Gyrate rhombicosidodecahedron

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Gyrate rhombicosidodecahedron
Rank3
TypeCRF
Notation
Bowers style acronymGyrid
Elements
Faces
Edges8×5+8×10
Vertices4×5+4×10
Vertex figures5+45 isosceles trapezoids, edge length 1, 2, (1+5)/2, 2
 10 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 complexity48
Related polytopes
ArmyGyrid
RegimentGyrid
DualDeltogyrate deltoidal hexecontahedron
ConjugateGyrate quasirhombicosidodecahedron
Abstract & topological properties
Flag count480
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryH2×I, order 10
Flag orbits48
ConvexYes
NatureTame

The gyrate rhombicosidodecahedron (OBSA: gyrid) is one of the 92 Johnson solids (J72). It consists of 5+5+5+5 triangles, 5+5+5+5+10 squares, and 1+1+5+5 pentagons. It can be constructed by rotating one of the pentagonal cupolaic caps of the small rhombicosidodecahedron by 36°.

Vertex coordinates[edit | edit source]

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

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

External links[edit | edit source]