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- Johnson_solid abstract "In geometry, a Johnson solid is a strictly convex polyhedron, which is not uniform (i.e., not a Platonic solid, Archimedean solid, prism or antiprism), and 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 (J1); it has 1 square face and 4 triangular faces.As in any strictly convex solid, at least three faces meet at every vertex, and the total of their angles is less than 360 degrees. Since a regular polygon has angles at least 60 degrees, it follows that at most five faces meet at any vertex. The pentagonal pyramid (J2) is an example that actually has a degree-5 vertex.Although there is no obvious restriction that any given regular polygon cannot be a face of a Johnson solid, it turns out that the faces of Johnson solids always have 3, 4, 5, 6, 8, or 10 sides.In 1966, Norman Johnson published a list which included all 92 solids, and gave them their names and numbers. He did not prove that there were only 92, but he did conjecture that there were no others. Victor Zalgaller in 1969 proved that Johnson's list was complete.Of the Johnson solids, the elongated square gyrobicupola (J37), also called the pseudorhombicuboctahedron, is unique in being locally vertex-uniform: there are 4 faces at each vertex, and their arrangement is always the same: 3 squares and 1 triangle. However, it is not vertex-transitive, as it has different isometry at different vertices, making it a Johnson solid rather than an Archimedean solid.".
- Johnson_solid thumbnail Elongated_square_gyrobicupola.png?width=300.
- Johnson_solid wikiPageExternalLink johnson-info.html.
- Johnson_solid wikiPageExternalLink johnson.
- Johnson_solid wikiPageExternalLink crf.
- Johnson_solid wikiPageExternalLink st6-11-a7-ocr.pdf.
- Johnson_solid wikiPageExternalLink CRF_polychora_discovery_project.
- Johnson_solid wikiPageExternalLink www.korthalsaltes.com.
- Johnson_solid wikiPageExternalLink johnson.html.
- Johnson_solid wikiPageExternalLink johnsonp.htm.
- Johnson_solid wikiPageID "16034".
- Johnson_solid wikiPageLength "42177".
- Johnson_solid wikiPageOutDegree "732".
- Johnson_solid wikiPageRevisionID "703186495".
- Johnson_solid wikiPageWikiLink Antiprism.
- Johnson_solid wikiPageWikiLink Archimedean_solid.
- Johnson_solid wikiPageWikiLink Augmented_dodecahedron.
- Johnson_solid wikiPageWikiLink Augmented_hexagonal_prism.
- Johnson_solid wikiPageWikiLink Augmented_pentagonal_prism.
- Johnson_solid wikiPageWikiLink Augmented_sphenocorona.
- Johnson_solid wikiPageWikiLink Augmented_triangular_prism.
- Johnson_solid wikiPageWikiLink Augmented_tridiminished_icosahedron.
- Johnson_solid wikiPageWikiLink Augmented_truncated_cube.
- Johnson_solid wikiPageWikiLink Augmented_truncated_dodecahedron.
- Johnson_solid wikiPageWikiLink Augmented_truncated_tetrahedron.
- Johnson_solid wikiPageWikiLink Biaugmented_pentagonal_prism.
- Johnson_solid wikiPageWikiLink Biaugmented_triangular_prism.
- Johnson_solid wikiPageWikiLink Biaugmented_truncated_cube.
- Johnson_solid wikiPageWikiLink Bicupola_(geometry).
- Johnson_solid wikiPageWikiLink Bigyrate_diminished_rhombicosidodecahedron.
- Johnson_solid wikiPageWikiLink Bilunabirotunda.
- Johnson_solid wikiPageWikiLink Bipyramid.
- Johnson_solid wikiPageWikiLink Catalan_solid.
- Johnson_solid wikiPageWikiLink Category:Johnson_solids.
- Johnson_solid wikiPageWikiLink Convex_polytope.
- Johnson_solid wikiPageWikiLink Cube.
- Johnson_solid wikiPageWikiLink Cuboctahedron.
- Johnson_solid wikiPageWikiLink Cuboid.
- Johnson_solid wikiPageWikiLink Cupola_(geometry).
- Johnson_solid wikiPageWikiLink Decagonal_antiprism.
- Johnson_solid wikiPageWikiLink Decagonal_prism.
- Johnson_solid wikiPageWikiLink Deltahedron.
- Johnson_solid wikiPageWikiLink Diminished_rhombicosidodecahedron.
- Johnson_solid wikiPageWikiLink Disphenocingulum.
- Johnson_solid wikiPageWikiLink Dodecahedron.
- Johnson_solid wikiPageWikiLink Elongated_bicupola.
