Small icosihemidodecahedron

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Small icosihemidodecahedron
Small icosihemidodecahedron.png
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 Small icosihemidodecahedron vertfig.png
3.10.3/2.10
Bowers acronym Seihid

In geometry, the small icosihemidodecahedron (or small icosahemidodecahedron) is a uniform star polyhedron, indexed as U49. Its vertex figure alternates two regular triangles and decagons as a crossed quadrilateral.

It is given a Wythoff symbol, 3/2 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[edit]

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.png
Icosidodecahedron
Small icosihemidodecahedron.png
Small icosihemidodecahedron
Small dodecahemidodecahedron.png
Small dodecahemidodecahedron

See also[edit]

External links[edit]

  • Weisstein, Eric W. "Small icosihemidodecahedron". MathWorld.
  • Uniform polyhedra and duals