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- Regular_polytope abstract "In mathematics, a regular polytope is a polytope whose symmetry is transitive on its flags, thus giving it the highest degree of symmetry. All its elements or j-faces (for all 0 ≤ j ≤ n, where n is the dimension of the polytope) — cells, faces and so on — are also transitive on the symmetries of the polytope, and are regular polytopes of dimension ≤ n. Regular polytopes are the generalized analog in any number of dimensions of regular polygons (for example, the square or the regular pentagon) and regular polyhedra (for example, the cube). The strong symmetry of the regular polytopes gives them an aesthetic quality that interests both non-mathematicians and mathematicians.Classically, a regular polytope in n dimensions may be defined as having regular facets [(n − 1)-faces] and regular vertex figures. These two conditions are sufficient to ensure that all faces are alike and all vertices are alike. Note, however, that this definition does not work for abstract polytopes.A regular polytope can be represented by a Schläfli symbol of the form {a, b, c, ...., y, z}, with regular facets as {a, b, c, ..., y}, and regular vertex figures as {b, c, ..., y, z}.".
- Regular_polytope thumbnail Regular_pentagon.svg?width=300.
- Regular_polytope wikiPageExternalLink 600-Cell.html.
- Regular_polytope wikiPageExternalLink index.html.
- Regular_polytope wikiPageExternalLink home.html.
- Regular_polytope wikiPageExternalLink projPoly.html.
- Regular_polytope wikiPageExternalLink polytope.shtml.
- Regular_polytope wikiPageExternalLink galery1-en.htm.
- Regular_polytope wikiPageID "518693".
- Regular_polytope wikiPageLength "37823".
- Regular_polytope wikiPageOutDegree "261".
- Regular_polytope wikiPageRevisionID "679297877".
- Regular_polytope wikiPageWikiLink 11-cell.
- Regular_polytope wikiPageWikiLink 120-cell.
- Regular_polytope wikiPageWikiLink 16-cell.
- Regular_polytope wikiPageWikiLink 24-cell.
- Regular_polytope wikiPageWikiLink 4-orthoplex.
- Regular_polytope wikiPageWikiLink 4-polytope.
- Regular_polytope wikiPageWikiLink 4-simplex.
- Regular_polytope wikiPageWikiLink 5-cell.
- Regular_polytope wikiPageWikiLink 5-cube.
- Regular_polytope wikiPageWikiLink 5-orthoplex.
- Regular_polytope wikiPageWikiLink 5-simplex.
- Regular_polytope wikiPageWikiLink 57-cell.
- Regular_polytope wikiPageWikiLink 600-cell.
- Regular_polytope wikiPageWikiLink 8-cube.
- Regular_polytope wikiPageWikiLink Abstract_polytope.
- Regular_polytope wikiPageWikiLink Aesthetics.
- Regular_polytope wikiPageWikiLink Alicia_Boole_Stott.
- Regular_polytope wikiPageWikiLink Ancient_Greece.
- Regular_polytope wikiPageWikiLink Animation.
- Regular_polytope wikiPageWikiLink Apeirotope.
- Regular_polytope wikiPageWikiLink Archimedean_solid.
- Regular_polytope wikiPageWikiLink Arthur_Cayley.
- Regular_polytope wikiPageWikiLink Augustin-Louis_Cauchy.
- Regular_polytope wikiPageWikiLink Augustin_Cauchy.
- Regular_polytope wikiPageWikiLink Bartel_Leendert_van_der_Waerden.
- Regular_polytope wikiPageWikiLink Branko_Grünbaum.
- Regular_polytope wikiPageWikiLink CAT_scan.
- Regular_polytope wikiPageWikiLink CT_scan.
- Regular_polytope wikiPageWikiLink Category:Multi-dimensional_geometry.
- Regular_polytope wikiPageWikiLink Category:Polytopes.
- Regular_polytope wikiPageWikiLink Category:Symmetry.
- Regular_polytope wikiPageWikiLink Cell_(geometry).
