Stellated truncated hexahedron

In geometry, the stellated truncated hexahedron (or quasitruncated hexahedron, and stellatruncated cube^[1]) is a uniform star polyhedron, indexed as U₁₉. It has 14 faces (8 triangles and 6 octagrams), 36 edges, and 24 vertices.^[2] It is represented by Schläfli symbol t'{4,3} or t{4/3,3}, and Coxeter-Dynkin diagram, . It is sometimes called quasitruncated hexahedron because it is related to the truncated cube, , except that the square faces become inverted into {8/3} octagrams.

Stellated truncated hexahedron
Type	Uniform star polyhedron
Elements	F = 14, E = 36 V = 24 (χ = 2)
Faces by sides	8{3}+6{8/3}
Coxeter diagram
Wythoff symbol	2 3 | 4/3 2 3/2 | 4/3
Symmetry group	Oh, [4,3], *432
Index references	U19, C66, W92
Dual polyhedron	Great triakis octahedron
Vertex figure	3.8/3.8/3
Bowers acronym	Quith

3D model of a stellated truncated hexahedron

Even though the stellated truncated hexahedron is a stellation of the truncated hexahedron, its core is a regular octahedron.

Orthographic projections

Related polyhedra

It shares the vertex arrangement with three other uniform polyhedra: the convex rhombicuboctahedron, the small rhombihexahedron, and the small cubicuboctahedron.

Rhombicuboctahedron

Small cubicuboctahedron

Small rhombihexahedron

Stellated truncated hexahedron

See also

• List of uniform polyhedra