Small stellated truncated dodecahedron

Small stellated truncated dodecahedron
Small stellated truncated dodecahedron.png
Type Uniform star polyhedron
Elements F = 24, E = 90
V = 60 (χ = −6)
Faces by sides 12{5}+12{10/3}
Wythoff symbol 2 5 | 5/3
2 5/4 | 5/3
Symmetry group Ih, [5,3], *532
Index references U58, C74, W97
Dual polyhedron Great pentakis dodecahedron
Vertex figure Small stellated truncated dodecahedron vertfig.png
5.10/3.10/3
Bowers acronym Quit Sissid

In geometry, the small stellated truncated dodecahedron (or quasitruncated small stellated dodecahedron or small stellatruncated dodecahedron) is a nonconvex uniform polyhedron, indexed as U58. It has 24 faces (12 pentagons and 12 decagrams), 90 edges, and 60 vertices.[1] It is given a Schläfli symbol t{​53,5}, and Coxeter diagram CDel node 1.pngCDel 5-3.pngCDel node 1.pngCDel 5.pngCDel node.png.

3D model of a small stellated truncated dodecahedron

Related polyhedraEdit

It shares its vertex arrangement with three other uniform polyhedra: the convex rhombicosidodecahedron, the small dodecicosidodecahedron and the small rhombidodecahedron.

It also has the same vertex arrangement as the uniform compounds of 6 or 12 pentagrammic prisms.

 
Rhombicosidodecahedron
 
Small dodecicosidodecahedron
 
Small rhombidodecahedron
 
Small stellated truncated dodecahedron
 
Compound of six pentagrammic prisms
 
Compound of twelve pentagrammic prisms

ReferencesEdit

  1. ^ Maeder, Roman. "58: small stellated truncated dodecahedron". MathConsult.

See alsoEdit

External linksEdit