Great ditrigonary icosidodecahedron

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Great ditrigonary icosidodecahedron
Rank3
TypeUniform
Notation
Bowers style acronymGidtid
Coxeter diagramo5x3/2o3*a ()
Elements
Faces20 triangles, 12 pentagons
Edges60
Vertices20
Vertex figureTripod, edge lengths 1 and (1+5)/2
Measures (edge length 1)
Circumradius
Volume
Dihedral angle
Central density6
Number of external pieces300
Level of complexity15
Related polytopes
ArmyDoe, edge length
RegimentSidtid
DualGreat triambic icosahedron
ConjugateSmall ditrigonary icosidodecahedron
Convex coreDodecahedron
Abstract & topological properties
Flag count240
Euler characteristic–8
OrientableYes
Genus5
Properties
SymmetryH3, order 120
Flag orbits2
ConvexNo
NatureTame

The great ditrigonary icosidodecahedron or gidtid is a quasiregular uniform polyhedron. It consists of 20 equilateral triangles and 12 pentagons, with three of each joining at a vertex.

It is a faceting of the small ditrigonary icosidodecahedron, using its 20 triangles along with 12 additional pentagons.

It can be constructed as a holosnub great stellated dodecahedron.

This polyhedron is the vertex figure of the great ditrigonary hexacosihecatonicosachoron.

Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the small ditrigonary icosidodecahedron.

Representations[edit | edit source]

A great ditrigonary icosidodecahedron has the following Coxeter diagrams:

  • o5x3/2o3*a ()
  • ß5/2o3o () (as holosnub)

External links[edit | edit source]