# Great dodecahemicosahedron

(Redirected from Gidhei)
Great dodecahemicosahedron
Rank3
TypeUniform
Notation
Bowers style acronymGidhei
Coxeter diagram(o5/4x3x5*a)/2
()/2
Elements
Faces12 pentagons, 10 hexagons
Edges60
Vertices30
Vertex figureBowtie, edge lengths (1+5)/2 and 3
Measures (edge length 1)
Dihedral angle${\displaystyle \arccos \left({\sqrt {\frac {5+2{\sqrt {5}}}{15}}}\right)\approx 37.37737^{\circ }}$
Number of external pieces312
Level of complexity18
Related polytopes
ArmyId, edge length ${\displaystyle {\frac {{\sqrt {5}}-1}{2}}}$
RegimentDid
DualGreat dodecahemicosacron
ConjugateSmall dodecahemicosahedron
Abstract & topological properties
Flag count240
Euler characteristic–8
OrientableNo
Genus10
Properties
SymmetryH3, order 120
Flag orbits2
ConvexNo
NatureTame

The great dodecahemicosahedron, or gidhei, is a quasiregular polyhedron and one of 10 uniform hemipolyhedra. It consists of 12 pentagons and 10 "hemi" hexagons, passing through its center, with two of each joining at a vertex.

It can be constructed as the rectification of the Petrial small stellated dodecahedron.

It is a faceting of the dodecadodecahedron, keeping the original's pentagons while also using its equatorial hexagons.

## Name

Its pentagonal faces are parallel to those of a dodecahedron, and its hemi hexagonal faces are parallel to those of an icosahedron, hence the name "dodecahemicosahedron". The "great" modifier, used for stellations in general, distinguishes it from the small dodecahemicosahedron, which also has this face arrangement.

## Vertex coordinates

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