Metabidiminished rhombicosidodecahedron

Metabidiminished rhombicosidodecahedron
Type	Johnson J80 – J81 – J82
Faces	3×2+4 triangles 2+2+4×4 squares 3×2+4 pentagons 2 decagons
Edges	90
Vertices	50
Vertex configuration	5×4(4.5.10) 3×2+6×4(3.4.5.4)
Symmetry group	C2v
Dual polyhedron	-
Properties	Convex
Net

In geometry, the metabidiminished rhombicosidodecahedron is one of the Johnson solids (J₈₁).

3D model of a metabidiminished 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. Related Johnson solids are:

• The diminished rhombicosidodecahedron (J₇₆) where one cupola is removed,
• The parabidiminished rhombicosidodecahedron (J₈₀) where two opposing cupolae are removed,
• The gyrate bidiminished rhombicosidodecahedron (J₈₂) where two non-opposing cupolae are removed and a third is rotated 36 degrees,
• 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., "Metabidiminished rhombicosidodecahedron" ("Johnson solid") at MathWorld .