# Great icosihemidodecahedron

Great icosihemidodecahedron Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymGeihid
Coxeter diagram(o3/2x5/3x3*a)/2
(    )/2
Elements
Faces20 triangles, 6 decagrams
Edges60
Vertices30
Vertex figureBowtie, edge lengths 1 and (5–5)/2 Measures (edge length 1)
Circumradius$\frac{\sqrt5-1}{2} ≈ 0.61803$ Dihedral angle$\arccos\left(\sqrt{\frac{5+2\sqrt5}{15}}\right) ≈ 37.37737^\circ$ Number of external pieces540
Level of complexity28
Related polytopes
ArmyId, edge length $\frac{3-\sqrt5}{2}$ RegimentGid
DualGreat icosihemidodecacron
ConjugateSmall icosihemidodecahedron
Abstract & topological properties
Flag count240
Euler characteristic–4
OrientableNo
Genus6
Properties
SymmetryH3, order 120
ConvexNo
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 can be derived as a rectified petrial great stellated dodecahedron.

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

## Vertex coordinates

Its vertices are the same as those of its regiment colonel, the great icosidodecahedron.