Great icosihemidodecahedron

Great icosihemidodecahedron
(3D model) (OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Geihid
Coxeter diagram	(o3/2x5/3x3*a)/2 ( )/2
Elements
Faces	20 triangles, 6 decagrams
Edges	60
Vertices	30
Vertex figure	Bowtie, edge lengths 1 and √(5–√5)/2
Measures (edge length 1)
Circumradius	$\frac{\sqrt5-1}{2} ≈ 0.61803$
Dihedral angle	$\arccos\left(\sqrt{\frac{5+2\sqrt5}{15}}\right) ≈ 37.37737^\circ$
Number of external pieces	540
Level of complexity	28
Related polytopes
Army	Id, edge length $\frac{3-\sqrt5}{2}$
Regiment	Gid
Dual	Great icosihemidodecacron
Conjugate	Small icosihemidodecahedron
Abstract & topological properties
Flag count	240
Euler characteristic	–4
Orientable	No
Genus	6
Properties
Symmetry	H3, order 120
Convex	No
Nature	Tame

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

Vertex coordinates

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

External links

• Bowers, Jonathan. "Polyhedron Category 3: Quasiregulars" (#32).

• Bowers, Jonathan. "Batch 3: Id, Did, and Gid Facetings" (#2 under gid).

• Klitzing, Richard. "geihid".

• Wikipedia Contributors. "Great icosihemidodecahedron".
• McCooey, David. "Great Icosihemidodecahedron"