Great disdyakis triacontahedron

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Great disdyakis triacontahedron
Rank3
TypeUniform dual
Notation
Coxeter diagramm5/3m3m
Elements
Faces120 scalene triangles
Edges60+60+60
Vertices12+20+30
Vertex figure30 squares, 20 hexagons, 12 decagrams
Measures (edge length 1)
Inradius
Dihedral angle
Central density13
Number of external pieces120
Related polytopes
DualGreat quasitruncated icosidodecahedron
ConjugateDisdyakis triacontahedron
Abstract & topological properties
Flag count720
Euler characteristic2
OrientableYes
Genus0
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

The great disdyakis triacontahedron is a uniform dual polyhedron. It consists of 120 scalene triangles.

If its dual, the great quasitruncated icosidodecahedron, has an edge length of 1, then the triangle faces' short edges will measure , the medium edges will be , and the long edges will be . The triangles have one interior angle of , one of , and one of .

Vertex coordinates[edit | edit source]

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

External links[edit | edit source]