Transitivity (InstanceTopic, 3)
From Hi.gher. Space
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(New page: '''Transitivity''' is a property applied to the hypercells of a polytope. A polytope is said to be ''n''-transitive iff there is an automorphism on the polytope mapping any particu...) |
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'''Transitivity''' is a property applied to the [[hypercell]]s of a [[polytope]]. A polytope is said to be ''n''-transitive iff there is an automorphism on the polytope mapping any particular ''n''-cell to any other ''n''-cell in the polytope. | '''Transitivity''' is a property applied to the [[hypercell]]s of a [[polytope]]. A polytope is said to be ''n''-transitive iff there is an automorphism on the polytope mapping any particular ''n''-cell to any other ''n''-cell in the polytope. | ||
| - | Usually, ''n''-transitivity for 0 ≤ ''n'' ≤ 3 is referred to as vertex-, edge-, face- and cell-transitivity respectively. In addition, a polytope exhibiting ''n''-transitivity is isogonal, isotoxal, isohedral, isochoric, isoteral, isopetal etc. | + | Usually, ''n''-transitivity for 0 ≤ ''n'' ≤ 3 is referred to as vertex-, edge-, face- and cell-transitivity respectively. In addition, a polytope exhibiting ''n''-transitivity is ''isogonal'', ''isotoxal'', ''isohedral'', ''isochoric'', ''isoteral'', ''isopetal'' etc. |
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Latest revision as of 19:18, 9 March 2011
Transitivity is a property applied to the hypercells of a polytope. A polytope is said to be n-transitive iff there is an automorphism on the polytope mapping any particular n-cell to any other n-cell in the polytope.
Usually, n-transitivity for 0 ≤ n ≤ 3 is referred to as vertex-, edge-, face- and cell-transitivity respectively. In addition, a polytope exhibiting n-transitivity is isogonal, isotoxal, isohedral, isochoric, isoteral, isopetal etc.
