Small icosihemidodecahedron

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.

Small icosihemidodecahedron
TypeUniform star polyhedron
ElementsF = 26, E = 60
V = 30 (χ = 4)
Faces by sides20{3}+6{10}
Wythoff symbol5 (double covering)
Symmetry groupIh, [5,3], *532
Index referencesU49, C63, W89
Dual polyhedronSmall icosihemidodecacron
Vertex figure
3.10.3/2.10
Bowers acronymSeihid
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.

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

See also

References

  1. Maeder, Roman. "49: small icosihemidodecahedron". MathConsult.


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