In
geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
, the metabigyrate rhombicosidodecahedron is one of the
Johnson solid
In geometry, a Johnson solid is a strictly convex polyhedron each face of which is a regular polygon. There is no requirement that isohedral, each face must be the same polygon, or that the same polygons join around each Vertex (geometry), ver ...
s (). It can be constructed as a
rhombicosidodecahedron
In geometry, the rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces.
It has 20 regular triangular faces, 30 square (geometry), square face ...
with two non-opposing
pentagonal cupola
In geometry, the pentagonal cupola is one of the Johnson solids (). It can be obtained as a slice of the rhombicosidodecahedron. The pentagonal cupola consists of 5 equilateral triangles, 5 squares, 1 pentagon, and 1 decagon.
Formulae
The fol ...
e rotated through 36 degrees. It is also a
canonical polyhedron.
Alternative Johnson solids, constructed by rotating different cupolae of a rhombicosidodecahedron, are:
* The
gyrate rhombicosidodecahedron
In geometry, the gyrate rhombicosidodecahedron is one of the Johnson solids (). It is also a canonical polyhedron.
Related polyhedron
It can be constructed as a rhombicosidodecahedron with one pentagonal cupola rotated through 36 degrees. ...
() where only one cupola is rotated;
* The
parabigyrate rhombicosidodecahedron
In geometry, the parabigyrate rhombicosidodecahedron is one of the Johnson solids (). It can be constructed as a rhombicosidodecahedron with two opposing pentagonal cupolae rotated through 36 degrees. It is also a canonical polyhedron.
Alter ...
() where two opposing cupolae are rotated;
* And the
trigyrate rhombicosidodecahedron
In geometry, the trigyrate rhombicosidodecahedron is one of the Johnson solids (). It contains 20 triangles, 30 squares and 12 pentagons. It is also a canonical polyhedron.
It can be constructed as a rhombicosidodecahedron with three pentag ...
() where three cupolae are rotated.
External links
*
World of Polyhedra - metabigyrate rhombicosidodecahedron(interactive rotatable wireframe applet)
Johnson solids
{{Polyhedron-stub