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
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.

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


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

See alsoEdit

External linksEdit