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• Regular
  In two dimensions, there are infinitely many regular polytopes, each one having a different number of sides. ...o each other. In three or four dimensions only, there are two more regular polytopes: the [[dodecahedron]] and the [[icosahedron]], which are dual to each other
  1 KB (210 words) - 17:22, 19 September 2012
• Octahedron
  ...mesotruncated [[simplices]]. In addition, it is the central vertex-first [[cross-section]] of the [[tesseract]]. *The [[planar]] [[cross-section]]s (''n'') of an octahedron with side length ''l'' are:
  2 KB (273 words) - 13:14, 26 March 2017
• Aeroteron
  ...'''triacontaditeron''' and the '''pentacross''', is the five-dimensional [[cross polytope]], and is the [[dual]] of the [[geoteron]]. *The [[flunic]] [[cross-section]]s (''n'') of a n icosidodecateron are:
  1 KB (146 words) - 20:14, 14 March 2014
• Xylochoron
  ...et the same polytope. In all other dimensions above 2D, the only self-dual polytopes are the n-simplices: the [[tetrahedron]], [[pentachoron]], etc. ...he only regular, [[tessellating]] polytope that isn't a [[hypercube]] or [[cross polytope]], besides the [[triangle]] and [[hexagon]] in 2D. This means that
  7 KB (1,077 words) - 14:26, 26 March 2017
• Aerochoron
  *The cross sections of the aerochoron are: ...ope. Only 2D has the same phenomenon, although in 2D the hypercube and the cross polytope are in fact the same object (the square).
  5 KB (871 words) - 14:16, 26 March 2017
• SSC2
  ...l shapes, the families are <tt>x</tt> for [[simplex]] and <tt>c</tt> for [[cross polytope]] or [[hypercube]]. *Uniform polytopes (the set of which includes kanitopes, regular polygons and regular polygon
  11 KB (1,890 words) - 20:11, 8 February 2014
• Aeropeton
  ...on''', also known as the '''tricositetrapeton''', is the six-dimensional [[cross polytope]], and is the dual of the [[geopeton]]. {{Cross polytopes|6}}
  658 B (71 words) - 18:15, 9 March 2011
• Cross polytope
  ...vially in all dimensionalities of at least three, with the two-dimensional cross polytope being a rotated [[square]]. They can be represented by the [[brack In all dimensions above 4, the cross polytope is the [[regular polytope]] with the highest [[facet]] count.
  725 B (105 words) - 13:08, 15 March 2014
• Dimensional Features Summary
  *There are only five regular polytopes in this dimension. *3D is the only dimension where the cross product is a binary operator. Generalizations to other dimensions are eithe
  11 KB (1,862 words) - 20:00, 30 October 2017
• Ursatope
  The [[ursatope]]s are bistratic polytopes that may be constructed from any polytope P. P with unit edge length, P sca ... bottom, scaling factor being f. This one features just as pseudo face, or cross-section.
  9 KB (1,304 words) - 18:21, 17 July 2017
• Elemental naming scheme
  ... unwieldly long names as a result. Under the elemental naming scheme, most polytopes have shorter, simpler names, and immediately convey some important properti == Regular polytopes ==
  6 KB (947 words) - 22:55, 18 March 2021