Great truncated cuboctahedron


In geometry, the great truncated cuboctahedron is a nonconvex uniform polyhedron, indexed as U20. It has 26 faces, 72 edges, and 48 vertices. It is represented by the Schläfli symbol tr, 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 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.

Convex hull

Great truncated cuboctahedron

Orthographic projections

Cartesian coordinates

for the vertices of a great truncated cuboctahedron centered at the origin are all permutations of