Editing Johnson solid (section)

== Naming and enumeration ==
{{main article|List of Johnson solids}}
[[File:Triaugmented triangular prism (symmetric view).svg|thumb|An example is [[triaugmented triangular prism]]. Here, it is constructed from triangular prism by joining three equilateral square pyramids onto each of its squares (tri-). The process of this construction known as "augmentation", making its first name is "triaugmented".]]
The naming of Johnson solids follows a flexible and precise descriptive formula that allows many solids to be named in multiple different ways without compromising the accuracy of each name as a description. Most Johnson solids can be constructed from the first few solids ([[Pyramid (geometry)|pyramids]], [[cupola (geometry)|cupolae]], and a [[rotunda (geometry)|rotunda]]), together with the [[Platonic solid|Platonic]] and [[Archimedean solid|Archimedean]] solids, [[prism (geometry)|prisms]], and [[antiprism]]s; the center of a particular solid's name will reflect these ingredients. From there, a series of prefixes are attached to the word to indicate additions, rotations, and transformations:{{r|berman}}
* ''Bi-'' indicates that two copies of the solid are joined base-to-base. For cupolae and rotundas, the solids can be joined so that either like faces (''ortho-'') or unlike faces (''gyro-'') meet. Using this nomenclature, a [[pentagonal bipyramid]] is a solid constructed by attaching two bases of pentagonal pyramids. [[Triangular orthobicupola]] is constructed by two triangular cupolas along their bases.
* ''Elongated'' indicates a [[prism (geometry)|prism]] is joined to the base of the solid, or between the bases; ''gyroelongated'' indicates an [[antiprism]]. ''Augmented'' indicates another polyhedron, namely a [[pyramid (geometry)|pyramid]] or [[Cupola (geometry)|cupola]], is joined to one or more faces of the solid in question.
*''Diminished'' indicates a pyramid or cupola is removed from one or more faces of the solid in question.
*''[[gyration|Gyrate]]'' indicates a cupola mounted on or featured in the solid in question is rotated such that different edges match up, as in the difference between ortho- and gyrobicupolae.
{{multiple image
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 | footer = Examples of ''para-'' and ''meta-'' can be found in [[parabiaugmented hexagonal prism]] and [[metabiaugmented hexagonal prism]]
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The last three operations—''augmentation'', ''diminution'', and ''gyration''—can be performed multiple times for certain large solids.  ''Bi-'' & ''Tri-'' indicate a double and triple operation respectively. For example, a ''bigyrate'' solid has two rotated cupolae, and a ''tridiminished'' solid has three removed pyramids or cupolae. In certain large solids, a distinction is made between solids where altered faces are parallel and solids where altered faces are oblique. ''Para-'' indicates the former, that the solid in question has altered parallel faces, and ''meta-'' the latter, altered oblique faces. For example, a ''parabiaugmented'' solid has had two parallel faces augmented, and a ''metabigyrate'' solid has had two oblique faces gyrated.{{r|berman}}

The last few Johnson solids have names based on certain polygon complexes from which they are assembled. These names are defined by Johnson with the following nomenclature:{{r|berman}}
*A ''lune'' is a complex of two triangles attached to opposite sides of a square.
*''Spheno''- indicates a wedgelike complex formed by two adjacent lunes. ''Dispheno-'' indicates two such complexes.
*''Hebespheno''- indicates a blunt complex of two lunes separated by a third lune.
*''Corona'' is a crownlike complex of eight triangles.
*''Megacorona'' is a larger crownlike complex of twelve triangles.
*The suffix -''cingulum'' indicates a belt of twelve triangles.

