Great icosihemidodecahedron

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Great icosihemidodecahedron
Rank3
TypeUniform
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
Dihedral angle
Number of external pieces540
Level of complexity28
Related polytopes
ArmyId, edge length
RegimentGid
DualGreat icosihemidodecacron
ConjugateSmall icosihemidodecahedron
Abstract & topological properties
Flag count240
Euler characteristic–4
OrientableNo
Genus6
Properties
SymmetryH3, order 120
Flag orbits2
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.

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.

Name[edit | edit source]

Its face planes are the same as those of an icosahedron and a dodecahedron in the dual configuration, hence the name "icosihemidodecahedron". The "great" prefix, used for stellations in general, distinguishes it from the small icosihemidodecahedron, which also has this face arrangement.

Vertex coordinates[edit | edit source]

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

External links[edit | edit source]