Square-cuboctahedral duoprism

The square-cuboctahedral duoprism or squaco is a convex uniform duoprism that consists of 4 cuboctahedral prisms, 6 tesseracts, and 8 triangular-square duoprisms. Each vertex joins 2 cuboctahedral prisms, 2 triangular-square duoprisms, and 2 tesseracts. It is a duoprism based on a square and a cuboctahedron, which makes it a convex segmentoteron.

The square-cuboctahedral duoprism can be vertex-inscribed into the penteractitriacontaditeron.

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

Representations
A square-cuboctahedral duoprism has the following Coxeter diagrams:
 * x4o o4x3o (full symmetry)
 * x x o4x3o (cuboctahedral prismatic prism)
 * x4o x3o3x
 * x x x3o3x
 * xx oo3xx4oo&#x (cuboctahedral prism atop cuboctahedral prism)
 * xx xx3oo3xx&#x
 * xxo3oxx xxx4ooo&#xt ((triangular-square duoprism || pseudo square-hexagonal duoprism || dual-para triangular-square duoprism)