# Great dodecicosahedron

Great dodecicosahedron Rank3
TypeUniform
Notation
Bowers style acronymGiddy
Elements
Faces20 hexagons, 12 decagrams
Edges60+60
Vertices60
Vertex figureButterfly, edge lengths 3 and (5–5)/2 Measures (edge length 1)
Circumradius${\sqrt {\frac {17-3{\sqrt {5}}}{8}}}\approx 1.13423$ Dihedral angles6–10/3 #1: $\arccos \left(-{\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 100.81232^{\circ }$ 6–10/3 #2: $\arccos \left({\sqrt {\frac {5+2{\sqrt {5}}}{15}}}\right)\approx 37.37737^{\circ }$ Central densityeven
Number of external pieces912
Level of complexity56
Related polytopes
ArmyTid, edge length ${\frac {3-{\sqrt {5}}}{2}}$ RegimentGidditdid
DualGreat dodecicosacron
ConjugateSmall dodecicosahedron
Convex coreIcosahedron
Abstract & topological properties
Flag count480
Euler characteristic–28
OrientableNo
Genus30
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

The great dodecicosahedron, or giddy, is a uniform polyhedron. It consists of 20 hexagons and 12 decagrams. Two hexagons and two decagrams meet at each vertex.

It is a faceting of the great ditrigonal dodecicosidodecahedron, using its 12 decagrams along with the 20 hexagons of the great icosicosidodecahedron.

## Vertex coordinates

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