The enumeration of Johnson solids may be denoted as <math> J_n </math>, where <math> n </math> denoted the list's enumeration (an example is <math> J_1 </math> denoted the first Johnson solid, the equilateral square pyramid).{{r|uehara}} The following is the list of ninety-two Johnson solids, with the enumeration followed according to the list of {{harvtxt|Johnson|1966}}:
{{columns-list|colwidth=25em|
# [[Equilateral square pyramid]]
# [[Pentagonal pyramid]]
# [[Triangular cupola]]
# [[Square cupola]]
# [[Pentagonal cupola]]
# [[Pentagonal rotunda]]
# [[Elongated triangular pyramid]]
# [[Elongated square pyramid]]
# [[Elongated pentagonal pyramid]]
# [[Gyroelongated square pyramid]]
# [[Gyroelongated pentagonal pyramid]]
# [[Triangular bipyramid]]
# [[Pentagonal bipyramid]]
# [[Elongated triangular bipyramid]]
# [[Elongated square bipyramid]]
# [[Elongated pentagonal bipyramid]]
# [[Gyroelongated square bipyramid]]
# [[Elongated triangular cupola]]
# [[Elongated square cupola]]
# [[Elongated pentagonal cupola]]
# [[Elongated pentagonal rotunda]]
# [[Gyroelongated triangular cupola]]
# [[Gyroelongated square cupola]]
# [[Gyroelongated pentagonal cupola]]
# [[Gyroelongated pentagonal rotunda]]
# [[Gyrobifastigium]]
# [[Triangular orthobicupola]]
# [[Square orthobicupola]]
# [[Square gyrobicupola]]
# [[Pentagonal orthobicupola]]
# [[Pentagonal gyrobicupola]]
# [[Pentagonal orthocupolarotunda]]
# [[Pentagonal gyrocupolarotunda]]
# [[Pentagonal orthobirotunda]]
# [[Elongated triangular orthobicupola]]
# [[Elongated triangular gyrobicupola]]
# [[Elongated square gyrobicupola]]
# [[Elongated pentagonal orthobicupola]]
# [[Elongated pentagonal gyrobicupola]]
# [[Elongated pentagonal orthocupolarotunda]]
# [[Elongated pentagonal gyrocupolarotunda]]
# [[Elongated pentagonal orthobirotunda]]
# [[Elongated pentagonal gyrobirotunda]]
# [[Gyroelongated triangular bicupola]]
# [[Gyroelongated square bicupola]]
# [[Gyroelongated pentagonal bicupola]]
# [[Gyroelongated pentagonal cupolarotunda]]
# [[Gyroelongated pentagonal birotunda]]
# [[Augmented triangular prism]]
# [[Biaugmented triangular prism]]
# [[Triaugmented triangular prism]]
# [[Augmented pentagonal prism]]
# [[Biaugmented pentagonal prism]]
# [[Augmented hexagonal prism]]
# [[Parabiaugmented hexagonal prism]]
# [[Metabiaugmented hexagonal prism]]
# [[Triaugmented hexagonal prism]]
# [[Augmented dodecahedron]]
# [[Parabiaugmented dodecahedron]]
# [[Metabiaugmented dodecahedron]]
# [[Triaugmented dodecahedron]]
# [[Metabidiminished icosahedron]]
# [[Tridiminished icosahedron]]
# [[Augmented tridiminished icosahedron]]
# [[Augmented truncated tetrahedron]]
# [[Augmented truncated cube]]
# [[Biaugmented truncated cube]]
# [[Augmented truncated dodecahedron]]
# [[Parabiaugmented truncated dodecahedron]]
# [[Metabiaugmented truncated dodecahedron]]
# [[Triaugmented truncated dodecahedron]]
# [[Gyrate rhombicosidodecahedron]]
# [[Parabigyrate rhombicosidodecahedron]]
# [[Metabigyrate rhombicosidodecahedron]]
# [[Trigyrate rhombicosidodecahedron]]
# [[Diminished rhombicosidodecahedron]]
# [[Paragyrate diminished rhombicosidodecahedron]]
# [[Metagyrate diminished rhombicosidodecahedron]]
# [[Bigyrate diminished rhombicosidodecahedron]]
# [[Parabidiminished rhombicosidodecahedron]]
# [[Metabidiminished rhombicosidodecahedron]]
# [[Gyrate bidiminished rhombicosidodecahedron]]
# [[Tridiminished rhombicosidodecahedron]]
# [[Snub disphenoid]]
# [[Snub square antiprism]]
# [[Sphenocorona]]
# [[Augmented sphenocorona]]
# [[Sphenomegacorona]]
# [[Hebesphenomegacorona]]
# [[Disphenocingulum]]
# [[Bilunabirotunda]]
# [[Triangular hebesphenorotunda]]
}}

Some of the Johnson solids may be categorized as [[elementary polyhedra]]. This means the polyhedron cannot be separated by a plane to create two small convex polyhedra with regular faces; examples of Johnson solids are the first six Johnson solids—[[square pyramid]], [[pentagonal pyramid]], [[triangular cupola]], [[square cupola]], [[pentagonal cupola]], and [[pentagonal rotunda]]—[[tridiminished icosahedron]], [[parabidiminished rhombicosidodecahedron]], [[tridiminished rhombicosidodecahedron]], [[snub disphenoid]], [[snub square antiprism]], [[sphenocorona]], [[sphenomegacorona]], [[hebesphenomegacorona]], [[disphenocingulum]], [[bilunabirotunda]], and [[triangular hebesphenorotunda]].{{r|johnson|hartshorne}} The other Johnson solids are [[composite polyhedron]] because they are constructed by attaching some elementary polyhedra.{{r|timofeenko-2010}}