# Great ditrigonal dodecicosidodecahedron

(Redirected from Gidditdid)
Great ditrigonal dodecicosidodecahedron
Rank3
TypeUniform
Notation
Bowers style acronymGidditdid
Coxeter diagramx5/3x3o5*a ()
Elements
Faces20 triangles, 12 pentagons, 12 decagrams
Edges60+60
Vertices60
Vertex figureIsosceles trapezoid, edge lengths 1, (5–5)/2, (1+5)/2, (5–5)/2
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {17-3{\sqrt {5}}}{8}}}\approx 1.13423}$
Volume${\displaystyle 7{\frac {15-{\sqrt {5}}}{6}}\approx 14.89125}$
Dihedral angles3–10/3: ${\displaystyle \arccos \left(-{\sqrt {\frac {5+2{\sqrt {5}}}{15}}}\right)\approx 142.62263^{\circ }}$
5–10/3: ${\displaystyle \arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }}$
Central density4
Number of external pieces152
Level of complexity13
Related polytopes
ArmyTid, edge length ${\displaystyle {\frac {3-{\sqrt {5}}}{2}}}$
RegimentGidditdid
DualGreat ditrigonal dodecacronic hexecontahedron
ConjugateSmall ditrigonal dodecicosidodecahedron
Convex coreDodecahedron
Abstract & topological properties
Flag count480
Euler characteristic-16
OrientableYes
Genus9
Properties
SymmetryH3, order 120
Flag orbits4
ConvexNo
NatureTame

The great ditrigonal dodecicosidodecahedron, or gidditdid, is a uniform polyhedron. It consists of 20 triangles, 12 pentagons, and 12 decagrams. One triangle, one pentagon, and two decagrams join at each vertex.

## Vertex coordinates

A great ditrigonal dodecicosidodecahedron of edge length 1 has vertex coordinates given by all even permutations of:

• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {1+{\sqrt {5}}}{4}}\right),}$
• ${\displaystyle \left(0,\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {\sqrt {5}}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {3-{\sqrt {5}}}{4}}\right).}$

## Related polyhedra

The great ditrigonal dodecicosidodecahedron is the colonel of a three-member regiment that also includes the great icosicosidodecahedron and the great dodecicosahedron.

o5/3o3o5*a truncations
Name OBSA CD diagram Picture