In geometry, the great truncated cuboctahedron (or quasitruncated cuboctahedron or stellatruncated cuboctahedron) is a nonconvex uniform polyhedron, indexed as U<sub>20</sub>. 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</sup>/<sub>3</sub>,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</sup>/<sub>3</sub>} 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