Trigyrate rhombicosidodecahedron
Encyclopedia
In geometry
, the trigyrate rhombicosidodecahedron is one of the
Johnson solid
s (J75).
It can be constructed as a rhombicosidodecahedron
with three pentagonal cupolae
rotated through 36 degrees.
Related Johnson solids are
the gyrate rhombicosidodecahedron
(J72) where one cupola is rotated,
the parabigyrate rhombicosidodecahedron
(J73) where two opposing cupolae are rotated and
the metabigyrate rhombicosidodecahedron
(J74) where two non-opposing cupolae are rotated.
The 92 Johnson solids were named and described by Norman Johnson in 1966.
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 trigyrate 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 (J75).
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 three pentagonal cupolae
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....
rotated through 36 degrees.
Related Johnson solids are
the gyrate rhombicosidodecahedron
Gyrate rhombicosidodecahedron
In geometry, the gyrate rhombicosidodecahedron is one of theJohnson solids .The 92 Johnson solids were named and described by Norman Johnson in 1966.- Related polyhedron :...
(J72) where one cupola is rotated,
the parabigyrate rhombicosidodecahedron
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....
(J73) where two opposing cupolae are rotated and
the metabigyrate rhombicosidodecahedron
Metabigyrate rhombicosidodecahedron
In geometry, the metabigyrate rhombicosidodecahedron is one of the Johnson solids . It can be constructed as a rhombicosidodecahedron with two non-opposing pentagonal cupolae rotated through 36 degrees....
(J74) where two non-opposing cupolae are rotated.
The 92 Johnson solids were named and described by Norman Johnson in 1966.