Great icosihemidodecahedron

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.

Great icosihemidodecahedron
TypeUniform star polyhedron
ElementsF = 26, E = 60
V = 30 (χ = −4)
Faces by sides20{3}+6{10/3}
Wythoff symbol5/3
Symmetry groupIh, [5,3], *532
Index referencesU71, C85, W106
Dual polyhedronGreat icosihemidodecacron
Vertex figure
3.10/3.3/2.10/3
Bowers acronymGeihid
3D model of a great icosihemidodecahedron

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

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)



Traditional filling
Modulo-2 filling

See also

References
  1. Maeder, Roman. "71: great icosihemidodecahedron". MathConsult.


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