Parabigyrate rhombicosidodecahedron

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Parabigyrate rhombicosidodecahedron
Rank3
TypeCRF
Notation
Bowers style acronymPabgyrid
Elements
Faces
Edges4×10+4×20
Vertices10+10+20+20
Vertex figures10+10+20 isosceles trapezoids, edge length 1, 2, (1+5)/2, 2
 20 irregular tetragons, edge lengths 1, 2, 2, (1+5)/2
Measures (edge length 1)
Circumradius
Volume
Dihedral angles3–4:
 3–5:
 4–4:
 4–5:
Central density1
Number of external pieces62
Level of complexity24
Related polytopes
ArmyPabgyrid
RegimentPabgyrid
DualParabideltogyrate deltoidal hexecontahedron
ConjugateParabigyrate quasirhombicosidodecahedron
Abstract & topological properties
Flag count480
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry(I2(10)×A1)/2, order 20
Flag orbits24
ConvexYes
NatureTame

The parabigyrate rhombicosidodecahedron (OBSA: pabgyrid) is one of the 92 Johnson solids (J73). It consists of 10+10 triangles, 10+10+10 squares, and 2+10 pentagons. It can be constructed by rotating two opposite pentagonal cupolaic caps of the small rhombicosidodecahedron by 36°.

Vertex coordinates[edit | edit source]

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

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

External links[edit | edit source]