# Great dodecicosahedron

(Redirected from Giddy)
Great dodecicosahedron Rank3
TypeUniform
SpaceSpherical
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$\sqrt{\frac{17-3\sqrt5}{8}} ≈ 1.13423$ Dihedral angles6–10/3 #1: $\arccos\left(-\sqrt{\frac{5-2\sqrt5}{15}}\right) ≈ 100.81232^\circ$ 6–10/3 #2: $\arccos\left(\sqrt{\frac{5+2\sqrt5}{15}}\right) ≈ 37.37737^\circ$ Central densityeven
Number of pieces912
Level of complexity56
Related polytopes
ArmyTid
RegimentGidditdid
DualGreat dodecicosacron
ConjugateSmall dodecicosahedron
Convex coreIcosahedron
Abstract properties
Euler characteristic–28
Topological properties
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.