Stellated truncated hexahedron

Stellated truncated hexahedron
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}
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 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, CDel node 1.pngCDel 4.pngCDel rat.pngCDel d3.pngCDel node 1.pngCDel 3.pngCDel node.png. It is sometimes called quasitruncated hexahedron because it is related to the truncated cube, CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.png, except that the square faces become inverted into {8/3} octagrams.

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 projectionsEdit

 

Related polyhedraEdit

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 alsoEdit

ReferencesEdit

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

External linksEdit