Regular (InstanceAttribute, 4)
From Hi.gher. Space
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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. | 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: | + | [[Category:Geometrical properties]] |
Revision as of 21:18, 15 June 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 finitely many regular polytopes, but there are two important sets: the simplices, and the hypercubes.
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.
