Great icosihemidodecahedron

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Great icosihemidodecahedron
Great icosihemidodecahedron.png
Rank3
TypeUniform
SpaceSpherical
Bowers style acronymGeihid
Info
Coxeter diagram(o3/2x5/3x3*a)/2
SymmetryH3, order 120
ArmyId
RegimentGid
Elements
Vertex figureBowtie, edge lengths 1 and (5–5)/2
Faces20 triangles, 6 decagrams
Edges60
Vertices30
Measures (edge length 1)
Circumradius
Dihedral angle
Euler characteristic-4
Number of pieces540
Level of complexity28
Related polytopes
DualGreat icosihemidodecacron
ConjugateSmall icosihemidodecahedron
Properties
ConvexNo
OrientableNo
NatureTame

The great icosihemidodecahedron, or geihid, is a quasiregular polyhedron and one of 10 uniform hemipolyhedra. It consists of 20 equilateral triangles and 6 "hemi" decagrams, with two of each joining at a vertex. Its triangular faces are parallel to those of an icosahedron, and its hemi decagrammic faces are parallel to those of a dodecahedron: hence the name "icosihemidodecahedron". The "great" suffix, used for stellations in general, distinguishes it from the small icosihemidodecahedron, which also has this face arrangement.

It is a faceting of the great icosidodecahedron, keeping the original's triangles while also using its equatorial decagrams.

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