Editing Johnson solid (section)

== Definition and background ==
{{multiple image
 | image1 = Elongated square gyrobicupola.png
 | image2 = Stella octangula.png
 | image3 = Partial cubic honeycomb.png
 | total_width = 500
 | align = right
 | footer = Among these three polyhedra, only the first, the [[elongated square gyrobicupola]], is a Johnson solid. The second, the [[stella octangula]], is not [[Convex polyhedron|convex]], as some of its [[diagonal]]s (line segments connecting pairs of vertices) lie outside the shape. The third presents [[Coplanarity|coplanar]] faces.
}}
A Johnson solid is a [[convex polyhedron]] whose faces are all [[regular polygon]]s.{{r|diudea}} The convex polyhedron means as bounded intersections of finitely many [[Half-space (geometry)|half-spaces]], or as the [[convex hull]] of finitely many points.{{r|bk}} Although there is no restriction that any given regular polygon cannot be a face of a Johnson solid, some authors required that Johnson solids are not [[Uniform polyhedron|uniform]]. This means that a Johnson solid is not a [[Platonic solid]], [[Archimedean solid]], [[Prism (geometry)|prism]], or [[antiprism]].{{r|todesco|williams}} A convex polyhedron in which all faces are nearly regular, but some are not precisely regular, is known as a [[near-miss Johnson solid]].{{r|kaplan-hart}}

The solids were named after the mathematicians [[Norman Johnson (mathematician)|Norman Johnson]] and [[Victor Zalgaller]].{{r|uehara}} {{harvtxt|Johnson|1966}} published a list including ninety-two solids&mdash;excluding the five Platonic solids, the thirteen Archimedean solids, the infinitely many uniform prisms, and the infinitely many uniform antiprisms&mdash;and gave them their names and numbers. He did not prove that there were only ninety-two, but he did conjecture that there were no others.{{r|johnson}} {{harvtxt|Zalgaller|1969}} proved that Johnson's list was complete.{{r|zalgaller}}