# Small icosihemidodecahedron

Small icosihemidodecahedron
Type Uniform star polyhedron
Elements F = 26, E = 60
V = 30 (χ = −4)
Faces by sides 20{3}+6{10}
Wythoff symbol 3/2 3 | 5 (double covering)
Symmetry group Ih, [5,3], *532
Index references U49, C63, W89
Dual polyhedron Small icosihemidodecacron
Vertex figure
3.10.3/2.10
Bowers acronym Seihid

In geometry, the small icosihemidodecahedron (or small icosahemidodecahedron) is a uniform star polyhedron, indexed as U49. It has 26 faces (20 triangles and 6 decagons), 60 edges, and 30 vertices.[1] Its vertex figure alternates two regular triangles and decagons as a crossed quadrilateral.

3D model of a small icosihemidodecahedron

It is given a Wythoff symbol, 32 3 | 5, but that construction represents a double covering of this model.

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

## Related polyhedra

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

 Icosidodecahedron Small icosihemidodecahedron Small dodecahemidodecahedron