In geometry, the cubitruncated cuboctahedron or cuboctatruncated cuboctahedron is a nonconvex uniform polyhedron, indexed as U<sub>16</sub>. It has 20 faces (8 hexagons, 6 octagons, and 6 octagrams), 72 edges, and 48 vertices, and has a shäfli symbol of tr{4,<sup>3</sup>/<sub>2</sub>}
Its convex hull is a nonuniform truncated cuboctahedron.
Cartesian coordinates for the vertices of a cubitruncated cuboctahedron are all the permutations of
The tetradyakis hexahedron (or great disdyakis dodecahedron) is a nonconvex isohedral polyhedron. It has 48 intersecting scalene triangle faces, 72 edges, and 20 vertices.
The triangles have one angle of , one of and one of . The dihedral angle equals . Part of each triangle lies within the solid, hence is invisible in solid models.
It is the dual of the uniform cubitruncated cuboctahedron.