- Regular_polytope wikiPageWikiLink Chessboard.
- Regular_polytope wikiPageWikiLink Co-prime.
- Regular_polytope wikiPageWikiLink Compass-and-straightedge_construction.
- Regular_polytope wikiPageWikiLink Compass_and_straightedge.
- Regular_polytope wikiPageWikiLink Complex_number.
- Regular_polytope wikiPageWikiLink Complex_polytope.
- Regular_polytope wikiPageWikiLink Constructible_polygon.
- Regular_polytope wikiPageWikiLink Convex_polygon.
- Regular_polytope wikiPageWikiLink Convex_regular_4-polytope.
- Regular_polytope wikiPageWikiLink Coprime_integers.
- Regular_polytope wikiPageWikiLink Cosmology.
- Regular_polytope wikiPageWikiLink Coxeter_group.
- Regular_polytope wikiPageWikiLink Cross-polytope.
- Regular_polytope wikiPageWikiLink Cross_polytope.
- Regular_polytope wikiPageWikiLink Cube.
- Regular_polytope wikiPageWikiLink Cubic_honeycomb.
- Regular_polytope wikiPageWikiLink Cuboctahedron.
- Regular_polytope wikiPageWikiLink Dodecahedron.
- Regular_polytope wikiPageWikiLink Dodecaplex.
- Regular_polytope wikiPageWikiLink Dual_polyhedron.
- Regular_polytope wikiPageWikiLink Dual_polytope.
- Regular_polytope wikiPageWikiLink Duncan_MacLaren_Young_Sommerville.
- Regular_polytope wikiPageWikiLink Duncan_Sommerville.
- Regular_polytope wikiPageWikiLink E8_(mathematics).
- Regular_polytope wikiPageWikiLink Edge_(geometry).
- Regular_polytope wikiPageWikiLink Equilateral_triangle.
- Regular_polytope wikiPageWikiLink Euclid.
- Regular_polytope wikiPageWikiLink Euclidean_space.
- Regular_polytope wikiPageWikiLink Euclids_Elements.
- Regular_polytope wikiPageWikiLink Face_(geometry).
- Regular_polytope wikiPageWikiLink Facet_(geometry).
- Regular_polytope wikiPageWikiLink File:8-cell-simple.gif.
- Regular_polytope wikiPageWikiLink File:Hypercube.svg.
- Regular_polytope wikiPageWikiLink Flag_(geometry).
- Regular_polytope wikiPageWikiLink Grand_stellated_120-cell.
- Regular_polytope wikiPageWikiLink Great_120-cell.
- Regular_polytope wikiPageWikiLink Great_dodecahedron.
- Regular_polytope wikiPageWikiLink Great_icosahedron.
- Regular_polytope wikiPageWikiLink Great_stellated_dodecahedron.
- Regular_polytope wikiPageWikiLink Group_(mathematics).
- Regular_polytope wikiPageWikiLink Group_action.
- Regular_polytope wikiPageWikiLink H._S._M._Coxeter.
- Regular_polytope wikiPageWikiLink Harold_Scott_MacDonald_Coxeter.
- Regular_polytope wikiPageWikiLink Hexagonal_tiling_honeycomb.
- Regular_polytope wikiPageWikiLink Hexateron.
- Regular_polytope wikiPageWikiLink Hilbert_space.
- Regular_polytope wikiPageWikiLink Hologram.
- Regular_polytope wikiPageWikiLink Holography.
- Regular_polytope wikiPageWikiLink Homology_sphere.
- Regular_polytope wikiPageWikiLink Honeycomb_(geometry).
- Regular_polytope wikiPageWikiLink Hyperbolic_space.
- Regular_polytope wikiPageWikiLink Hypercube.
- Regular_polytope wikiPageWikiLink Icosahedral_honeycomb.
- Regular_polytope wikiPageWikiLink Icosahedron.
- Regular_polytope wikiPageWikiLink Infinity.
- Regular_polytope wikiPageWikiLink Johannes_Kepler.