Bracketope (EntityClass, 3)
From Hi.gher. Space
(Difference between revisions)
(add) |
(add) |
||
| Line 2: | Line 2: | ||
== Sets of bracketopes by complexity == | == Sets of bracketopes by complexity == | ||
| - | ;[[Totally useless bracketope]] (&, ampersand) | + | ;[[Totally useless bracketope]]s (&, ampersand) |
:A ''totally useless bracketope'' is a bracketope which is [[similar]] to a pure bracketope. | :A ''totally useless bracketope'' is a bracketope which is [[similar]] to a pure bracketope. | ||
| - | ;[[Partially useless bracketope]] (*, asterisk) | + | ;[[Partially useless bracketope]]s (*, asterisk) |
:A ''partially equivalent bracketope'' is a bracketope whose [[vertex graph]] is identical to that of a pure bracketope. | :A ''partially equivalent bracketope'' is a bracketope whose [[vertex graph]] is identical to that of a pure bracketope. | ||
| - | ;[[Pure bracketope]] | + | ;[[Pure bracketope]]s |
:A ''pure bracketope'' is a bracketope which is not partially or totally useless. | :A ''pure bracketope'' is a bracketope which is not partially or totally useless. | ||
| Line 15: | Line 15: | ||
=== Determining bracketopes' purity === | === Determining bracketopes' purity === | ||
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. | 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. | ||
| + | |||
| + | == Bracketopic statistics == | ||
| + | Here is a table to show the number and percentage of various types of bracketopes in each dimension. | ||
| + | |||
| + | {|style="border: 1px solid; border-color:#808080; border-collapse: collapse;" cellpadding="2" width="100%" | ||
| + | |width="12%" style="background-color:#ddddff; text-align:center;"|'''Dimension''' | ||
| + | |width="12%" style="background-color:#ccccff; text-align:center;"|'''Bracketopes''' | ||
| + | |width="12%" style="background-color:#ddddff; text-align:center;"|'''Totally useless''' | ||
| + | |width="12%" style="background-color:#ccccff; text-align:center;"|'''Partially useless''' | ||
| + | |width="12%" style="background-color:#ddddff; text-align:center;"|'''Pure''' | ||
| + | |width="12%" style="background-color:#ccccff; text-align:center;"|'''[[Rotope]]s''' | ||
| + | |width="12%" style="background-color:#ddddff; text-align:center;"|'''[[Strange rotope]]s''' | ||
| + | |width="12%" style="background-color:#ccccff; text-align:center;"|'''[[Pure rotope]]s''' | ||
| + | |- | ||
| + | |style="background-color:#eeeeff; text-align:center;"|1 | ||
| + | |style="background-color:#ddddff; text-align:center;"|[[Line (shape)|1]] | ||
| + | |style="background-color:#eeeeff; text-align:center;"|0 (0%) | ||
| + | |style="background-color:#ddddff; text-align:center;"|0 (0%) | ||
| + | |style="background-color:#eeeeff; text-align:center;"|[[Line (shape)|1 (100%)]] | ||
| + | |style="background-color:#ddddff; text-align:center;"|[[Line (shape)|1 (100%)]] | ||
| + | |style="background-color:#eeeeff; text-align:center;"|0 (0%) | ||
| + | |style="background-color:#ddddff; text-align:center;"|[[Line (shape)|1 (100%)]] | ||
| + | |- | ||
| + | |style="background-color:#eeeeff; text-align:center;"|2 | ||
| + | |style="background-color:#ddddff; text-align:center;"|[[:Category:Brackegons|3]] | ||
| + | |style="background-color:#eeeeff; text-align:center;"|[[Diamond|1 (33%)]] | ||
| + | |style="background-color:#ddddff; text-align:center;"|0 (0%) | ||
| + | |style="background-color:#eeeeff; text-align:center;"|[[List of brackegons by attributes#Pure|2 (67%)]] | ||
| + | |style="background-color:#ddddff; text-align:center;"|[[List of brackegons by attributes#Rotopes|2 (67%)]] | ||
| + | |style="background-color:#eeeeff; text-align:center;"|0 (0%) | ||
| + | |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:#ddddff; text-align:center;"|[[:Category:Brackehedra|9]] | ||
| + | |style="background-color:#eeeeff; text-align:center;"|0 (0%) | ||
| + | |style="background-color:#ddddff; text-align:center;"|[[List of brackehedra by attributes#Partially useless|3 (33%)]] | ||
