Great truncated cuboctahedron

In geometry, the great truncated cuboctahedron (or quasitruncated cuboctahedron or stellatruncated cuboctahedron) is a nonconvex uniform polyhedron, indexed as U20. It has 26 faces (12 squares, 8 hexagons and 6 octagrams), 72 edges, and 48 vertices. It is represented by the Schläfli symbol tr{{{sup|4}}/3,3}, and Coxeter-Dynkin diagram. It is sometimes called the quasitruncated cuboctahedron because it is related to the truncated cuboctahedron,, except that the octagonal faces are replaced by {{{sup|8}}/3} octagrams.

Convex hull
Its convex hull is a nonuniform truncated cuboctahedron. The truncated cuboctahedron and the great truncated cuboctahedron form isomorphic graphs despite their different geometric structure.

Cartesian coordinates
Cartesian coordinates for the vertices of a great truncated cuboctahedron centered at the origin are all permutations of $$\Bigl( \pm 1, \ \pm\left[1-\sqrt 2 \right], \ \pm\left[1-2\sqrt 2\right]\Bigr).$$