From Hi.gher. Space
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| - | A '''regular''' [[polytope]] is a polytope whose [[hypercells]] are all [[congruent]].
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| - | In two dimensions, there are infinitely many regular polytopes, each one having a different number of sides.
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| - | In three dimensions and above, there are five distinct sets of regular polytopes:
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| - | *[[Simplex|Simplices]]
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| - | *[[Hypercube]]s
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| - | *[[Cross polytope]]s
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| - | *[[Hyperdodecahedron|Hyperdodecahedra]]
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| - | *[[Hypericosahedron|Hypericosahedra]]
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| - | In four dimensions and no other dimension, there is also a sixth regular polytope, with several unique properties: the [[icositetrachoron]].
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| - | Note that it does not make sense to speak of regularity in dimensions less than two.
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| - | Since [[shape]]s can have curved hypercells, there are infinitely many regular ''shapes'' in any dimension, which is why we specify that regularity usually applies only to polytopes.
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| - | [[Category:Geometric properties]]
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Revision as of 10:28, 9 August 2007
Pages in this category (15)
