# Great rhombidodecahedron

Great rhombidodecahedron
Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymGird
Elements
Faces30 squares, 12 decagrams
Edges60+60
Vertices60
Vertex figureButterfly, edge lengths 2 and (5–5)/2
Measures (edge length 1)
Circumradius${\displaystyle \frac{\sqrt{11-4\sqrt5}}{2} ≈ 0.71689}$
Dihedral angles4–10/3 #1: ${\displaystyle \arccos\left(\sqrt{\frac{5-\sqrt5}{10}}\right) ≈ 58.28253^\circ}$
4–10/3 #2: ${\displaystyle \arccos\left(\sqrt{\frac{5+\sqrt5}{10}}\right) ≈ 31.71747^\circ}$
Central densityodd
Number of external pieces1332
Level of complexity85
Related polytopes
ArmySemi-uniform Ti, edge lengths ${\displaystyle \sqrt5-2}$ (pentagons), ${\displaystyle \frac{3-\sqrt5}{2}}$ (between ditrigons)
DualGreat rhombidodecacron
ConjugateSmall rhombidodecahedron
Convex coreRhombic triacontahedron
Abstract & topological properties
Flag count480
Euler characteristic–18
OrientableNo
Genus20
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

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.