Gyrate bidiminished rhombicosidodecahedron

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Gyrate bidiminished rhombicosidodecahedron
Rank3
TypeCRF
Notation
Bowers style acronymGybadrid
Elements
Faces
Edges8×1+41×2
Vertices4×1+23×2
Vertex figures5+15 isosceles trapezoids, edge length 1, 2, (1+5)/2, 2
 20 scalene triangles, edge lengths 2, (1+5)/2, (5+5)/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:
 4–10:
 5–10:
Central density1
Number of external pieces42
Level of complexity180
Related polytopes
ArmyGybadrid
RegimentGybadrid
DualGyrate bistellated deltoidal hexecontahedron
ConjugateGyrate bireplenished quasirhombicosidodecahedron
Abstract & topological properties
Flag count360
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryA1×I×I, order 2
Flag orbits180
ConvexYes
NatureTame

The gyrate bidiminished rhombicosidodecahedron (OBSA: gybadrid) is one of the 92 Johnson solids (J82). It consists of 4×1+3×2 triangles, 4×1+8×2 squares, 4×1+3×2 pentagons, and 2 decagons. It can be constructed by removing two non-opposite pentagonal cupolaic caps of the small rhombicosidodecahedron, and rotating a third cap by 36°.

Vertex coordinates[edit | edit source]

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

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  • .

External links[edit | edit source]