Diminished rhombicosidodecahedron

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Diminished rhombicosidodecahedron
Rank3
TypeCRF
Notation
Bowers style acronymDirid
Elements
Faces5+5+5 triangles, 5+5+5+10 squares, 1+5+5 pentagons, 1 decagon
Edges5+5+5+5+5+5+5+10+10+10+10+10+10+10
Vertices5+5+5+10+10+10+10
Vertex figures45 isosceles trapezoids, edge length 1, 2, (1+5)/2, 2
 10 scalene triangles, edge lengths 2, (1+5)/2, (5+5)/2
Measures (edge length 1)
Circumradius
Volume
Dihedral angles3–4:
 4–5:
 4–10:
 5–10:
Central density1
Number of external pieces52
Level of complexity42
Related polytopes
ArmyDirid
RegimentDirid
DualStellated deltoidal hexecontahedron
ConjugateReplenished quasirhombicosidodecahedron
Abstract & topological properties
Flag count420
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryH2×I, order 10
ConvexYes
NatureTame

The diminished rhombicosidodecahedron is one of the 92 Johnson solids (J76). It consists of 5+5+5 triangles, 5+5+5+10 squares, 1+5+5 pentagons, and 1 decagon. It can be constructed by removing one of the pentagonal cupolaic caps of the small rhombicosidodecahedron.

Vertex coordinates[edit | edit source]

A diminished rhombicosidodecahedron of edge length 1 has vertices given by:

  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • .

External links[edit | edit source]