices of a truncated tetrahedral prism of edge length 1 are given by all permutations and even sign changes of the first three coordinates of:
 * $$\left(\frac{3\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,±\frac12\right).$$

Representations
A truncated tetrahedral prism has the following Coxeter diagrams:


 * x x3x3o (full symmetry)
 * xx3xx3oo&#x (bases considered separately)
 * x2s4o3x (bases as snub)
 * xxx xux3oox&#xt (A2×A1 symmetry, triangular prism-first)
 * x(xu)(xu)x-3-x(xo)(oo)o-&#xr (A2 axial)
 * xxxx xuxo oxux&#xt (A1×A1×A1 axial, square-first)