In geometry, a Johnson solid, sometimes also known as a Johnson–Zalgaller solid, is a strictly convex polyhedron whose faces are regular polygons. They are sometimes defined to exclude the uniform polyhedrons. There are ninety-two solids with such a property: the first solids are the pyramids, cupolas. and a rotunda; some of the solids may be constructed by attaching with those previous solids, whereas others may not. These solids are named after mathematicians Norman Johnson and Victor Zalgaller.
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.
In geometry, the metabidiminished icosahedron is one of the Johnson solids. The name refers to one way of constructing it, by removing two pentagonal pyramids from a regular icosahedron, replacing two sets of five triangular faces of the icosahedron with two adjacent pentagonal faces. If two pentagonal pyramids are removed to form nonadjacent pentagonal faces, the result is instead the pentagonal antiprism.
In geometry, the square orthobicupola is one of the Johnson solids. As the name suggests, it can be constructed by joining two square cupolae along their octagonal bases, matching like faces. A 45-degree rotation of one cupola before the joining yields a square gyrobicupola.
In geometry, the gyroelongated square bicupola is the Johnson solid constructed by attaching two square cupolae on each base of octagonal antiprism. It has the property of chirality.
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.
In geometry, the diminished rhombicosidodecahedron is one of the Johnson solids. It can be constructed as a rhombicosidodecahedron with one pentagonal cupola removed.
In geometry, the gyrate rhombicosidodecahedron is one of the Johnson solids. It is also a canonical polyhedron.
In geometry, the parabidiminished rhombicosidodecahedron is one of the Johnson solids. It is also a canonical polyhedron.
In geometry, the tridiminished rhombicosidodecahedron is one of the Johnson solids. It can be constructed as a rhombicosidodecahedron with three pentagonal cupolae removed.
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.
In geometry, the pentagonal orthobicupola is one of the Johnson solids. As the name suggests, it can be constructed by joining two pentagonal cupolae along their decagonal bases, matching like faces. A 36-degree rotation of one cupola before the joining yields a pentagonal gyrobicupola.
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.
In geometry, the paragyrate diminished rhombicosidodecahedron is one of the Johnson solids. It can be constructed as a rhombicosidodecahedron with one pentagonal cupola rotated through 36 degrees, and the opposing pentagonal cupola removed.
In geometry, the metagyrate diminished rhombicosidodecahedron is one of the Johnson solids. It can be constructed as a rhombicosidodecahedron with one pentagonal cupola rotated through 36 degrees, and a non-opposing pentagonal cupola removed.
In geometry, the bigyrate diminished rhombicosidodecahedron is one of the Johnson solids. It can be constructed as a rhombicosidodecahedron with two pentagonal cupolae rotated through 36 degrees, and a third pentagonal cupola removed.
In geometry, the gyrate bidiminished rhombicosidodecahedron is one of the Johnson solids.
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. It is also a canonical polyhedron.
In geometry, the gyroelongated triangular cupola is one of the Johnson solids (J22). It can be constructed by attaching a hexagonal antiprism to the base of a triangular cupola (J3). This is called "gyroelongation", which means that an antiprism is joined to the base of a solid, or between the bases of more than one solid.
