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- Isohedral_figure abstract "In geometry, a polytope of dimension 3 (a polyhedron) or higher is isohedral or face-transitive when all its faces are the same. More specifically, all faces must be not merely congruent but must be transitive, i.e. must lie within the same symmetry orbit. In other words, for any faces A and B, there must be a symmetry of the entire solid by rotations and reflections that maps A onto B. For this reason, convex isohedral polyhedra are the shapes that will make fair dice.Isohedral polyhedra are called isohedra. They can be described by their face configuration. A form that is isohedral and has regular vertices is also edge-transitive (isotoxal) and is said to be a quasiregular dual: some theorists regard these figures as truly quasiregular because they share the same symmetries, but this is not generally accepted.A polyhedron which is isohedral has a dual polyhedron that is vertex-transitive (isogonal). The Catalan solids, the bipyramids and the trapezohedra are all isohedral. They are the duals of the isogonal Archimedean solids, prisms and antiprisms, respectively. The Platonic solids, which are either self-dual or dual with another Platonic solid, are vertex, edge, and face-transitive (isogonal, isotoxal, and isohedral). A polyhedron which is isohedral and isogonal is said to be noble.".
- Isohedral_figure thumbnail Hexagonale_bipiramide.png?width=300.
- Isohedral_figure wikiPageID "6286120".
- Isohedral_figure wikiPageLength "6445".
- Isohedral_figure wikiPageOutDegree "64".
- Isohedral_figure wikiPageRevisionID "686149742".
- Isohedral_figure wikiPageWikiLink Anisohedral_tiling.
- Isohedral_figure wikiPageWikiLink Antiprism.
- Isohedral_figure wikiPageWikiLink Archimedean_solid.
- Isohedral_figure wikiPageWikiLink Bipyramid.
- Isohedral_figure wikiPageWikiLink Cairo_pentagonal_tiling.
- Isohedral_figure wikiPageWikiLink Catalan_solid.
- Isohedral_figure wikiPageWikiLink Category:Polychora.
- Isohedral_figure wikiPageWikiLink Category:Polyhedra.
- Isohedral_figure wikiPageWikiLink Category:Polytopes.
- Isohedral_figure wikiPageWikiLink Congruence_(geometry).
- Isohedral_figure wikiPageWikiLink Deltoidal_icositetrahedron.
- Isohedral_figure wikiPageWikiLink Dice.
- Isohedral_figure wikiPageWikiLink Dual_polyhedron.
- Isohedral_figure wikiPageWikiLink Elongated_square_gyrobicupola.
- Isohedral_figure wikiPageWikiLink Euclidean_tilings_by_convex_regular_polygons.
- Isohedral_figure wikiPageWikiLink Face_(geometry).
- Isohedral_figure wikiPageWikiLink Facet_(geometry).
- Isohedral_figure wikiPageWikiLink Geometry.
- Isohedral_figure wikiPageWikiLink Group_action.
- Isohedral_figure wikiPageWikiLink Herringbone_pattern.
- Isohedral_figure wikiPageWikiLink Hexagonal_bipyramid.
- Isohedral_figure wikiPageWikiLink Honeycomb_(geometry).
- Isohedral_figure wikiPageWikiLink Icosahedron.
- Isohedral_figure wikiPageWikiLink Isogonal_figure.
- Isohedral_figure wikiPageWikiLink Isohedron.
- Isohedral_figure wikiPageWikiLink Isotoxal_figure.
- Isohedral_figure wikiPageWikiLink Noble_polyhedron.
- Isohedral_figure wikiPageWikiLink Pentagonal_tiling.
- Isohedral_figure wikiPageWikiLink Platonic_solid.
- Isohedral_figure wikiPageWikiLink Polyhedron.
- Isohedral_figure wikiPageWikiLink Polytope.
- Isohedral_figure wikiPageWikiLink Prism_(geometry).
- Isohedral_figure wikiPageWikiLink Pseudo-deltoidal_icositetrahedron.
- Isohedral_figure wikiPageWikiLink Pythagorean_tiling.
- Isohedral_figure wikiPageWikiLink Quasiregular_polyhedron.
- Isohedral_figure wikiPageWikiLink Regular_polyhedron.
- Isohedral_figure wikiPageWikiLink Rhombic_dodecahedral_honeycomb.
