Bracketope (EntityClass, 3)

From Hi.gher. Space

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A '''bracketope''' is any [[shape]] 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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;[[Totally useless bracketope]]s (&, ampersand)
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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]]s (*, asterisk)
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:A ''partially useless bracketope'' is a bracketope whose [[vertex graph]] is identical to that of a pure bracketope.
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;[[Pure bracketope]]s
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:A ''pure bracketope'' is a bracketope which is not partially or totally useless.
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*A question mark indicates that it is unknown whether this bracketope is pure.
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=== Determining bracketopes' purity ===
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If two or more bracketopes are similar to each other, the one with the lowest [[bracketopic index]] is pure and all others are totally useless.
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== Bracketopic statistics ==
== Bracketopic statistics ==
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{|style="border: 1px solid; border-color:#808080; border-collapse: collapse;" cellpadding="2" width="100%"
{|style="border: 1px solid; border-color:#808080; border-collapse: collapse;" cellpadding="2" width="100%"
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|width="12%" style="background-color:#ddddff; text-align:center;"|'''Dimension'''
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|width="20%" style="background-color:#ddddff; text-align:center;"|'''Dimension'''
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|width="12%" style="background-color:#ccccff; text-align:center;"|'''Bracketopes'''
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|width="20%" style="background-color:#ccccff; text-align:center;"|'''Bracketopes'''
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|width="12%" style="background-color:#ddddff; text-align:center;"|'''Totally useless'''
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|width="20%" style="background-color:#ddddff; text-align:center;"|'''Rotatopes'''
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|width="12%" style="background-color:#ccccff; text-align:center;"|'''Partially useless'''
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|width="20%" style="background-color:#ccccff; text-align:center;"|'''Linear'''
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|width="12%" style="background-color:#ddddff; text-align:center;"|'''Pure'''
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|width="20%" style="background-color:#ddddff; text-align:center;"|'''Non-linear'''
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|width="12%" style="background-color:#ccccff; text-align:center;"|'''[[Rotope]]s'''
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|width="12%" style="background-color:#ddddff; text-align:center;"|'''[[Strange rotope]]s'''
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|width="12%" style="background-color:#ccccff; text-align:center;"|'''[[Pure rotope]]s'''
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|-
|-
|style="background-color:#eeeeff; text-align:center;"|1
|style="background-color:#eeeeff; text-align:center;"|1
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|style="background-color:#ddddff; text-align:center;"|[[Line (shape)|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%)]]
|style="background-color:#eeeeff; text-align:center;"|0 (0%)
|style="background-color:#eeeeff; text-align:center;"|0 (0%)
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|style="background-color:#ddddff; text-align:center;"|0 (0%)
 
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|style="background-color:#eeeeff; text-align:center;"|[[Line (shape)|1 (100%)]]
 
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|style="background-color:#ddddff; text-align:center;"|[[Line (shape)|1 (100%)]]
 
-
|style="background-color:#eeeeff; text-align:center;"|0 (0%)
 
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|style="background-color:#ddddff; text-align:center;"|[[Line (shape)|1 (100%)]]
 
|-
|-
|style="background-color:#eeeeff; text-align:center;"|2
|style="background-color:#eeeeff; text-align:center;"|2
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|style="background-color:#ddddff; text-align:center;"|[[:Category:Brackegons|3]]
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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;"|[[Diamond|1 (33%)]]
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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;"|0 (0%)
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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;"|[[List of brackegons by attributes#Pure|2 (67%)]]
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|style="background-color:#ddddff; text-align:center;"|[[List of brackegons by attributes#Rotopes|2 (67%)]]
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|style="background-color:#eeeeff; text-align:center;"|0 (0%)
|style="background-color:#eeeeff; text-align:center;"|0 (0%)
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|style="background-color:#ddddff; text-align:center;"|[[List of brackegons by attributes#Pure rotopes|2 (67%)]]
 
|-
|-
|style="background-color:#eeeeff; text-align:center;"|3
|style="background-color:#eeeeff; text-align:center;"|3
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|style="background-color:#ddddff; text-align:center;"|[[:Category:Brackehedra|9]]
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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%)]]
|style="background-color:#eeeeff; text-align:center;"|0 (0%)
|style="background-color:#eeeeff; text-align:center;"|0 (0%)
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|style="background-color:#ddddff; text-align:center;"|[[List of brackehedra by attributes#Partially useless|3 (33%)]]
 
