Square-octahedral duoprism

The square-octahedral duoprism or squoct is a convex uniform duoprism that consists of 4 octahedral prisms and 8 triangular-square duoprisms. Each vertex joins 2 octahedral prisms and 4 triangular-square duoprisms. It is a duoprism based on a square and an octahedron, which makes it a convex segmentoteron.

Vertex coordinates
The vertices of a square-octahedral duoprism of edge length 1 are given by all permutations and sign changes of the last three coordinates of:
 * $$\left(±\frac12,\,±\frac12,\,0,\,0,\,\frac{\sqrt2}{2}\right).$$

Representations
A square-octahedral duoprism has the following Coxeter diagrams:
 * x4o o4o3x (full symmetry)
 * x4o o3x3o (octahedra as tetratetrahedra)
 * x x x3o4o (octahedral prismatic prism)
 * x x o3x3o
 * xx xx3oo4oo&#x (octahedral prism atop octahedral prism)
 * xx oo3xx3oo&#x
 * xo3ox xx4oo&#x (triangular-square duoprism atop gyro triangular-square duoprism)
 * xx xx xo3ox&#x