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 square bipyramid, heccaidecadeltahedron, or tetrakis square antiprism is one of the Johnson solids. As the name suggests, it can be constructed by gyroelongating an octahedron by inserting a square antiprism between its congruent halves. It is one of the eight strictly-convex deltahedra.
In geometry, the triaugmented triangular prism, tetracaidecadeltahedron, or tetrakis triangular prism is one of the Johnson solids (J51). Each of its 14 faces is an equilateral triangle, making it a deltahedron. As the name suggests, it can be constructed by attaching equilateral square pyramids (J1) to each of the three square faces of the triangular prism.
In geometry, the pentagonal bipyramid is third of the infinite set of face-transitive bipyramids, and the 13th Johnson solid. Each bipyramid is the dual of a uniform prism.
In geometry, the gyroelongated square pyramid is one of the Johnson solids. As its name suggests, it can be constructed by taking a square pyramid and "gyroelongating" it, which in this case involves joining a square antiprism to its base.
In geometry, the elongated pentagonal pyramid is one of the Johnson solids. As the name suggests, it can be constructed by elongating a pentagonal pyramid by attaching a pentagonal prism to its base.
In geometry, the elongated square cupola is one of the Johnson solids (J19). As the name suggests, it can be constructed by elongating a square cupola (J4) by attaching an octagonal prism to its base. The solid can be seen as a rhombicuboctahedron with its "lid" removed.
In geometry, the elongated square gyrobicupola or pseudo-rhombicuboctahedron is one of the Johnson solids. It is not usually considered to be an Archimedean solid, even though its faces consist of regular polygons that meet in the same pattern at each of its vertices, because unlike the 13 Archimedean solids, it lacks a set of global symmetries that map every vertex to every other vertex. It strongly resembles, but should not be mistaken for, the small rhombicuboctahedron, which is an Archimedean solid. It is also a canonical polyhedron.
In geometry, the elongated pentagonal rotunda is one of the Johnson solids (J21). As the name suggests, it can be constructed by elongating a pentagonal rotunda (J6) by attaching a decagonal prism to its base. It can also be seen as an elongated pentagonal orthobirotunda (J42) with one pentagonal rotunda removed.
In geometry, the square orthobicupola is one of the Johnson solids (J28). As the name suggests, it can be constructed by joining two square cupolae (J4) along their octagonal bases, matching like faces. A 45-degree rotation of one cupola before the joining yields a square gyrobicupola (J29).
In geometry, the elongated pentagonal gyrobirotunda is one of the Johnson solids (J43). As the name suggests, it can be constructed by elongating a "pentagonal gyrobirotunda," or icosidodecahedron, by inserting a decagonal prism between its congruent halves. Rotating one of the pentagonal rotundae (J6) through 36 degrees before inserting the prism yields an elongated pentagonal orthobirotunda (J42).
In geometry, the elongated pentagonal orthobirotunda is one of the Johnson solids (J42). Its Conway polyhedron notation is at5jP5. As the name suggests, it can be constructed by elongating a pentagonal orthobirotunda (J34) by inserting a decagonal prism between its congruent halves. Rotating one of the pentagonal rotundae (J6) through 36 degrees before inserting the prism yields the elongated pentagonal gyrobirotunda (J43).
In geometry, the elongated triangular bipyramid or triakis triangular prism is one of the Johnson solids, convex polyhedra whose faces are regular polygons. As the name suggests, it can be constructed by elongating a triangular bipyramid by inserting a triangular prism between its congruent halves.
In geometry, the elongated square bipyramid is one of the Johnson solids. As the name suggests, it can be constructed by elongating an octahedron by inserting a cube between its congruent halves.
In geometry, the elongated pentagonal cupola is one of the Johnson solids (J20). As the name suggests, it can be constructed by elongating a pentagonal cupola (J5) by attaching a decagonal prism to its base. The solid can also be seen as an elongated pentagonal orthobicupola (J38) with its "lid" removed.
In geometry, the elongated pentagonal orthobicupola or cantellated pentagonal prism is one of the Johnson solids (J38). As the name suggests, it can be constructed by elongating a pentagonal orthobicupola (J30) by inserting a decagonal prism between its two congruent halves. Rotating one of the cupolae through 36 degrees before inserting the prism yields an elongated pentagonal gyrobicupola (J39).
In geometry, the elongated pentagonal gyrobicupola is one of the Johnson solids (J39). As the name suggests, it can be constructed by elongating a pentagonal gyrobicupola (J31) by inserting a decagonal prism between its congruent halves. Rotating one of the pentagonal cupolae (J5) through 36 degrees before inserting the prism yields an elongated pentagonal orthobicupola (J38).
In geometry, the elongated pentagonal gyrocupolarotunda is one of the Johnson solids (J41). As the name suggests, it can be constructed by elongating a pentagonal gyrocupolarotunda (J33) by inserting a decagonal prism between its halves. Rotating either the pentagonal cupola (J5) or the pentagonal rotunda (J6) through 36 degrees before inserting the prism yields an elongated pentagonal orthocupolarotunda (J40).
The pentagonal bifrustum or truncated pentagonal bipyramid is the third in an infinite series of bifrustum polyhedra. It has 10 trapezoid and 2 pentagonal faces.
In geometry, the elongated pyramids are an infinite set of polyhedra, constructed by adjoining an n-gonal pyramid to an n-gonal prism. Along with the set of pyramids, these figures are topologically self-dual.
