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- Johnson_solid abstract "In geometry, a Johnson solid is a strictly convex polyhedron, each face of which is a regular polygon, but which is not uniform, i.e., not a Platonic solid, Archimedean solid, prism or antiprism. 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.
- Johnson_solid wikiPageExternalLink crf.
- Johnson_solid wikiPageExternalLink st6-11-a7-ocr.pdf.
- Johnson_solid wikiPageExternalLink CRF_polychora_discovery_project.
- Johnson_solid wikiPageExternalLink johnson-info.html.
- Johnson_solid wikiPageExternalLink www.korthalsaltes.com.
- Johnson_solid wikiPageExternalLink johnson.html.
- Johnson_solid wikiPageExternalLink johnsonp.htm.
- Johnson_solid wikiPageID "16034".
- Johnson_solid wikiPageRevisionID "605481867".
- Johnson_solid hasPhotoCollection Johnson_solid.
- Johnson_solid title "Johnson Solid".
- Johnson_solid urlname "JohnsonSolid".
- Johnson_solid subject Category:Johnson_solids.
- Johnson_solid type JohnsonSolids.
- Johnson_solid type Matter100020827.
- Johnson_solid type PhysicalEntity100001930.
- Johnson_solid type Solid115046900.
- Johnson_solid comment "In geometry, a Johnson solid is a strictly convex polyhedron, each face of which is a regular polygon, but which is not uniform, i.e., not a Platonic solid, Archimedean solid, prism or antiprism. There is no requirement that each face must be the same polygon, or that the same polygons join around each vertex.".
- Johnson_solid label "Johnson solid".
- Johnson_solid label "Johnson-Körper".
- Johnson_solid label "Johnson-lichaam".
- Johnson_solid label "Solide de Johnson".
- Johnson_solid label "Solido di Johnson".
- Johnson_solid label "Sólido de Johnson".
- Johnson_solid label "Sólidos de Johnson".
- Johnson_solid label "Многогранник Джонсона".
- Johnson_solid label "ジョンソンの立体".
- Johnson_solid label "约翰逊多面体".
- Johnson_solid sameAs Johnson-Körper.
- Johnson_solid sameAs Sólido_de_Johnson.
- Johnson_solid sameAs Johnson-en_solido.
- Johnson_solid sameAs Solide_de_Johnson.
- Johnson_solid sameAs Solido_di_Johnson.
- Johnson_solid sameAs ジョンソンの立体.
- Johnson_solid sameAs 존슨의_다면체.
- Johnson_solid sameAs Johnson-lichaam.
- Johnson_solid sameAs Sólidos_de_Johnson.
- Johnson_solid sameAs m.042zp.
- Johnson_solid sameAs Q1059659.
- Johnson_solid sameAs Q1059659.
- Johnson_solid sameAs Johnson_solid.
- Johnson_solid wasDerivedFrom Johnson_solid?oldid=605481867.
- Johnson_solid depiction Elongated_square_gyrobicupola.png.
- Johnson_solid isPrimaryTopicOf Johnson_solid.
