Stellated truncated hexahedron
| Stellated truncated hexahedron | |
|---|---|
| File:Stellated truncated hexahedron.png | |
| Type | Uniform star polyhedron |
| Elements | F = 14, E = 36 V = 24 (χ = 2) |
| Faces by sides | 8{3}+6{8/3} |
| Coxeter diagram | File:CDel node 1.pngFile:CDel 4.pngFile:CDel rat.pngFile:CDel 3x.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png |
| 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 | File:Stellated truncated hexahedron vertfig.png 3.8/3.8/3 |
| Bowers acronym | Quith |
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, File:CDel node 1.pngFile:CDel 4.pngFile:CDel rat.pngFile:CDel d3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png. It is sometimes called quasitruncated hexahedron because it is related to the truncated cube, File:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png, except that the square faces become inverted into {8/3} octagrams. Even though the stellated truncated hexahedron is a stellation of the truncated hexahedron, its core is a regular octahedron.
Orthographic projections
File:Stellated truncated hexahedron ortho wireframes.png
Related polyhedra
It shares the vertex arrangement with three other uniform polyhedra: the convex rhombicuboctahedron, the small rhombihexahedron, and the small cubicuboctahedron.
See also
References
- ↑ Weisstein, Eric W. "Uniform Polyhedron". MathWorld.
- ↑ Maeder, Roman. "19: stellated truncated hexahedron". MathConsult.
