# Great dodecahemidodecahedron

Great dodecahemidodecahedron
Rank3
TypeUniform
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${\displaystyle {\frac {{\sqrt {5}}-1}{2}}\approx 0.61803}$
Dihedral angle${\displaystyle \arccos \left({\frac {\sqrt {5}}{5}}\right)\approx 63.43495^{\circ }}$
Number of external pieces420
Level of complexity22
Related polytopes
ArmyId, edge length ${\displaystyle {\frac {3-{\sqrt {5}}}{2}}}$
RegimentGid
DualGreat dodecahemidodecacron
ConjugateSmall dodecahemidodecahedron
Abstract & topological properties
Flag count240
Euler characteristic–12
OrientableNo
Genus14
Properties
SymmetryH3, order 120
Flag orbits2
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. 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.

## Name

Its pentagrammic faces, as well as its decagrammic faces, are parallel to those of a dodecahedron, hence the name "dodecahemidodecahedron". The "great" modifier, used for stellations in general, distinguishes it from the small dodecahemidodecahedron, which also has this face arrangement.

## Vertex coordinates

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