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{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 {⁸/₃} octagrams.

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 for the vertices of a great truncated cuboctahedron with side length 2 centered at the origin are all permutations of $${\displaystyle {\Bigl (}\pm 1,\ \pm \left[1-{\sqrt {2}}\right],\ \pm \left[1-2{\sqrt {2}}\right]{\Bigr )}.}$$

• List of uniform polyhedra

• Weisstein, Eric W. "Great truncated cuboctahedron". MathWorld.