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- Catalan_solid abstract "In mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid. The Catalan solids are named for the Belgian mathematician, Eugène Catalan, who first described them in 1865.The Catalan solids are all convex. They are face-transitive but not vertex-transitive. This is because the dual Archimedean solids are vertex-transitive and not face-transitive. Note that unlike Platonic solids and Archimedean solids, the faces of Catalan solids are not regular polygons. However, the vertex figures of Catalan solids are regular, and they have constant dihedral angles. Additionally, two of the Catalan solids are edge-transitive: the rhombic dodecahedron and the rhombic triacontahedron. These are the duals of the two quasi-regular Archimedean solids.Just as prisms and antiprisms are generally not considered Archimedean solids, so bipyramids and trapezohedra are generally not considered Catalan solids, despite being face-transitive.Two of the Catalan solids are chiral: the pentagonal icositetrahedron and the pentagonal hexecontahedron, dual to the chiral snub cube and snub dodecahedron. These each come in two enantiomorphs. Not counting the enantiomorphs, bipyramids, and trapezohedra, there are a total of 13 Catalan solids.".
- Catalan_solid thumbnail Rhombic_dodecahedron_v3434.png?width=300.
- Catalan_solid wikiPageExternalLink Catalan.htm.
- Catalan_solid wikiPageExternalLink archimedean-duals-info.html.
- Catalan_solid wikiPageID "564393".
- Catalan_solid wikiPageRevisionID "606561191".
- Catalan_solid anchor "Catalan".
- Catalan_solid hasPhotoCollection Catalan_solid.
- Catalan_solid title "Catalan Solids".
- Catalan_solid title "Catalan".
- Catalan_solid urlname "CatalanSolid".
- Catalan_solid subject Category:Catalan_solids.
- Catalan_solid type CatalanSolids.
- Catalan_solid type Matter100020827.
- Catalan_solid type PhysicalEntity100001930.
- Catalan_solid type Solid115046900.
- Catalan_solid comment "In mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid. The Catalan solids are named for the Belgian mathematician, Eugène Catalan, who first described them in 1865.The Catalan solids are all convex. They are face-transitive but not vertex-transitive. This is because the dual Archimedean solids are vertex-transitive and not face-transitive. Note that unlike Platonic solids and Archimedean solids, the faces of Catalan solids are not regular polygons.".
- Catalan_solid label "Catalan solid".
- Catalan_solid label "Catalan-lichaam".
- Catalan_solid label "Catalanischer Körper".
- Catalan_solid label "Solide de Catalan".
- Catalan_solid label "Solido di Catalan".
- Catalan_solid label "Sólidos de Catalan".
- Catalan_solid label "Sólidos de Catalan".
- Catalan_solid label "Wielościany Catalana".
- Catalan_solid label "カタランの立体".
- Catalan_solid label "卡塔蘭立體".
- Catalan_solid sameAs Catalanischer_Körper.
- Catalan_solid sameAs Sólidos_de_Catalan.
- Catalan_solid sameAs Catalan-en_solido.
- Catalan_solid sameAs Solide_de_Catalan.
- Catalan_solid sameAs Solido_di_Catalan.
- Catalan_solid sameAs カタランの立体.
- Catalan_solid sameAs 카탈란의_다면체.
- Catalan_solid sameAs Catalan-lichaam.
- Catalan_solid sameAs Wielościany_Catalana.
- Catalan_solid sameAs Sólidos_de_Catalan.
- Catalan_solid sameAs m.02qh_2.
- Catalan_solid sameAs Q258921.
- Catalan_solid sameAs Q258921.
- Catalan_solid sameAs Catalan_solid.
- Catalan_solid wasDerivedFrom Catalan_solid?oldid=606561191.
- Catalan_solid depiction Rhombic_dodecahedron_v3434.png.
- Catalan_solid isPrimaryTopicOf Catalan_solid.