- Johnson_solid wikiPageWikiLink Elongated_bipyramid.
- Johnson_solid wikiPageWikiLink Elongated_cupola.
- Johnson_solid wikiPageWikiLink Elongated_digonal_cupola.
- Johnson_solid wikiPageWikiLink Elongated_digonal_gyrobicupola.
- Johnson_solid wikiPageWikiLink Elongated_digonal_orthobicupola.
- Johnson_solid wikiPageWikiLink Elongated_pentagonal_bipyramid.
- Johnson_solid wikiPageWikiLink Elongated_pentagonal_cupola.
- Johnson_solid wikiPageWikiLink Elongated_pentagonal_gyrobicupola.
- Johnson_solid wikiPageWikiLink Elongated_pentagonal_gyrobirotunda.
- Johnson_solid wikiPageWikiLink Elongated_pentagonal_gyrocupolarotunda.
- Johnson_solid wikiPageWikiLink Elongated_pentagonal_orthobicupola.
- Johnson_solid wikiPageWikiLink Elongated_pentagonal_orthobirotunda.
- Johnson_solid wikiPageWikiLink Elongated_pentagonal_orthocupolarotunda.
- Johnson_solid wikiPageWikiLink Elongated_pentagonal_pyramid.
- Johnson_solid wikiPageWikiLink Elongated_pentagonal_rotunda.
- Johnson_solid wikiPageWikiLink Elongated_pyramid.
- Johnson_solid wikiPageWikiLink Elongated_square_bipyramid.
- Johnson_solid wikiPageWikiLink Elongated_square_cupola.
- Johnson_solid wikiPageWikiLink Elongated_square_gyrobicupola.
- Johnson_solid wikiPageWikiLink Elongated_square_pyramid.
- Johnson_solid wikiPageWikiLink Elongated_triangular_bipyramid.
- Johnson_solid wikiPageWikiLink Elongated_triangular_cupola.
- Johnson_solid wikiPageWikiLink Elongated_triangular_gyrobicupola.
- Johnson_solid wikiPageWikiLink Elongated_triangular_orthobicupola.
- Johnson_solid wikiPageWikiLink Elongated_triangular_pyramid.
- Johnson_solid wikiPageWikiLink Equilateral_triangle.
- Johnson_solid wikiPageWikiLink Geometry.
- Johnson_solid wikiPageWikiLink Gyrate_bidiminished_rhombicosidodecahedron.
- Johnson_solid wikiPageWikiLink Gyrate_rhombicosidodecahedron.
- Johnson_solid wikiPageWikiLink Gyration.
- Johnson_solid wikiPageWikiLink Gyrobifastigium.
- Johnson_solid wikiPageWikiLink Gyroelongated_bicupola.
- Johnson_solid wikiPageWikiLink Gyroelongated_bipyramid.
- Johnson_solid wikiPageWikiLink Gyroelongated_cupola.
- Johnson_solid wikiPageWikiLink Gyroelongated_digonal_bicupola.
- Johnson_solid wikiPageWikiLink Gyroelongated_digonal_cupola.
- Johnson_solid wikiPageWikiLink Gyroelongated_pentagonal_bicupola.
- Johnson_solid wikiPageWikiLink Gyroelongated_pentagonal_birotunda.
- Johnson_solid wikiPageWikiLink Gyroelongated_pentagonal_cupola.
- Johnson_solid wikiPageWikiLink Gyroelongated_pentagonal_cupolarotunda.
- Johnson_solid wikiPageWikiLink Gyroelongated_pentagonal_pyramid.
- Johnson_solid wikiPageWikiLink Gyroelongated_pentagonal_rotunda.
- Johnson_solid wikiPageWikiLink Gyroelongated_pyramid.
- Johnson_solid wikiPageWikiLink Gyroelongated_square_bicupola.
- Johnson_solid wikiPageWikiLink Gyroelongated_square_bipyramid.
- Johnson_solid wikiPageWikiLink Gyroelongated_square_cupola.
- Johnson_solid wikiPageWikiLink Gyroelongated_square_pyramid.
- Johnson_solid wikiPageWikiLink Gyroelongated_triangular_bicupola.
- Johnson_solid wikiPageWikiLink Gyroelongated_triangular_cupola.
- Johnson_solid wikiPageWikiLink Hebesphenomegacorona.
- Johnson_solid wikiPageWikiLink Hexagonal_antiprism.
- Johnson_solid wikiPageWikiLink Hexagonal_prism.
- Johnson_solid wikiPageWikiLink Icosahedron.
- Johnson_solid wikiPageWikiLink Icosidodecahedron.