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A uniform polyhedron is a polyhedron in which the faces are regular and they are isogonal; examples include Platonic and Archimedean solids as well as prisms and antiprisms. [3] The Johnson solids are named after American mathematician Norman Johnson (1930–2017), who published a list of 92 such polyhedra in 1966.
A Johnson solid is a convex polyhedron whose faces are all regular polygons. [1] Here, a polyhedron is said to be convex if the shortest path between any two of its vertices lies either within its interior or on its boundary, none of its faces are coplanar (meaning they do not share the same plane, and do not "lie flat"), and none of its edges are colinear (meaning they are not segments of the ...
They were named by Norman Johnson, who first listed these polyhedra in 1966. [1] The gyroelongated pentagonal cupolarotunda is one of five Johnson solids which are chiral, meaning that they have a "left-handed" and a "right-handed" form. In the illustration to the right, each pentagonal face on the bottom half of the figure is connected by a ...
The other three polyhedra with this property are the regular octahedron, the snub disphenoid, and an irregular polyhedron with 12 vertices and 20 triangular faces. [6] The dual polyhedron of a pentagonal bipyramid is the pentagonal prism. More generally, the dual polyhedron of every bipyramid is the prism, and the vice versa is true. [7]
They were named by Norman Johnson, who first listed these polyhedra in 1966. [1] The gyroelongated pentagonal birotunda is one of five Johnson solids which are chiral, meaning that they have a "left-handed" and a "right-handed" form. In the illustration to the right, each pentagonal face on the bottom half of the figure is connected by a path ...
In geometry, the gyrate rhombicosidodecahedron is one of the Johnson solids (J 72).It is also a canonical polyhedron.. A Johnson solid is one of 92 strictly convex polyhedra that is composed of regular polygon faces but are not uniform polyhedra (that is, they are not Platonic solids, Archimedean solids, prisms, or antiprisms).
One of the Johnson solids, elongated square pyramid, is composite. It can be constructed by attaching equilateral square pyramid and a cube. Any composite polyhedron can be constructed by attaching two or more non-composite polyhedra. Alternatively, it can be defined as a convex polyhedron that can separated into two or more non-composite ...
In geometry, a near-miss Johnson solid is a strictly convex polyhedron whose faces are close to being regular polygons but some or all of which are not precisely regular. Thus, it fails to meet the definition of a Johnson solid, a polyhedron whose faces are all regular, though it "can often be physically constructed without noticing the discrepancy" between its regular and irregular faces. [1]