Square-tetrahedral duoprism

The square-tetrahedral duoprism, squatet, or digonal-square duoprismatic cupoliprism is a convex uniform duoprism that consists of 4 tetrahedral prisms and 4 triangular-square duoprisms. Each vertex joins 2 tetrahedral prisms and 3 triangular-square duoprisms. It is a duoprism based on a square and a tetrahedron, which also makes it a convex segmentoteron as the prism of a tetrahedral prism.

It is also the digonal member of the family of isogonal duoprismatic cupoliprisms.

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

Representations
A square-tetrahedral duoprism has the following Coxeter diagrams:


 * x4o x3o3o (full symmetry)
 * x x x3o3o (A3×A1×A1 symmetry, square seen as rectangle)
 * xx xx3oo3oo&#x (A3×A1 symmetry, as tetrahedral prismatic prism)
 * ox3oo xx4oo&#x (A2×BC2 symmetry, square atop triangular-square duoprism)
 * ox3oo xx xx&#x (A2×A1×A1 symmetry, as above with rectangle symmetry)
 * ox xo xx4oo&#x (BC2×A1×A1 symetry, cube atop ortho cube)
 * ox xo xx xx&#x (A1×A1×A1×A1 symmetry, as above with squares under rectangle symmetry)
 * oox xxx xxx#&x (A1×A1×A1 symmetry, tetrahedra as bilateral)
 * xxxx xxxx&#x (A1×A1 symmetry, tetrahedra irregular)