# Great dodecahemidodecahedron

Great dodecahemidodecahedron Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymGidhid
Coxeter diagram(x5/3x5/3o5/2*a)/2
(    )/2
Elements
Faces12 pentagrams, 6 decagrams
Edges60
Vertices30
Vertex figureBowtie, edge lengths (5–1)/2 and (5–5)/2 Measures (edge length 1)
Circumradius$\frac{\sqrt5-1}{2} ≈ 0.61803$ Dihedral angle$\arccos\left(\frac{\sqrt5}{5}\right) ≈ 63.43495^\circ$ Number of external pieces420
Level of complexity22
Related polytopes
ArmyId, edge length $\frac{3-\sqrt5}{2}$ RegimentGid
DualGreat dodecahemidodecacron
ConjugateSmall dodecahemidodecahedron
Abstract & topological properties
Flag count240
Euler characteristic–12
OrientableNo
Genus14
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

The great dodecahemidodecahedron, or gidhid, is a quasiregular polyhedron and one of 10 uniform hemipolyhedra. It consists of 12 pentagrams and 6 "hemi" decagrams, with two of each joining at a vertex. Its pentagrammic faces, as well as its hemi decagrammic faces, are parallel to those of a dodecahedron: hence the name "dodecahemidodecahedron". The "great" suffix, used for stellations in general, distinguishes it from the small dodecahemidodecahedron, which also has this face arrangement. It can be derived as a rectified petrial great icosahedron.

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

It is notable as the only non-regular uniform polyhedron to use exclusively star polygons as faces.

## Vertex coordinates

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