Gyrate bidiminished rhombicosidodecahedron

Gyrate bidiminished rhombicosidodecahedron
Type	Johnson J81 – J82 – J83
Faces	10 triangles 20 squares 10 pentagons 2 decagons
Edges	90
Vertices	50
Vertex configuration	10.2(4.5.10) 5×2(3.42.5) 4+8.2(3.4.5.4)
Symmetry group	Cs
Dual polyhedron	-
Properties	Convex
Net

In geometry, the gyrate bidiminished rhombicosidodecahedron is one of the Johnson solids (J₈₂).

3D model of a gyrate bidiminished rhombicosidodecahedron

A Johnson solid is one of 92 strictly convex polyhedra that are composed of regular polygon faces but are not uniform polyhedra (that is, they are not Platonic solids , Archimedean solids , prisms , or antiprisms ). They were named by Norman Johnson , who first listed these polyhedra in 1966. ^[1]

It can be constructed as a rhombicosidodecahedron with two non-opposing pentagonal cupolae (J₅) removed and a third is rotated 36 degrees. Related Johnson solids are:

• The diminished rhombicosidodecahedron (J₇₆) where one cupola is removed,
• The parabidiminished rhombicosidodecahedron (J₈₀) where two opposing cupolae are removed,
• The metabidiminished rhombicosidodecahedron (J₈₁) where two non-opposing cupolae are removed,
• And the tridiminished rhombicosidodecahedron (J₈₃) where three cupolae are removed.

References

1. Johnson, Norman W. (1966), "Convex polyhedra with regular faces", Canadian Journal of Mathematics , 18: 169–200, doi: 10.4153/cjm-1966-021-8 , MR   0185507, Zbl   0132.14603 .

External links

• Weisstein, Eric W., "Gyrate bidiminished rhombicosidodecahedron" ("Johnson solid") at MathWorld .