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- 2_21_polytope abstract "In 6-dimensional geometry, the 221 polytope is a uniform 6-polytope, constructed within the symmetry of the E6 group. It was discovered by Thorold Gosset, published in his 1900 paper. He called it an 6-ic semi-regular figure.Its Coxeter symbol is 221, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of one of the 2-node sequences. He also studied its connection with the 27 lines on the cubic surface, which are naturally in correspondence with the vertices of 221.The rectified 221 is constructed by points at the mid-edges of the 221. The birectified 221 is constructed by points at the triangle face centers of the 221, and is the same as the rectified 122.These polytopes are a part of family of 39 convex uniform polytopes in 6-dimensions, made of uniform 5-polytope facets and vertex figures, defined by all permutations of rings in this Coxeter-Dynkin diagram: File:CDel nodea.pngFile:CDel 3a.pngFile:CDel nodea.pngFile:CDel 3a.pngFile:CDel branch.pngFile:CDel 3a.pngFile:CDel nodea.pngFile:CDel 3a.pngFile:CDel nodea.png.".
- 2_21_polytope thumbnail Up_2_21_t0_E6.svg?width=300.
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- 2_21_polytope wikiPageRevisionID "699160270".
- 2_21_polytope wikiPageWikiLink 1_22_polytope.
- 2_21_polytope wikiPageWikiLink 24-cell.
- 2_21_polytope wikiPageWikiLink 2_22_honeycomb.
- 2_21_polytope wikiPageWikiLink 4_21_polytope.
- 2_21_polytope wikiPageWikiLink 5-cell.
- 2_21_polytope wikiPageWikiLink 5-demicube.
- 2_21_polytope wikiPageWikiLink 5-orthoplex.
- 2_21_polytope wikiPageWikiLink 5-simplex.
- 2_21_polytope wikiPageWikiLink Category:6-polytopes.
- 2_21_polytope wikiPageWikiLink Convex_polytope.
- 2_21_polytope wikiPageWikiLink Coxeter_element.
- 2_21_polytope wikiPageWikiLink Coxeter_group.
- 2_21_polytope wikiPageWikiLink Coxeter–Dynkin_diagram.
- 2_21_polytope wikiPageWikiLink Cross-polytope.
- 2_21_polytope wikiPageWikiLink Cubic_surface.
- 2_21_polytope wikiPageWikiLink Dodecagon.
- 2_21_polytope wikiPageWikiLink Dynkin_diagram.
- 2_21_polytope wikiPageWikiLink E6_(mathematics).
- 2_21_polytope wikiPageWikiLink Emanuel_Lodewijk_Elte.
- 2_21_polytope wikiPageWikiLink Geometry.
- 2_21_polytope wikiPageWikiLink Gosset–Elte_figures.
- 2_21_polytope wikiPageWikiLink Harold_Scott_MacDonald_Coxeter.
- 2_21_polytope wikiPageWikiLink List_of_E6_polytopes.
- 2_21_polytope wikiPageWikiLink Petrie_polygon.
- 2_21_polytope wikiPageWikiLink Projection_(linear_algebra).
- 2_21_polytope wikiPageWikiLink Rectified_5-cell.
- 2_21_polytope wikiPageWikiLink Rectified_5-orthoplexes.
- 2_21_polytope wikiPageWikiLink Rectified_5-simplexes.
- 2_21_polytope wikiPageWikiLink Regular_polytope.
- 2_21_polytope wikiPageWikiLink Schläfli_symbol.
- 2_21_polytope wikiPageWikiLink Semiregular_polytope.
- 2_21_polytope wikiPageWikiLink Simplex.
- 2_21_polytope wikiPageWikiLink Tetrahedron.
- 2_21_polytope wikiPageWikiLink Thorold_Gosset.
- 2_21_polytope wikiPageWikiLink Triangle.
- 2_21_polytope wikiPageWikiLink Uniform_5-polytope.
- 2_21_polytope wikiPageWikiLink Uniform_6-polytope.
- 2_21_polytope wikiPageWikiLink Uniform_k_21_polytope.
- 2_21_polytope wikiPageWikiLink Uniform_polytope.
- 2_21_polytope wikiPageWikiLink Vertex_figure.
- 2_21_polytope wikiPageWikiLink File:2-simplex_t0.svg.
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- 2_21_polytope wikiPageWikiLink File:4-simplex_t0.svg.
- 2_21_polytope wikiPageWikiLink File:5-cube_t3.svg.
- 2_21_polytope wikiPageWikiLink File:5-demicube_t0_D5.svg.
- 2_21_polytope wikiPageWikiLink File:5-orthoplex.svg.
- 2_21_polytope wikiPageWikiLink File:5-simplex_t0.svg.
- 2_21_polytope wikiPageWikiLink File:5-simplex_t1.svg.
- 2_21_polytope wikiPageWikiLink File:E6_graph.svg.
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- 2_21_polytope wikiPageWikiLink File:Up_2_21_t1_D5.svg.
- 2_21_polytope wikiPageWikiLink File:Up_2_21_t1_E6.svg.
- 2_21_polytope wikiPageWikiLink File:Up_2_21_t2_E6.svg.
- 2_21_polytope wikiPageWikiLinkText "2 21 polytope".
- 2_21_polytope wikiPageWikiLinkText "2 21 polytope#Rectified_2_21_polytope".
- 2_21_polytope wikiPageUsesTemplate Template:2_2k_polytopes.
- 2_21_polytope wikiPageUsesTemplate Template:2_k1_polytopes.
- 2_21_polytope wikiPageUsesTemplate Template:CDD.
- 2_21_polytope wikiPageUsesTemplate Template:Citation.
- 2_21_polytope wikiPageUsesTemplate Template:Dynkin.
- 2_21_polytope wikiPageUsesTemplate Template:Dynkin2.
- 2_21_polytope wikiPageUsesTemplate Template:K_21_polytopes.
- 2_21_polytope wikiPageUsesTemplate Template:KlitzingPolytopes.
- 2_21_polytope wikiPageUsesTemplate Template:Polytopes.
- 2_21_polytope wikiPageUsesTemplate Template:Reflist.
- 2_21_polytope subject Category:6-polytopes.
- 2_21_polytope hypernym Polytope.
- 2_21_polytope type Polytope.
- 2_21_polytope comment "In 6-dimensional geometry, the 221 polytope is a uniform 6-polytope, constructed within the symmetry of the E6 group. It was discovered by Thorold Gosset, published in his 1900 paper. He called it an 6-ic semi-regular figure.Its Coxeter symbol is 221, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of one of the 2-node sequences.".
- 2_21_polytope label "2 21 polytope".
- 2_21_polytope sameAs Q4633288.
- 2_21_polytope sameAs E6_hiperpluredro.
- 2_21_polytope sameAs m.04lfshk.
- 2_21_polytope sameAs Q4633288.
- 2_21_polytope wasDerivedFrom 2_21_polytope?oldid=699160270.
- 2_21_polytope depiction Up_2_21_t0_E6.svg.
- 2_21_polytope isPrimaryTopicOf 2_21_polytope.
