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- Snub_disphenoid abstract "In geometry, the snub disphenoid or dodecadeltahedron is a dodecahedron and one of the Johnson solids (J84). It is a three-dimensional solid that has only equilateral triangles as faces, and is therefore a deltahedron. It is not a regular polyhedron because some vertices have four faces and others have five. It is one of the elementary Johnson solids that do not arise from "cut and paste" manipulations of the Platonic and Archimedean solids.A Johnson solid is one of 92 strictly convex polyhedra that have regular faces but are not uniform (that is, they are not Platonic solids, Archimedean solids, prisms or antiprisms). They were named by Norman Johnson, who first listed these polyhedra in 1966.The snub disphenoid is constructed, as its name suggests, as a snub disphenoid, and represented as ss{2,4}, with s{2,4} as a digonal antiprism, being the first of an infinite set of snub antiprisms. This construction also produces two degenerate digonal faces from the digonal antiprism.It can also be seen as the 8 triangular faces of the square antiprism with the two squares replaced by pairs of triangles.It was called a Siamese dodecahedron in the paper by Freudenthal and van der Waerden which first described it in 1947 in the set of eight convex deltahedra.The snub disphenoid is 4-connected, meaning that it takes the removal of four vertices to disconnect the remaining vertices. It is one of only four 4-connected simplicial well-covered polyhedra, meaning that all of the maximal independent sets of its vertices have the same size. The other three polyhedra with this property are the regular octahedron, the pentagonal bipyramid, and an irregular polyhedron with 12 vertices and 20 triangular faces (Finbow et al. 2010).The snub disphenoid has three dihedral angles, approximately 121.7°, 96.2°, 166.4°.".
- Snub_disphenoid thumbnail Snub_disphenoid.png?width=300.
- Snub_disphenoid wikiPageID "1133565".
- Snub_disphenoid wikiPageLength "3520".
- Snub_disphenoid wikiPageOutDegree "36".
- Snub_disphenoid wikiPageRevisionID "653857075".
- Snub_disphenoid wikiPageWikiLink Antiprism.
- Snub_disphenoid wikiPageWikiLink Archimedean_solid.
- Snub_disphenoid wikiPageWikiLink Category:Deltahedra.
- Snub_disphenoid wikiPageWikiLink Category:Johnson_solids.
- Snub_disphenoid wikiPageWikiLink Convex_set.
- Snub_disphenoid wikiPageWikiLink Deltahedron.
- Snub_disphenoid wikiPageWikiLink Digon.
- Snub_disphenoid wikiPageWikiLink Digonal_antiprism.
- Snub_disphenoid wikiPageWikiLink Disphenoid.
- Snub_disphenoid wikiPageWikiLink Dodecahedron.
- Snub_disphenoid wikiPageWikiLink Equilateral_triangle.
- Snub_disphenoid wikiPageWikiLink Face_(geometry).
- Snub_disphenoid wikiPageWikiLink Geometry.
- Snub_disphenoid wikiPageWikiLink Johnson_solid.
- Snub_disphenoid wikiPageWikiLink K-vertex-connected_graph.
- Snub_disphenoid wikiPageWikiLink Maximal_independent_set.
- Snub_disphenoid wikiPageWikiLink Octahedron.
- Snub_disphenoid wikiPageWikiLink Pentagonal_bipyramid.
- Snub_disphenoid wikiPageWikiLink Platonic_solid.
- Snub_disphenoid wikiPageWikiLink Regular_octahedron.
- Snub_disphenoid wikiPageWikiLink Regular_polyhedron.
- Snub_disphenoid wikiPageWikiLink Simon_Stevin_(journal).
- Snub_disphenoid wikiPageWikiLink Simplicial_polytope.
- Snub_disphenoid wikiPageWikiLink Snub_(geometry).
- Snub_disphenoid wikiPageWikiLink Snub_antiprism.
- Snub_disphenoid wikiPageWikiLink Snub_square_antiprism.
- Snub_disphenoid wikiPageWikiLink Square_antiprism.
- Snub_disphenoid wikiPageWikiLink Tetrahedron.
