# Great dodecicosahedron

Great dodecicosahedron
Rank3
TypeUniform
Notation
Bowers style acronymGiddy
Coxeter diagramx5/3x5/2x3*a -12{10/2}
Elements
Faces20 hexagons, 12 decagrams
Edges60+60
Vertices60
Vertex figureButterfly, edge lengths 3 and (5–5)/2
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {17-3{\sqrt {5}}}{8}}}\approx 1.13423}$
Dihedral angles6–10/3 #1: ${\displaystyle \arccos \left(-{\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 100.81232^{\circ }}$
6–10/3 #2: ${\displaystyle \arccos \left({\sqrt {\frac {5+2{\sqrt {5}}}{15}}}\right)\approx 37.37737^{\circ }}$
Central densityeven
Number of external pieces912
Level of complexity56
Related polytopes
ArmyTid, edge length ${\displaystyle {\frac {3-{\sqrt {5}}}{2}}}$
RegimentGidditdid
DualGreat dodecicosacron
ConjugateSmall dodecicosahedron
Convex coreIcosahedron
Abstract & topological properties
Flag count480
Euler characteristic–28
OrientableNo
Genus30
Properties
SymmetryH3, order 120
Flag orbits4
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.

## Representations

A great dodecicosahedron has representations as two reduced Coxeter diagrams:

• x5/3x5/2x3*a -12{10/2}
• x5/3x3/2x3*a -20{6/2}