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- List_of_regular_polytopes_and_compounds abstract "This page lists the regular polytopes and regular polytope compounds in Euclidean, spherical and hyperbolic spaces.The Schläfli symbol describes every regular tessellation of an n-sphere, Euclidean and hyperbolic spaces. A Schläfli symbol describing an n-polytope equivalently describes a tessellation of a (n-1)-sphere. In addition, the symmetry of a regular polytope or tessellation is expressed as a Coxeter group, which Coxeter expressed identically to the Schläfli symbol, except delimiting by square brackets, a notation that is called Coxeter notation. Another related symbol is the Coxeter-Dynkin diagram which represents a symmetry group with no rings, and the represents regular polytope or tessellation with a ring on the first node. For example the cube has Schläfli symbol {4,3}, and with its octahedral symmetry, [4,3] or File:CDel node.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.png, is represented by Coxeter diagram File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.png.The regular polytopes are grouped by dimension and subgrouped by convex, nonconvex and infinite forms. Nonconvex forms use the same vertices as the convex forms, but have intersecting facets. Infinite forms tessellate a one-lower-dimensional Euclidean space.Infinite forms can be extended to tessellate a hyperbolic space. Hyperbolic space is like normal space at a small scale, but parallel lines diverge at a distance. This allows vertex figures to have negative angle defects, like making a vertex with seven equilateral triangles and allowing it to lie flat. It cannot be done in a regular plane, but can be at the right scale of a hyperbolic plane.A more general definition of regular polytopes which do not have simple Schläfli symbols includes regular skew polytopes and regular skew apeirotopes with nonplanar facets or vertex figures.".
- List_of_regular_polytopes_and_compounds thumbnail Regular_pentagon.svg?width=300.
- List_of_regular_polytopes_and_compounds wikiPageExternalLink icm1954.3.0155.0169.ocr.pdf.
- List_of_regular_polytopes_and_compounds wikiPageExternalLink 1511.02851.
- List_of_regular_polytopes_and_compounds wikiPageExternalLink hyperbolichoneycombs.org.
- List_of_regular_polytopes_and_compounds wikiPageExternalLink hovinga.
- List_of_regular_polytopes_and_compounds wikiPageExternalLink glossary.html.
- List_of_regular_polytopes_and_compounds wikiPageExternalLink atlas.
- List_of_regular_polytopes_and_compounds wikiPageExternalLink MDA2012_Abstracts_Book.pdf.
- List_of_regular_polytopes_and_compounds wikiPageExternalLink ibs-25-p07.pdf.
- List_of_regular_polytopes_and_compounds wikiPageExternalLink kepler-poinsot-info.html.
- List_of_regular_polytopes_and_compounds wikiPageExternalLink bibperm?q1=ABN8623.0001.001.
- List_of_regular_polytopes_and_compounds wikiPageExternalLink polyhedra.html.
- List_of_regular_polytopes_and_compounds wikiPageExternalLink TesseractApplet.html.
- List_of_regular_polytopes_and_compounds wikiPageExternalLink polytope.shtml.
- List_of_regular_polytopes_and_compounds wikiPageExternalLink Course_notes.pdf.
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- List_of_regular_polytopes_and_compounds wikiPageWikiLink 10-cube.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 10-orthoplex.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 10-simplex.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 11-cell.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 120-cell.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 120-cell_honeycomb.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 16-cell.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 16-cell_honeycomb.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 16-cell_honeycomb_honeycomb.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 24-cell.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 24-cell_honeycomb.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 24-cell_honeycomb_honeycomb.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 3-sphere.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 4-polytope.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 5-cell.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 5-cube.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 5-cubic_honeycomb.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 5-orthoplex.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 5-orthoplex_honeycomb.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 5-simplex.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 57-cell.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 6-cube.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 6-cubic_honeycomb.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 6-orthoplex.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 6-simplex.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 600-cell.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 7-cube.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 7-cubic_honeycomb.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 7-orthoplex.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 7-simplex.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 8-cube.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 8-cubic_honeycomb.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 8-orthoplex.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 8-simplex.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 9-cube.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 9-orthoplex.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink 9-simplex.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Abstract_polytope.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Angular_defect.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Antiprism.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Apeirogon.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Apeirogonal_hosohedron.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Apeirotope.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Binomial_coefficient.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Cartesian_product.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Category:Mathematics-related_lists.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Category:Multi-dimensional_geometry.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Category:Polytopes.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Chamfer_(geometry).
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Circle.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Circumscribed_circle.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Clifford_torus.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Compound_of_five_cubes.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Compound_of_five_octahedra.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Compound_of_five_tetrahedra.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Compound_of_ten_tetrahedra.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Compound_of_two_tetrahedra.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Convex_polygon.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Convex_uniform_honeycomb.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Coprime_integers.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Coxeter_element.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Coxeter_group.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Coxeter_notation.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Coxeter–Dynkin_diagram.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Cross-polytope.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Cube.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Cubic_honeycomb.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Cubic_honeycomb_honeycomb.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Cuboctahedron.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Decagon.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Decagram_(geometry).
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Degeneracy_(mathematics).
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Density_(polytope).
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Digon.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Dihedron.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Ditrigonal_dodecadodecahedron.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Dodecadodecahedron.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Dodecagon.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Dodecagram.
- List_of_regular_polytopes_and_compounds wikiPageWikiLink Dodecahedron.