Great icosacronic hexecontahedron

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Great icosacronic hexecontahedron
Rank3
TypeUniform dual
Notation
Coxeter diagramo3/2m3m5*a
Elements
Faces60 darts
Edges60+60
Vertices12+20+20
Vertex figure20 triangles, 12 pentagons, 20 hexagons
Measures (edge length 1)
Inradius
Dihedral angle
Central density6
Number of external pieces180
Related polytopes
DualGreat icosicosidodecahedron
ConjugateSmall icosacronic hexecontahedron
Convex coreTriakis icosahedron
Abstract & topological properties
Flag count480
Euler characteristic–8
OrientableYes
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

The great icosacronic hexecontahedron is a uniform dual polyhedron. It consists of 60 darts.

If its dual, the great icosicosidodecahedron, has an edge length of 1, then the short edges of the darts will measure , and the long edges will be . ​The dart faces will have length , and width . The darts have two interior angles of , one of , and one of .

Vertex coordinates[edit | edit source]

A great icosacronic hexecontahedron with dual edge length 1 has vertex coordinates given by all even permutations of:

External links[edit | edit source]