In geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, the metabidiminished rhombicosidodecahedron is one of the
Johnson solid

Johnson solid

In geometry, a Johnson solid is a strictly convex polyhedron, each face of which is a regular polygon, but which is not uniform, i.e., not a Platonic solid, Archimedean solid, prism or antiprism. There is no requirement that each face must be the same polygon, or that the same polygons join around...

s (J₈₁).
It can be constructed as a rhombicosidodecahedron

Rhombicosidodecahedron

In geometry, the rhombicosidodecahedron, or small rhombicosidodecahedron, is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces....

 with two non-opposing pentagonal cupola

Pentagonal cupola

In geometry, the pentagonal cupola is one of the Johnson solids . It can be obtained as a slice of the rhombicosidodecahedron.The 92 Johnson solids were named and described by Norman Johnson in 1966....

e removed.
Related Johnson solids are
the diminished rhombicosidodecahedron

Diminished rhombicosidodecahedron

In geometry, the diminished rhombicosidodecahedron is one of theJohnson solids .It can be constructed as a rhombicosidodecahedron with one pentagonal cupola removed.The 92 Johnson solids were named and described by Norman Johnson in 1966....

 (J₇₆) where one cupola is removed,
the parabidiminished rhombicosidodecahedron

Parabidiminished rhombicosidodecahedron

In geometry, the parabidiminished rhombicosidodecahedron is one of theJohnson solids .It can be constructed as a rhombicosidodecahedron with two opposing pentagonal cupola removed.Related Johnson solids are...

 (J₈₀) where two opposing cupolae are removed,
the gyrate bidiminished rhombicosidodecahedron

Gyrate bidiminished rhombicosidodecahedron

In geometry, the gyrate bidiminished rhombicosidodecahedron is one of the Johnson solids .The 92 Johnson solids were named and described by Norman Johnson in 1966.-External links:**...

 (J₈₂) where two non-opposing cupolae are removed and a third is rotated 36 degrees, and
the tridiminished rhombicosidodecahedron

Tridiminished rhombicosidodecahedron

In geometry, the tridiminished rhombicosidodecahedron is one of theJohnson solids .It can be constructed as a rhombicosidodecahedron with three pentagonal cupola removed.Related Johnson solids are:...

 (J₈₃) where three cupolae are removed.

The 92 Johnson solids were named and described by Norman Johnson in 1966.

External links