| + | |style="background-color:#eeeeff; text-align:center;"|[[List of brackehedra by attributes#Pure|6 (67%)]] | ||
| + | |style="background-color:#ddddff; text-align:center;"|[[List of brackehedra by attributes#Rotopes|3 (33%)]] | ||
| + | |style="background-color:#eeeeff; text-align:center;"|0 (0%) | ||
| + | |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:#ddddff; text-align:center;"|[[:Category:Brackechora|36]] | ||
| + | |style="background-color:#eeeeff; text-align:center;"|[[List of brackechora by attributes#Totally useless|3 (8%)]] | ||
| + | |style="background-color:#ddddff; text-align:center;"|[[List of brackechora by attributes#Partially useless|9 (25%)]] | ||
| + | |style="background-color:#eeeeff; text-align:center;"|[[List of brackechora by attributes#Pure|24 (67%)]] | ||
| + | |style="background-color:#ddddff; text-align:center;"|[[List of brackechora by attributes#Rotopes|5 (14%)]] | ||
| + | |style="background-color:#eeeeff; text-align:center;"|[[Duocylinder|1 (3%)]] | ||
| + | |style="background-color:#ddddff; text-align:center;"|[[List of brackechora by attributes#Pure rotopes|4 (11%)]] | ||
| + | |- | ||
| + | |style="background-color:#eeeeff; text-align:center;"|5 | ||
| + | |style="background-color:#ddddff; text-align:center;"|[[:Category:Bracketera|144]] | ||
| + | |style="background-color:#eeeeff; text-align:center;"|0 (0%) | ||
| + | |style="background-color:#ddddff; text-align:center;"|[[List of bracketera by attributes#Partially useless|65 (45%)]] | ||
| + | |style="background-color:#eeeeff; text-align:center;"|[[List of bracketera by attributes#Pure|79 (55%)]] | ||
| + | |style="background-color:#ddddff; text-align:center;"|[[List of bracketera by attributes#Rotopes|7 (5%)]] | ||
| + | |style="background-color:#eeeeff; text-align:center;"|[[List of bracketera by attributes#Strange rotopes|2 (1%)]] | ||
| + | |style="background-color:#ddddff; text-align:center;"|[[List of bracketera by attributes#Pure rotopes|5 (3%)]] | ||
| + | |- | ||
| + | |style="background-color:#ddddff; text-align:center;"|'''Trend''' | ||
| + | |style="background-color:#ccccff; text-align:center;"|Increasing | ||
| + | |style="background-color:#ddddff; text-align:center;"|''Unknown'' | ||
| + | |style="background-color:#ccccff; text-align:center;"|''Unknown'' | ||
| + | |style="background-color:#ddddff; text-align:center;"|Decreasing % | ||
| + | |style="background-color:#ccccff; text-align:center;"|Decreasing % | ||
| + | |style="background-color:#ddddff; text-align:center;"|''Unknown'' | ||
| + | |style="background-color:#ccccff; text-align:center;"|Decreasing % | ||
| + | |} | ||
[[Category:Bracketopes|*]] | [[Category:Bracketopes|*]] | ||
Revision as of 21:06, 19 June 2007
A bracketope is any polytope which can be defined using bracket notation.
Sets of bracketopes by complexity
- Totally useless bracketopes (&, ampersand)
- A totally useless bracketope is a bracketope which is similar to a pure bracketope.
- Partially useless bracketopes (*, asterisk)
- A partially equivalent bracketope is a bracketope whose vertex graph is identical to that of a pure bracketope.
- Pure bracketopes
- A pure bracketope is a bracketope which is not partially or totally useless.
- A question mark indicates that it is unknown whether this bracketope is pure.
Determining bracketopes' purity
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.
Bracketopic statistics
Here is a table to show the number and percentage of various types of bracketopes in each dimension.
| Dimension | Bracketopes | Totally useless | Partially useless | Pure | Rotopes | Strange rotopes | Pure rotopes |
| 1 | 1 | 0 (0%) | 0 (0%) | 1 (100%) | 1 (100%) | 0 (0%) | 1 (100%) |
| 2 | 3 | 1 (33%) | 0 (0%) | 2 (67%) | 2 (67%) | 0 (0%) | 2 (67%) |
| 3 | 9 | 0 (0%) | 3 (33%) | 6 (67%) | 3 (33%) | 0 (0%) | 3 (33%) |
| 4 | 36 | 3 (8%) | 9 (25%) | 24 (67%) | 5 (14%) | 1 (3%) | 4 (11%) |
| 5 | 144 | 0 (0%) | 65 (45%) | 79 (55%) | 7 (5%) | 2 (1%) | 5 (3%) |
| Trend | Increasing | Unknown | Unknown | Decreasing % | Decreasing % | Unknown | Decreasing % |
