Great rhombidodecahedron

Great rhombidodecahedron
(3D model) (OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gird
Elements
Faces	30 squares, 12 decagrams
Edges	60+60
Vertices	60
Vertex figure	Butterfly, edge lengths √2 and √(5–√5)/2
Measures (edge length 1)
Circumradius	$\frac{\sqrt{11-4\sqrt5}}{2} ≈ 0.71689$
Dihedral angles	4–10/3 #1: $\arccos\left(\sqrt{\frac{5-\sqrt5}{10}}\right) ≈ 58.28253^\circ$
	4–10/3 #2: $\arccos\left(\sqrt{\frac{5+\sqrt5}{10}}\right) ≈ 31.71747^\circ$
Central density	odd
Number of external pieces	1332
Level of complexity	85
Related polytopes
Army	Semi-uniform Ti, edge lengths $\sqrt5-2$ (pentagons), $\frac{3-\sqrt5}{2}$ (between ditrigons)
Regiment	Gaddid
Dual	Great rhombidodecacron
Conjugate	Small rhombidodecahedron
Convex core	Rhombic triacontahedron
Abstract & topological properties
Flag count	480
Euler characteristic	–18
Orientable	No
Genus	20
Properties
Symmetry	H3, order 120
Convex	No
Nature	Tame

The great rhombidodecahedron, or gird, is a uniform polyhedron. It consists of 30 squares and 12 decagrams. Two squares and two decagrams meet at each vertex..

It is a faceting of the great dodecicosidodecahedron, using its 12 decagrams along with the 30 squares of the quasirhombicosidodecahedron.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Polyhedron Category 4: Trapeziverts" (#56).

• Klitzing, Richard. "gird".

• Wikipedia Contributors. "Great rhombidodecahedron".
• McCooey, David. "Great Rhombidodecahedron"