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- Isohedral_figure abstract "In geometry, a polytope (a polyhedron or a polychoron for example) or tiling 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 wikiPageRevisionID "587979170".
- Isohedral_figure anchor "Isotope".
- Isohedral_figure hasPhotoCollection Isohedral_figure.
- Isohedral_figure title "Isohedral tiling".
- Isohedral_figure title "Isohedron".
- Isohedral_figure title "Isotope".
- Isohedral_figure urlname "IsohedralTiling".
- Isohedral_figure urlname "Isohedron".
- Isohedral_figure subject Category:Polychora.
- Isohedral_figure subject Category:Polyhedra.
- Isohedral_figure subject Category:Polytopes.
- Isohedral_figure comment "In geometry, a polytope (a polyhedron or a polychoron for example) or tiling 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 label "Poliedro de caras uniformes".
- Isohedral_figure sameAs Poliedro_de_caras_uniformes.
- Isohedral_figure sameAs 면추이.
- Isohedral_figure sameAs m.0f_hw2.
- Isohedral_figure sameAs Q3847067.
- Isohedral_figure sameAs Q3847067.
- Isohedral_figure wasDerivedFrom Isohedral_figure?oldid=587979170.
- Isohedral_figure depiction Hexagonale_bipiramide.png.
- Isohedral_figure isPrimaryTopicOf Isohedral_figure.
