Tetrahedral prism

The tetrahedral prism or tepe is a prismatic uniform polychoron that consists of 2 tetrahedra and 4 triangular prisms. Each vertex joins 1 tetrahedron and 3 triangular prisms. As the name suggests, it is a prism based on a tetrahedron, and as such is also a segmentochoron (designated K-4.9 in Richard Klitzing's list).

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

Representations
A tetrahedral prism has the following Coxeter diagrams:


 * x x3o3o (full symmetry)
 * x2s4o3o (prism of alternated cube)
 * x2s2s4o (prism of alternated square prism)
 * x2s2s2s (prism of alternated cuboid)
 * xx3oo3oo&#x (bases considered separate)
 * xx ox3oo&#x (A2×A1 axial, dyad atop triangular prism)
 * xx xo ox&#x (A1×A1×A1 axial, square atop orthogonal square)
 * oox xxx&#x (base has one symmetry axis only)
 * xxxx&#x (irregular bases)
 * xxoo ooxx&#xr (A1×A1 axial)
 * oxxo3oooo&#xr (A2 axial)