Medial disdyakis triacontahedron

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Medial disdyakis triacontahedron
Rank3
TypeUniform dual
Notation
Coxeter diagramm5/3m5m
Elements
Faces120 scalene triangles
Edges60+60+60
Vertices12+12+30
Vertex figure30 squares, 12 decagons, 12 decagrams
Measures (edge length 1)
Inradius
Dihedral angles120 edges:
 60 edges:
Central density–3
Number of external pieces120
Related polytopes
DualQuasitruncated dodecadodecahedron
ConjugateMedial disdyakis triacontahedron
Convex coreNon-Catalan disdyakis triacontahedron
Abstract & topological properties
Flag count720
Euler characteristic–6
OrientableYes
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

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

If its dual, the quasitruncated dodecadodecahedron, has an edge length of 1, then the triangle's short edges will be , 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 medial disdyakis triacontahedron with dual edge length 1 has vertex coordinates given by all even permutations of:

External links[edit | edit source]