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{{Uniform polyhedra db|Uniform polyhedron stat table|lIhD}}
{{Uniform polyhedra db|Uniform polyhedron stat table|lIhD}}
In [[geometry]], the '''small icosihemidodecahedron''' is a [[uniform star polyhedron]], indexed as U<sub>49</sub>. Its [[vertex figure]] is a [[quadrilateral#More quadrilaterals|crossed quadrilateral]].
In [[geometry]], the '''small icosihemidodecahedron''' is a [[uniform star polyhedron]], indexed as U<sub>49</sub>. Its [[vertex figure]] alternates two regular triangles and decagrams as a [[quadrilateral#More quadrilaterals|crossed quadrilateral]].


It is a [[hemipolyhedron]] with 6 [[decagon]]al faces passing through the model center.
It is a [[hemipolyhedron]] with 6 [[decagon]]al faces passing through the model center.

Revision as of 15:03, 15 October 2010

Small icosihemidodecahedron
Type Uniform star polyhedron
Elements F = 26, E = 60
V = 30 (χ = −4)
Faces by sides 20{3}+6{10}
Coxeter diagram (double covering)
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 is a uniform star polyhedron, indexed as U49. Its vertex figure alternates two regular triangles and decagrams as a crossed quadrilateral.

It is a hemipolyhedron with 6 decagonal faces passing through the model center.

Its 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

See also

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