In geometry, a Johnson solid is a strictly convex polyhedron each face of which is a regular polygon. There is no requirement that each face must be the same polygon, or that the same polygons join around each vertex. An example of a Johnson solid is the square-based pyramid with equilateral sides ; it has 1 square face and 4 triangular faces. Some authors require that the solid not be uniform before they refer to it as a “Johnson solid”.
In geometry, the gyroelongated pentagonal pyramid is one of the Johnson solids. As its name suggests, it is formed by taking a pentagonal pyramid and "gyroelongating" it, which in this case involves joining a pentagonal antiprism to its base.
In geometry, the tridiminished icosahedron is one of the Johnson solids. The name refers to one way of constructing it, by removing three pentagonal pyramids from a regular icosahedron, which replaces three sets of five triangular faces from the icosahedron with three mutually adjacent pentagonal 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 diminished rhombicosidodecahedron is one of the Johnson solids. It can be constructed as a rhombicosidodecahedron with one pentagonal cupola removed.
In geometry, the parabidiminished rhombicosidodecahedron is one of the Johnson solids. It is also a canonical polyhedron.
In geometry, the metabidiminished rhombicosidodecahedron is one of the Johnson solids.
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 bilunabirotunda is one of the Johnson solids. A Johnson solid is one of 92 strictly convex polyhedra that is composed of regular polygon faces but are not uniform polyhedra. They were named by Norman Johnson, who first listed these polyhedra in 1966.
In geometry, the augmented triangular prism is one of the Johnson solids. As the name suggests, it can be constructed by augmenting a triangular prism by attaching a square pyramid to one of its equatorial faces. The resulting solid bears a superficial resemblance to the gyrobifastigium, the difference being that the latter is constructed by attaching a second triangular prism, rather than a square pyramid.
In geometry, the biaugmented triangular prism is one of the Johnson solids. As the name suggests, it can be constructed by augmenting a triangular prism by attaching square pyramids to two of its equatorial faces.
In geometry, the augmented pentagonal prism is one of the Johnson solids. As the name suggests, it can be constructed by augmenting a pentagonal prism by attaching a square pyramid to one of its equatorial faces.
In geometry, the biaugmented pentagonal prism is one of the Johnson solids. As the name suggests, it can be constructed by doubly augmenting a pentagonal prism by attaching square pyramids to two of its nonadjacent equatorial faces.
In geometry, the augmented hexagonal prism is one of the Johnson solids. As the name suggests, it can be constructed by augmenting a hexagonal prism by attaching a square pyramid to one of its equatorial faces. When two or three such pyramids are attached, the result may be a parabiaugmented hexagonal prism, a metabiaugmented hexagonal prism, or a triaugmented hexagonal prism.
In geometry, the parabiaugmented hexagonal prism is one of the Johnson solids. As the name suggests, it can be constructed by doubly augmenting a hexagonal prism by attaching square pyramids to two of its nonadjacent, parallel (opposite) equatorial faces. Attaching the pyramids to nonadjacent, nonparallel equatorial faces yields a metabiaugmented hexagonal prism.
In geometry, the augmented dodecahedron is one of the Johnson solids, consisting of a dodecahedron with a pentagonal pyramid attached to one of the faces. When two or three such pyramids are attached, the result may be a parabiaugmented dodecahedron, a metabiaugmented dodecahedron, or a triaugmented dodecahedron.
In geometry, the gyrate bidiminished rhombicosidodecahedron is one of the Johnson solids.
In geometry, the augmented truncated tetrahedron is one of the Johnson solids. It is created by attaching a triangular cupola to one hexagonal face of a truncated tetrahedron.
In geometry, the augmented truncated cube is one of the Johnson solids. As its name suggests, it is created by attaching a square cupola onto one octagonal face of a truncated cube.
In geometry, the augmented truncated dodecahedron is one of the Johnson solids. As its name suggests, it is created by attaching a pentagonal cupola onto one decagonal face of a truncated dodecahedron.
