Small stellapentakis dodecahedron

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Small stellapentakis dodecahedron
Rank3
TypeUniform dual
Notation
Coxeter diagramo5/2m5m ()
Elements
Faces60 isosceles triangles
Edges30+60
Vertices12+12
Vertex figure12 pentagrams, 12 decagons
Measures (edge length 1)
Inradius
Dihedral angle
Central density3
Number of external pieces120
Related polytopes
DualTruncated great dodecahedron
ConjugateGreat pentakis dodecahedron
Convex coreNon-Catalan pentakis dodecahedron
Abstract & topological properties
Flag count360
Euler characteristic–6
OrientableYes
Genus4
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

The small stellapentakis dodecahedron is a uniform dual polyhedron. It consists of 60 isosceles triangles.

If its dual, the truncated great dodecahedron, has an edge length of 1, then the side edges of the triangles will measure , and the base edges will be . The triangles have two interior angles of , and one of .

Vertex coordinates[edit | edit source]

A small stellapentakis dodecahedron with dual edge length 1 has vertex coordinates given by all even permutations of:

  • ,
  • .

External links[edit | edit source]