Bracketope (EntityClass, 3)

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A '''bracketope''' is any [[polytope]] which can be defined using [[bracket notation]].
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<[#ontology [kind class] [cats Shape]]>
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A '''bracketope''' is any [[shape]] which can be defined using [[bracket notation]]. As of November 18, 2011, bracketopes are restricted to exclude the tegmal constructions which duplicate other shapes. These constructions were previously referred to as ''useless'', for good reason.
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== Sets of bracketopes by complexity ==
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== Bracketopic statistics ==
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;[[Totally useless bracketope]] (&, ampersand)
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Here is a table to show the number and percentage of various types of bracketopes in each dimension.
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:A ''totally useless bracketope'' is a bracketope which is [[similar]] to a pure bracketope.
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;[[Partially useless bracketope]] (*, asterisk)
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{|style="border: 1px solid; border-color:#808080; border-collapse: collapse;" cellpadding="2" width="100%"
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:A ''partially equivalent bracketope'' is a bracketope whose [[vertex graph]] is identical to that of a pure bracketope.
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|width="20%" style="background-color:#ddddff; text-align:center;"|'''Dimension'''
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|width="20%" style="background-color:#ccccff; text-align:center;"|'''Bracketopes'''
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|width="20%" style="background-color:#ddddff; text-align:center;"|'''Rotatopes'''
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|width="20%" style="background-color:#ccccff; text-align:center;"|'''Linear'''
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|width="20%" style="background-color:#ddddff; text-align:center;"|'''Non-linear'''
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|-
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|style="background-color:#eeeeff; text-align:center;"|1
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|style="background-color:#ddddff; text-align:center;"|[[Digon|1]]
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|style="background-color:#eeeeff; text-align:center;"|[[Digon|1 (100%)]]
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|style="background-color:#ddddff; text-align:center;"|[[Digon|1 (100%)]]
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|style="background-color:#eeeeff; text-align:center;"|0 (0%)
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|-
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|style="background-color:#eeeeff; text-align:center;"|2
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|style="background-color:#ddddff; text-align:center;"|[[:Category:Brackegons|2]]
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|style="background-color:#eeeeff; text-align:center;"|[[:Category:Rotagons|2 (100%)]]
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|style="background-color:#ddddff; text-align:center;"|[[:Category:Brackegons|2 (100%)]]
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|style="background-color:#eeeeff; text-align:center;"|0 (0%)
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|-
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|style="background-color:#eeeeff; text-align:center;"|3
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|style="background-color:#ddddff; text-align:center;"|[[:Category:Brackehedra|6]]
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|style="background-color:#eeeeff; text-align:center;"|[[:Category:Rotahedra|3 (50%)]]
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|style="background-color:#ddddff; text-align:center;"|[[:Category:Brackehedra|6 (100%)]]
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|style="background-color:#eeeeff; text-align:center;"|0 (0%)
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|-
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|style="background-color:#eeeeff; text-align:center;"|4
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|style="background-color:#ddddff; text-align:center;"|[[:Category:Brackechora|21]]
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|style="background-color:#eeeeff; text-align:center;"|[[:Category:Rotachora|5 (24%)]]
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|style="background-color:#ddddff; text-align:center;"|[[List_of_brackechora_by_attributes#Linear|18 (86%)]]
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|style="background-color:#eeeeff; text-align:center;"|[[List_of_brackechora_by_attributes#Non-linear|3 (14%)]]
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|-
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|style="background-color:#eeeeff; text-align:center;"|5
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|style="background-color:#ddddff; text-align:center;"|[[:Category:Bracketera|75]]
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|style="background-color:#eeeeff; text-align:center;"|[[:Category:Rotatera|7 (9%)]]
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|style="background-color:#ddddff; text-align:center;"|[[List_of_bracketera_by_attributes#Linear|54 (72%)]]
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|style="background-color:#eeeeff; text-align:center;"|[[List_of_bracketera_by_attributes#Non-linear|21 (28%)]]
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|-
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|style="background-color:#ddddff; text-align:center;"|'''Trend'''
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|style="background-color:#ccccff; text-align:center;"|Increasing
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|style="background-color:#ddddff; text-align:center;"|Decreasing %
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|style="background-color:#ccccff; text-align:center;"|Decreasing %
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|style="background-color:#ddddff; text-align:center;"|Increasing %
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|}
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;[[Pure bracketope]]
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== Finding bracketopes ==
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:A ''pure bracketope'' is a bracketope which is not partially or totally useless.
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There is currently one main method for finding bracketopes:
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*[[List of bracketopes]]
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*A question mark indicates that this bracketope may or may not be a useless variant of another pure bracketope.
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[[Category:Bracketopes|*]]
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Latest revision as of 12:41, 26 November 2013

A bracketope is any shape which can be defined using bracket notation. As of November 18, 2011, bracketopes are restricted to exclude the tegmal constructions which duplicate other shapes. These constructions were previously referred to as useless, for good reason.

Bracketopic statistics

Here is a table to show the number and percentage of various types of bracketopes in each dimension.

Dimension Bracketopes Rotatopes Linear Non-linear
1 1 1 (100%) 1 (100%) 0 (0%)
2 2 2 (100%) 2 (100%) 0 (0%)
3 6 3 (50%) 6 (100%) 0 (0%)
4 21 5 (24%) 18 (86%) 3 (14%)
5 75 7 (9%) 54 (72%) 21 (28%)
Trend Increasing Decreasing % Decreasing % Increasing %

Finding bracketopes

There is currently one main method for finding bracketopes:

Retrieved from "http://hi.gher.space/wiki/Bracketope"

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