Great icosihemidodecahedron

Great icosihemidodecahedron
Type Uniform star polyhedron
Elements F = 26, E = 60
V = 30 (χ = −4)
Faces by sides 20{3}+6{10/3}
Wythoff symbol 3/2 3 | 5/3
Symmetry group Ih, [5,3], *532
Index references U71, C85, W106
Dual polyhedron Great icosihemidodecacron
Vertex figure
3.10/3.3/2.10/3
Bowers acronym Geihid

In geometry, the great icosihemidodecahedron (or great icosahemidodecahedron) is a nonconvex uniform polyhedron, indexed as U71. It has 26 faces (20 triangles and 6 decagrams), 60 edges, and 30 vertices.[1] Its vertex figure is a crossed quadrilateral.

3D model of a great icosihemidodecahedron

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

Related polyhedra

Its convex hull is the icosidodecahedron. It also shares its edge arrangement with the great icosidodecahedron (having the triangular faces in common), and with the great dodecahemidodecahedron (having the decagrammic faces in common).

 Great icosidodecahedron Great dodecahemidodecahedron Great icosihemidodecahedron Icosidodecahedron (convex hull)