# Small dodecahemidodecahedron

Small dodecahemidodecahedron
Type Uniform star polyhedron
Elements F = 18, E = 60
V = 30 (χ = −12)
Faces by sides 12{5}+6{10}
Wythoff symbol 5/4 5 | 5
Symmetry group Ih, [5,3], *532
Index references U51, C65, W91
Dual polyhedron Small dodecahemidodecacron
Vertex figure
5.10.5/4.10
Bowers acronym Sidhid

In geometry, the small dodecahemidodecahedron is a nonconvex uniform polyhedron, indexed as U51. It has 18 faces (12 pentagons and 6 decagons), 60 edges, and 30 vertices.[1] Its vertex figure alternates two regular pentagons and decagons as a crossed quadrilateral.

3D model of a small dodecahemidodecahedron

It is a hemipolyhedron with six decagonal faces passing through the model center.

## Related polyhedra

It shares its edge arrangement with the icosidodecahedron (its convex hull, having the pentagonal faces in common), and with the small icosihemidodecahedron (having the decagonal faces in common).

 Icosidodecahedron Small icosihemidodecahedron Small dodecahemidodecahedron

## References

1. ^ Maeder, Roman. "51: small dodecahemidodecahedron". MathConsult.