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|style="background-color:#eeeeff; text-align:center;"|[[List of brackehedra by attributes#Pure|6 (67%)]]
 
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|style="background-color:#ddddff; text-align:center;"|[[List of brackehedra by attributes#Rotopes|3 (33%)]]
 
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|style="background-color:#eeeeff; text-align:center;"|0 (0%)
 
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|style="background-color:#ddddff; text-align:center;"|[[List of brackehedra by attributes#Pure rotopes|3 (33%)]]
 
|-
|-
|style="background-color:#eeeeff; text-align:center;"|4
|style="background-color:#eeeeff; text-align:center;"|4
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|style="background-color:#ddddff; text-align:center;"|[[:Category:Brackechora|36]]
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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;"|[[List of brackechora by attributes#Totally useless|3 (8%)]]
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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#Partially useless|9 (25%)]]
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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#Pure|24 (67%)]]
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|style="background-color:#eeeeff; text-align:center;"|[[List_of_brackechora_by_attributes#Non-linear|3 (14%)]]
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|style="background-color:#ddddff; text-align:center;"|[[List of brackechora by attributes#Rotopes|5 (14%)]]
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|style="background-color:#eeeeff; text-align:center;"|[[Duocylinder|1 (3%)]]
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|style="background-color:#ddddff; text-align:center;"|[[List of brackechora by attributes#Pure rotopes|4 (11%)]]
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|-
|-
|style="background-color:#eeeeff; text-align:center;"|5
|style="background-color:#eeeeff; text-align:center;"|5
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|style="background-color:#ddddff; text-align:center;"|[[:Category:Bracketera|144]]
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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;"|0 (0%)
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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#Partially useless|65 (45%)]]
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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#Pure|79 (55%)]]
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|style="background-color:#eeeeff; text-align:center;"|[[List_of_bracketera_by_attributes#Non-linear|21 (28%)]]
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|style="background-color:#ddddff; text-align:center;"|[[List of bracketera by attributes#Rotopes|7 (5%)]]
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|style="background-color:#eeeeff; text-align:center;"|[[List of bracketera by attributes#Strange rotopes|2 (1%)]]
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|style="background-color:#ddddff; text-align:center;"|[[List of bracketera by attributes#Pure rotopes|5 (3%)]]
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|-
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|style="background-color:#ddddff; text-align:center;"|'''Trend'''
|style="background-color:#ddddff; text-align:center;"|'''Trend'''
|style="background-color:#ccccff; text-align:center;"|Increasing
|style="background-color:#ccccff; text-align:center;"|Increasing
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|style="background-color:#ddddff; text-align:center;"|''Unknown''
 
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|style="background-color:#ccccff; text-align:center;"|''Unknown''
 
|style="background-color:#ddddff; text-align:center;"|Decreasing %
|style="background-color:#ddddff; text-align:center;"|Decreasing %
|style="background-color:#ccccff; text-align:center;"|Decreasing %
|style="background-color:#ccccff; text-align:center;"|Decreasing %
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|style="background-color:#ddddff; text-align:center;"|''Unknown''
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|style="background-color:#ddddff; text-align:center;"|Increasing %
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|style="background-color:#ccccff; text-align:center;"|Decreasing %
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|}
|}
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There is currently one main method for finding bracketopes:
There is currently one main method for finding bracketopes:
*[[List of bracketopes]]
*[[List of bracketopes]]
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[[Category:Bracketopes|*]]
 

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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