# Great ditrigonary icosidodecahedron

(Redirected from Gidtid)
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${\displaystyle {\frac {\sqrt {3}}{2}}\approx 0.86603}$
Volume${\displaystyle {\frac {4{\sqrt {5}}}{3}}\approx 2.98142}$
Dihedral angle${\displaystyle \arccos \left({\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 79.18768^{\circ }}$
Central density6
Number of external pieces300
Level of complexity15
Related polytopes
ArmyDoe, edge length ${\displaystyle {\frac {{\sqrt {5}}-1}{2}}}$
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

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

## Representations

A great ditrigonary icosidodecahedron has the following Coxeter diagrams:

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