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

See also

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