Metabidiminished rhombicosidodecahedron

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Metabidiminished rhombicosidodecahedron
Metabidiminished rhombicosidodecahedron.png
TypeJohnson
J80 - J81 - J82
Faces3x2+4 triangles
2+2+4x4 squares
3x2+4 pentagons
2 decagons
Edges90
Vertices50
Vertex configuration5x4(4.5.10)
3x2+6x4(3.4.5.4)
Symmetry groupC2v
Dual polyhedron-
PropertiesConvex
Net
Johnson solid 81 net.png

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

A Johnson solid is one of 92 strictly convex polyhedra that have regular faces but are not uniform (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 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, and the tridiminished rhombicosidodecahedron (J83) where three cupolae are removed.

External links[edit]

  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.