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- Archimedean_solid abstract "In geometry, an Archimedean solid is a highly symmetric, semi-regular convex polyhedron composed of two or more types of regular polygons meeting in identical vertices. They are distinct from the Platonic solids, which are composed of only one type of polygon meeting in identical vertices, and from the Johnson solids, whose regular polygonal faces do not meet in identical vertices.\"Identical vertices\" are usually taken to mean that for any two vertices, there must be an isometry of the entire solid that takes one vertex to the other. Sometimes it is instead only required that the faces that meet at one vertex are related isometrically to the faces that meet at the other. This difference in definitions controls whether the elongated square gyrobicupola (pseudo-rhombicuboctahedron) is considered an Archimedean solid or a Johnson solid: it is the unique convex polyhedron that has regular polygons meeting in the same way at each vertex, but that does not have a global symmetry taking every vertex to every other vertex. Based on its existence, Branko Grünbaum (2009) has suggested a terminological distinction in which an Archimedean solid is defined as having the same vertex figure at each vertex (including the elongated square gyrobicupola) while a uniform polyhedron is defined as having each vertex symmetric to each other vertex (excluding the gyrobicupola).Prisms and antiprisms, whose symmetry groups are the dihedral groups, are generally not considered to be Archimedean solids, despite meeting the above definition. With this restriction, there are only finitely many Archimedean solids. All but the elongated square gyrobicupola can be made via Wythoff constructions from the Platonic solids with tetrahedral, octahedral and icosahedral symmetry.".
- Archimedean_solid thumbnail Uniform_polyhedron-53-t012.png?width=300.
- Archimedean_solid wikiPageExternalLink ArchimedeanSolids.
- Archimedean_solid wikiPageExternalLink Convex.htm.
- Archimedean_solid wikiPageExternalLink solids.html.
- Archimedean_solid wikiPageExternalLink intro.html.
- Archimedean_solid wikiPageExternalLink vp.html.
- Archimedean_solid wikiPageExternalLink cuadros.php?type=a.
- Archimedean_solid wikiPageExternalLink unipoly.
- Archimedean_solid wikiPageExternalLink www.polyedergarten.de.
- Archimedean_solid wikiPageExternalLink Archimedean.php.
- Archimedean_solid wikiPageExternalLink Stella.php.
- Archimedean_solid wikiPageID "1847".
- Archimedean_solid wikiPageLength "19561".
- Archimedean_solid wikiPageOutDegree "229".
- Archimedean_solid wikiPageRevisionID "707753902".
- Archimedean_solid wikiPageWikiLink Angular_defect.
- Archimedean_solid wikiPageWikiLink Antiprism.
- Archimedean_solid wikiPageWikiLink Aperiodic_tiling.
- Archimedean_solid wikiPageWikiLink Archimedean_graph.
- Archimedean_solid wikiPageWikiLink Archimedes.
- Archimedean_solid wikiPageWikiLink Artist.
- Archimedean_solid wikiPageWikiLink Bicupola_(geometry).
- Archimedean_solid wikiPageWikiLink Bipyramid.
- Archimedean_solid wikiPageWikiLink Bitruncation.
- Archimedean_solid wikiPageWikiLink Cantellation_(geometry).
- Archimedean_solid wikiPageWikiLink Catalan_solid.
- Archimedean_solid wikiPageWikiLink Category:Archimedean_solids.
- Archimedean_solid wikiPageWikiLink Chemical_compound.
- Archimedean_solid wikiPageWikiLink Chirality_(mathematics).
- Archimedean_solid wikiPageWikiLink Convex_polytope.
- Archimedean_solid wikiPageWikiLink Coxeter–Dynkin_diagram.
- Archimedean_solid wikiPageWikiLink Cube.
- Archimedean_solid wikiPageWikiLink Cuboctahedron.
- Archimedean_solid wikiPageWikiLink Decagon.
- Archimedean_solid wikiPageWikiLink Dihedral_group.
- Archimedean_solid wikiPageWikiLink Dodecahedron.
- Archimedean_solid wikiPageWikiLink Dual_polyhedron.
- Archimedean_solid wikiPageWikiLink Duncan_Sommerville.
- Archimedean_solid wikiPageWikiLink Elongated_square_gyrobicupola.
- Archimedean_solid wikiPageWikiLink Eric_W._Weisstein.
- Archimedean_solid wikiPageWikiLink Expansion_(geometry).
