Great ditrigonal dodecicosidodecahedron

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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
Volume
Dihedral angles3–10/3:
 5–10/3:
Central density4
Number of external pieces152
Level of complexity13
Related polytopes
ArmyTid, edge length
RegimentGidditdid
DualGreat ditrigonal dodecacronic hexecontahedron
ConjugateSmall ditrigonal dodecicosidodecahedron
Convex coreDodecahedron
Abstract & topological properties
Flag count480
Euler characteristic-16
OrientableYes
Genus9
Properties
SymmetryH3, order 120
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[edit | edit source]

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

Related polyhedra[edit | edit source]

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
Ditrigonary dodecadodecahedron ditdid
Small complex icosidodecahedron (degenerate, ike+gad) cid
Great complex icosidodecahedron (degenerate, sissid+gike) gacid
Icosidodecadodecahedron ided
Small ditrigonal dodecicosidodecahedron sidditdid
Great ditrigonal dodecicosidodecahedron gidditdid
Icosidodecatruncated icosidodecahedron idtid
Snub icosidodecadodecahedron sided


External links[edit | edit source]