- Snub_disphenoid wikiPageWikiLink Triangle.
- Snub_disphenoid wikiPageWikiLink Tridiminished_rhombicosidodecahedron.
- Snub_disphenoid wikiPageWikiLink Vertex_(geometry).
- Snub_disphenoid wikiPageWikiLink Well-covered_graph.
- Snub_disphenoid wikiPageWikiLink File:Digonal_antiprism.png.
- Snub_disphenoid wikiPageWikiLink File:Snub_digonal_antiprism.png.
- Snub_disphenoid wikiPageWikiLinkText "Snub disphenoid".
- Snub_disphenoid wikiPageWikiLinkText "Snub_disphenoid".
- Snub_disphenoid wikiPageWikiLinkText "dodecadeltahedral".
- Snub_disphenoid wikiPageWikiLinkText "snub disphenoid".
- Snub_disphenoid wikiPageWikiLinkText "ss{2,4}".
- Snub_disphenoid wikiPageWikiLinkText "trigonal dodecahedron".
- Snub_disphenoid dual "-".
- Snub_disphenoid edges "18".
- Snub_disphenoid faces "4".
- Snub_disphenoid hasPhotoCollection Snub_disphenoid.
- Snub_disphenoid net "Johnson_solid_84_net.png".
- Snub_disphenoid properties Convex_set.
- Snub_disphenoid properties Deltahedron.
- Snub_disphenoid symmetry "172800.0".
- Snub_disphenoid title "Johnson solid".
- Snub_disphenoid title "Snub disphenoid".
- Snub_disphenoid type Johnson_solid.
- Snub_disphenoid type "J83 - J84 - J85".
- Snub_disphenoid urlname "JohnsonSolid".
- Snub_disphenoid urlname "SnubDisphenoid".
- Snub_disphenoid vertexConfig "4".
- Snub_disphenoid vertices "8".
- Snub_disphenoid wikiPageUsesTemplate Template:Citation.
- Snub_disphenoid wikiPageUsesTemplate Template:Harv.
- Snub_disphenoid wikiPageUsesTemplate Template:Infobox_polyhedron.
- Snub_disphenoid wikiPageUsesTemplate Template:Johnson_solid.
- Snub_disphenoid wikiPageUsesTemplate Template:Mathworld2.
- Snub_disphenoid wikiPageUsesTemplate Template:Polyhedron-stub.
- Snub_disphenoid wikiPageUsesTemplate Template:Reflist.
- Snub_disphenoid subject Category:Deltahedra.
- Snub_disphenoid subject Category:Johnson_solids.
- Snub_disphenoid hypernym Dodecahedron.
- Snub_disphenoid comment "In geometry, the snub disphenoid or dodecadeltahedron is a dodecahedron and one of the Johnson solids (J84). It is a three-dimensional solid that has only equilateral triangles as faces, and is therefore a deltahedron. It is not a regular polyhedron because some vertices have four faces and others have five.".
- Snub_disphenoid label "Snub disphenoid".
- Snub_disphenoid sameAs Trigondodekaeder.
- Snub_disphenoid sameAs Riproĉa_dukojnosimilaĵo.
- Snub_disphenoid sameAs Biesfenoide_romo.
- Snub_disphenoid sameAs Biesfenoide_kamuts.
- Snub_disphenoid sameAs Disphénoïde_adouci.
- Snub_disphenoid sameAs Disfenoide_camuso.
- Snub_disphenoid sameAs 変形双五角錐.
- Snub_disphenoid sameAs 다듬은_맞붙인_쐐기꼴.
- Snub_disphenoid sameAs Siamese_dodecaëder.
- Snub_disphenoid sameAs m.0494gc.
- Snub_disphenoid sameAs Prirezan_disfenoid.
- Snub_disphenoid sameAs Q124656.
- Snub_disphenoid sameAs Q124656.
- Snub_disphenoid sameAs 變稜雙五角椎.
- Snub_disphenoid wasDerivedFrom Snub_disphenoid?oldid=653857075.
- Snub_disphenoid depiction Snub_disphenoid.png.
- Snub_disphenoid isPrimaryTopicOf Snub_disphenoid.