- Archimedean_solid wikiPageWikiLink File:Cuboctahedron.jpg.
- Archimedean_solid wikiPageWikiLink Geometry.
- Archimedean_solid wikiPageWikiLink Hexagon.
- Archimedean_solid wikiPageWikiLink Icosahedral_symmetry.
- Archimedean_solid wikiPageWikiLink Icosahedral_twins.
- Archimedean_solid wikiPageWikiLink Icosahedron.
- Archimedean_solid wikiPageWikiLink Icosidodecahedron.
- Archimedean_solid wikiPageWikiLink Isogonal_figure.
- Archimedean_solid wikiPageWikiLink Isohedral_figure.
- Archimedean_solid wikiPageWikiLink Isometry.
- Archimedean_solid wikiPageWikiLink Isotoxal_figure.
- Archimedean_solid wikiPageWikiLink Johannes_Kepler.
- Archimedean_solid wikiPageWikiLink Johnson_solid.
- Archimedean_solid wikiPageWikiLink Kepler–Poinsot_polyhedron.
- Archimedean_solid wikiPageWikiLink List_of_spherical_symmetry_groups.
- Archimedean_solid wikiPageWikiLink List_of_uniform_polyhedra.
- Archimedean_solid wikiPageWikiLink Mathematician.
- Archimedean_solid wikiPageWikiLink Mirror_image.
- Archimedean_solid wikiPageWikiLink Net_(polyhedron).
- Archimedean_solid wikiPageWikiLink Octagon.
- Archimedean_solid wikiPageWikiLink Octahedral_symmetry.
- Archimedean_solid wikiPageWikiLink Octahedron.
- Archimedean_solid wikiPageWikiLink Omnitruncation.
- Archimedean_solid wikiPageWikiLink Pappus_of_Alexandria.
- Archimedean_solid wikiPageWikiLink Pentagon.
- Archimedean_solid wikiPageWikiLink Platonic_solid.
- Archimedean_solid wikiPageWikiLink Prism_(geometry).
- Archimedean_solid wikiPageWikiLink Quasicrystal.
- Archimedean_solid wikiPageWikiLink Quasiregular_polyhedron.
- Archimedean_solid wikiPageWikiLink Rectification_(geometry).
- Archimedean_solid wikiPageWikiLink Regular_icosahedron.
- Archimedean_solid wikiPageWikiLink Regular_polygon.
- Archimedean_solid wikiPageWikiLink Regular_polyhedron.
- Archimedean_solid wikiPageWikiLink Renaissance.
- Archimedean_solid wikiPageWikiLink Rhombicosidodecahedron.
- Archimedean_solid wikiPageWikiLink Rhombicuboctahedron.
- Archimedean_solid wikiPageWikiLink Schläfli_symbol.
- Archimedean_solid wikiPageWikiLink Semiregular_polyhedron.
- Archimedean_solid wikiPageWikiLink Snub_(geometry).
- Archimedean_solid wikiPageWikiLink Snub_cube.
- Archimedean_solid wikiPageWikiLink Snub_dodecahedron.
- Archimedean_solid wikiPageWikiLink Square.
- Archimedean_solid wikiPageWikiLink Symmetry_group.
- Archimedean_solid wikiPageWikiLink Tetrahedral_symmetry.
- Archimedean_solid wikiPageWikiLink Tetrahedron.
- Archimedean_solid wikiPageWikiLink Toroidal_polyhedron.
- Archimedean_solid wikiPageWikiLink Trapezohedron.
- Archimedean_solid wikiPageWikiLink Triangle.
- Archimedean_solid wikiPageWikiLink Truncated_cube.
- Archimedean_solid wikiPageWikiLink Truncated_cuboctahedron.
- Archimedean_solid wikiPageWikiLink Truncated_dodecahedron.
- Archimedean_solid wikiPageWikiLink Truncated_icosahedron.
- Archimedean_solid wikiPageWikiLink Truncated_icosidodecahedron.
- Archimedean_solid wikiPageWikiLink Truncated_octahedron.
- Archimedean_solid wikiPageWikiLink Truncated_tetrahedron.
- Archimedean_solid wikiPageWikiLink Truncation_(geometry).
- Archimedean_solid wikiPageWikiLink Uniform_polyhedron.
- Archimedean_solid wikiPageWikiLink Vertex_(geometry).