In geometry, the great cubicuboctahedron is a nonconvex uniform polyhedron, indexed as U₁₄. It has 20 faces (8 triangles, 6 squares and 6 octagrams), 48 edges, and 24 vertices.^[1] Its square faces and its octagrammic faces are parallel to those of a cube, while its triangular faces are parallel to those of an octahedron: hence the name cubicuboctahedron. The prefix great serves to distinguish it from the small cubicuboctahedron, which also has faces in the aforementioned directions.^[2]

Great cubicuboctahedron
Type	Uniform star polyhedron
Elements	F = 20, E = 48 V = 24 (χ = −4)
Faces by sides	8{3}+6{4}+6{8/3}
Coxeter diagram
Wythoff symbol	3 4 | 4/3 4 3/2 | 4
Symmetry group	Oh, [4,3], *432
Index references	U14, C50, W77
Dual polyhedron	Great hexacronic icositetrahedron
Vertex figure	3.8/3.4.8/3
Bowers acronym	Gocco

It shares the vertex arrangement with the convex truncated cube and two other nonconvex uniform polyhedra. It additionally shares its edge arrangement with the nonconvex great rhombicuboctahedron (having the triangular faces and 6 square faces in common), and with the great rhombihexahedron (having the octagrammic faces in common).

• List of uniform polyhedra