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- Rhombic_triacontahedron abstract "In geometry, the rhombic triacontahedron is a convex polyhedron with 30 rhombic faces. It has 60 edges and 32 vertices of two types. It is a Catalan solid, and the dual polyhedron of the icosidodecahedron. It is a zonohedron.The ratio of the long diagonal to the short diagonal of each face is exactly equal to the golden ratio, φ, so that the acute angles on each face measure 2 tan−1(1/φ) = tan−1(2), or approximately 63.43°. A rhombus so obtained is called a golden rhombus.Being the dual of an Archimedean solid, the rhombic triacontahedron is face-transitive, meaning the symmetry group of the solid acts transitively on the set of faces. This means that for any two faces, A and B, there is a rotation or reflection of the solid that leaves it occupying the same region of space while moving face A to face B.The rhombic triacontahedron is somewhat special in being one of the nine edge-transitive convex polyhedra, the others being the five Platonic solids, the cuboctahedron, the icosidodecahedron, and the rhombic dodecahedron.The rhombic triacontahedron is also interesting in that it has all the vertices of eight tetrahedrons, four hexahedrons, or an icosahedron and a dodecahedron.".
- Rhombic_triacontahedron thumbnail GoldenRhombus.svg?width=300.
- Rhombic_triacontahedron wikiPageExternalLink rtc.
- Rhombic_triacontahedron wikiPageExternalLink 120RhombicTriacontahedra.
- Rhombic_triacontahedron wikiPageExternalLink 12RhombicTriacontahedra.
- Rhombic_triacontahedron wikiPageExternalLink 3012RhombicTriacontahedra.
- Rhombic_triacontahedron wikiPageExternalLink rhombic_triacontahedron.
- Rhombic_triacontahedron wikiPageExternalLink product.asp?ProdCode=2205.
- Rhombic_triacontahedron wikiPageExternalLink vp.html.
- Rhombic_triacontahedron wikiPageExternalLink E7P30WYB6IEVYDYWFG.
- Rhombic_triacontahedron wikiPageExternalLink www.iqlight.com.
- Rhombic_triacontahedron wikiPageExternalLink triacontahedron-box.html.
- Rhombic_triacontahedron wikiPageExternalLink b0089.jpg.
- Rhombic_triacontahedron wikiPageExternalLink www.vortexmaps.com.
- Rhombic_triacontahedron wikiPageID "665025".
- Rhombic_triacontahedron wikiPageRevisionID "585741777".
- Rhombic_triacontahedron hasPhotoCollection Rhombic_triacontahedron.
- Rhombic_triacontahedron title "Catalan solid".
- Rhombic_triacontahedron title "Rhombic triacontahedron".
- Rhombic_triacontahedron urlname "CatalanSolid".
- Rhombic_triacontahedron urlname "RhombicTriacontahedron".
- Rhombic_triacontahedron subject Category:Catalan_solids.
- Rhombic_triacontahedron subject Category:Quasiregular_polyhedra.
- Rhombic_triacontahedron subject Category:Zonohedra.
- Rhombic_triacontahedron type CatalanSolids.
- Rhombic_triacontahedron type Matter100020827.
- Rhombic_triacontahedron type PhysicalEntity100001930.
- Rhombic_triacontahedron type Solid115046900.
- Rhombic_triacontahedron comment "In geometry, the rhombic triacontahedron is a convex polyhedron with 30 rhombic faces. It has 60 edges and 32 vertices of two types. It is a Catalan solid, and the dual polyhedron of the icosidodecahedron. It is a zonohedron.The ratio of the long diagonal to the short diagonal of each face is exactly equal to the golden ratio, φ, so that the acute angles on each face measure 2 tan−1(1/φ) = tan−1(2), or approximately 63.43°.".
- Rhombic_triacontahedron label "Rhombentriakontaeder".
- Rhombic_triacontahedron label "Rhombic triacontahedron".
- Rhombic_triacontahedron label "Romboëdrisch triacontaëder".
- Rhombic_triacontahedron label "Triacontaedro rombico".
- Rhombic_triacontahedron label "Triacontaedro rómbico".
- Rhombic_triacontahedron label "Triacontaedro rômbico".
- Rhombic_triacontahedron label "Triacontaèdre rhombique".
- Rhombic_triacontahedron label "Trzydziestościan rombowy".
- Rhombic_triacontahedron label "Ромботриаконтаэдр".
- Rhombic_triacontahedron label "菱形三十面体".
- Rhombic_triacontahedron label "菱形三十面體".
- Rhombic_triacontahedron sameAs Rhombentriakontaeder.
- Rhombic_triacontahedron sameAs Triacontaedro_rómbico.
- Rhombic_triacontahedron sameAs Triakontaedro_erronbiko.
- Rhombic_triacontahedron sameAs Triacontaèdre_rhombique.
- Rhombic_triacontahedron sameAs Triacontaedro_rombico.
- Rhombic_triacontahedron sameAs 菱形三十面体.
- Rhombic_triacontahedron sameAs 마름모삼십면체.
- Rhombic_triacontahedron sameAs Romboëdrisch_triacontaëder.
- Rhombic_triacontahedron sameAs Trzydziestościan_rombowy.
- Rhombic_triacontahedron sameAs Triacontaedro_rômbico.
- Rhombic_triacontahedron sameAs m.030_x9.
- Rhombic_triacontahedron sameAs Q1141696.
- Rhombic_triacontahedron sameAs Q1141696.
- Rhombic_triacontahedron sameAs Rhombic_triacontahedron.
- Rhombic_triacontahedron wasDerivedFrom Rhombic_triacontahedron?oldid=585741777.
- Rhombic_triacontahedron depiction GoldenRhombus.svg.
- Rhombic_triacontahedron isPrimaryTopicOf Rhombic_triacontahedron.
