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
TypeUniform star polyhedron
ElementsF = 14, E = 36
V = 24 (χ = 2)
Faces by sides8{3}+6{8/3}
Wythoff symbol2 3 | 4/3
2 3/2 | 4/3
Symmetry groupOh, [4,3], *432
Index referencesU19, C66, W92
Dual polyhedronGreat triakis octahedron
Vertex figure
3.8/3.8/3
Bowers acronymQuith
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

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
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See also

References
  1. Weisstein, Eric W. "Uniform Polyhedron". MathWorld.
  2. Maeder, Roman. "19: stellated truncated hexahedron". MathConsult.
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