Regular (InstanceAttribute, 4)
From Hi.gher. Space
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| + | A '''regular''' [[polytope]] is a polytope whose [[hypercells]] are all [[congruent]]. | ||
| + | In two dimensions, there are infinitely many regular polytopes, each one having a different number of sides. | ||
| + | |||
| + | In three dimensions and above, there are five distinct sets of regular polytopes: | ||
| + | *[[Simplex|Simplices]] | ||
| + | *[[Hypercube]]s | ||
| + | *[[Cross polytope]]s | ||
| + | *[[Hyperdodecahedron|Hyperdodecahedra]] | ||
| + | *[[Hypericosahedron|Hypericosahedra]] | ||
| + | |||
| + | In four dimensions and no other dimension, there is also a sixth regular polytope, with several unique properties: the [[icositetrachoron]]. | ||
| + | |||
| + | Note that it does not make sense to speak of regularity in dimensions less than two. | ||
| + | |||
| + | 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. | ||
| + | |||
| + | [[Category:Geometric properties]] | ||
Revision as of 20:07, 9 August 2007
A regular polytope is a polytope whose hypercells are all congruent.
In two dimensions, there are infinitely many regular polytopes, each one having a different number of sides.
In three dimensions and above, there are five distinct sets of regular polytopes:
In four dimensions and no other dimension, there is also a sixth regular polytope, with several unique properties: the icositetrachoron.
Note that it does not make sense to speak of regularity in dimensions less than two.
Since shapes 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.
