Small stellated truncated dodecahedron

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 .

Small stellated truncated dodecahedron
TypeUniform star polyhedron
ElementsF = 24, E = 90
V = 60 (χ = 6)
Faces by sides12{5}+12{10/3}
Coxeter diagram
Wythoff symbol2 5 | 5/3
2 5/4 | 5/3
Symmetry groupIh, [5,3], *532
Index referencesU58, C74, W97
Dual polyhedronGreat pentakis dodecahedron
Vertex figure
5.10/3.10/3
Bowers acronymQuit Sissid
3D model of a small stellated truncated dodecahedron

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

See also

References

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


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