Great dodecahemidodecahedron

Great dodecahemidodecahedron
(3D model) (OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gidhid
Coxeter diagram	(x5/3x5/3o5/2*a)/2 ( )/2
Elements
Faces	12 pentagrams, 6 decagrams
Edges	60
Vertices	30
Vertex figure	Bowtie, 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 pieces	420
Level of complexity	22
Related polytopes
Army	Id, edge length $\frac{3-\sqrt5}{2}$
Regiment	Gid
Dual	Great dodecahemidodecacron
Conjugate	Small dodecahemidodecahedron
Abstract & topological properties
Flag count	240
Euler characteristic	–12
Orientable	No
Genus	14
Properties
Symmetry	H3, order 120
Convex	No
Nature	Tame

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.

External links

• Bowers, Jonathan. "Polyhedron Category 3: Quasiregulars" (#31).

• Bowers, Jonathan. "Batch 3: Id, Did, and Gid Facetings" (#3 under gid).

• Klitzing, Richard. "gidhid".

• Wikipedia Contributors. "Great dodecahemidodecahedron".
• McCooey, David. "Great dodecahemidodecahedron"