# Great rhombidodecahedron

Great rhombidodecahedron
Rank3
TypeUniform
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${\displaystyle {\frac {\sqrt {11-4{\sqrt {5}}}}{2}}\approx 0.71689}$
Dihedral angles4–10/3 #1: ${\displaystyle \arccos \left({\sqrt {\frac {5-{\sqrt {5}}}{10}}}\right)\approx 58.28253^{\circ }}$
4–10/3 #2: ${\displaystyle \arccos \left({\sqrt {\frac {5+{\sqrt {5}}}{10}}}\right)\approx 31.71747^{\circ }}$
Central densityodd
Number of external pieces1332
Level of complexity85
Related polytopes
ArmySemi-uniform Ti, edge lengths ${\displaystyle {\sqrt {5}}-2}$ (pentagons), ${\displaystyle {\frac {3-{\sqrt {5}}}{2}}}$ (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.