Small icosihemidodecahedron

Uniform star polyhedron with 26 faces
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
3D model of a 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. It is a hemipolyhedron with its six decagonal faces passing through the model center.

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

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

See also

References

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

External links

  • v
  • t
  • e
Kepler-Poinsot
polyhedra (nonconvex
regular polyhedra)Uniform truncations
of Kepler-Poinsot
polyhedraNonconvex uniform
hemipolyhedraDuals of nonconvex
uniform polyhedraDuals of nonconvex
uniform polyhedra with
infinite stellations


Stub icon

This polyhedron-related article is a stub. You can help Wikipedia by expanding it.

  • v
  • t
  • e