Great dodecahemicosahedron

Great dodecahemicosahedron
(3D model) (OFF file)
Rank	3
Type	Uniform
Notation
Bowers style acronym	Gidhei
Coxeter diagram	(o5/4x3x5*a)/2 ()/2
Elements
Faces	12 pentagons, 10 hexagons
Edges	60
Vertices	30
Vertex figure	Bowtie, edge lengths (1+√5)/2 and √3
Measures (edge length 1)
Circumradius	1
Dihedral angle	$\arccos \left({\sqrt {\frac {5+2{\sqrt {5}}}{15}}}\right)\approx 37.37737^{\circ }$
Number of external pieces	312
Level of complexity	18
Related polytopes
Army	Id, edge length ${\frac {{\sqrt {5}}-1}{2}}$
Regiment	Did
Dual	Great dodecahemicosacron
Conjugate	Small dodecahemicosahedron
Abstract & topological properties
Flag count	240
Euler characteristic	–8
Orientable	No
Genus	10
Properties
Symmetry	H3, order 120
Flag orbits	2
Convex	No
Nature	Tame

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.

External links

• Bowers, Jonathan. "Polyhedron Category 3: Quasiregulars" (#29).

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

• Klitzing, Richard. "gidhei".
• Wikipedia contributors. "Great dodecahemicosahedron".
• McCooey, David. "Great Dodecahemicosahedron"