- Isohedral_figure wikiPageWikiLink Rhombicuboctahedron.
- Isohedral_figure wikiPageWikiLink Tessellation.
- Isohedral_figure wikiPageWikiLink Trapezohedron.
- Isohedral_figure wikiPageWikiLink Uniform_polytope.
- Isohedral_figure wikiPageWikiLink Vertex_configuration.
- Isohedral_figure wikiPageWikiLink File:3-uniform_n57.png.
- Isohedral_figure wikiPageWikiLink File:Deltoidal_icositetrahedron_gyro.png.
- Isohedral_figure wikiPageWikiLink File:Distorted_truncated_square_tiling.png.
- Isohedral_figure wikiPageWikiLink File:Herringbone_bond.svg.
- Isohedral_figure wikiPageWikiLink File:Hexagonale_bipiramide.png.
- Isohedral_figure wikiPageWikiLink File:Johnson_solid_37.png.
- Isohedral_figure wikiPageWikiLink File:P5-type10.png.
- Isohedral_figure wikiPageWikiLink File:Pseudo-strombic_icositetrahedron.png.
- Isohedral_figure wikiPageWikiLink File:Rhombic_dodecahedra.png.
- Isohedral_figure wikiPageWikiLink File:Small_rhombicuboctahedron.png.
- Isohedral_figure wikiPageWikiLink File:Tiling_Dual_Semiregular_V3-3-4-3-4_Cairo_Pentagonal.svg.
- Isohedral_figure wikiPageWikiLinkText "Isohedral faces".
- Isohedral_figure wikiPageWikiLinkText "Isohedral figure".
- Isohedral_figure wikiPageWikiLinkText "Isohedral figure#Related terms".
- Isohedral_figure wikiPageWikiLinkText "Isohedral_figure#Related terms".
- Isohedral_figure wikiPageWikiLinkText "Isohedral_figure#Related_terms".
- Isohedral_figure wikiPageWikiLinkText "cell-transitive".
- Isohedral_figure wikiPageWikiLinkText "facet-transitive".
- Isohedral_figure wikiPageWikiLinkText "isohedra".
- Isohedral_figure wikiPageWikiLinkText "isohedral figure#k-isohedral figure".
- Isohedral_figure wikiPageWikiLinkText "isohedral".
- Isohedral_figure anchor "Isotope".
- Isohedral_figure title "Isohedral tiling".
- Isohedral_figure title "Isohedron".
- Isohedral_figure title "Isotope".
- Isohedral_figure urlname "IsohedralTiling".
- Isohedral_figure urlname "Isohedron".
- Isohedral_figure wikiPageUsesTemplate Template:For.
- Isohedral_figure wikiPageUsesTemplate Template:GlossaryForHyperspace.
- Isohedral_figure wikiPageUsesTemplate Template:Hatnote.
- Isohedral_figure wikiPageUsesTemplate Template:MathWorld.
- Isohedral_figure wikiPageUsesTemplate Template:Reflist.
- Isohedral_figure wikiPageUsesTemplate Template:Tessellation.
- Isohedral_figure subject Category:Polychora.
- Isohedral_figure subject Category:Polyhedra.
- Isohedral_figure subject Category:Polytopes.
- Isohedral_figure hypernym Isohedral.
- Isohedral_figure type Polytope.
- Isohedral_figure type Space.
- Isohedral_figure comment "In geometry, a polytope of dimension 3 (a polyhedron) or higher is isohedral or face-transitive when all its faces are the same. More specifically, all faces must be not merely congruent but must be transitive, i.e. must lie within the same symmetry orbit. In other words, for any faces A and B, there must be a symmetry of the entire solid by rotations and reflections that maps A onto B.".
- Isohedral_figure label "Isohedral figure".
- Isohedral_figure sameAs Q3847067.
- Isohedral_figure sameAs Edro-transitiva.
- Isohedral_figure sameAs Poliedro_de_caras_uniformes.
- Isohedral_figure sameAs m.0f_hw2.
- Isohedral_figure sameAs Izoederska_oblika.
- Isohedral_figure sameAs Q3847067.
- Isohedral_figure wasDerivedFrom Isohedral_figure?oldid=686149742.
- Isohedral_figure depiction Hexagonale_bipiramide.png.
- Isohedral_figure isPrimaryTopicOf Isohedral_figure.