List of bracketopes (Meta, 4)

From Hi.gher. Space

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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''12'''
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''12'''
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''(<xy>z)'''
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''(<xy>z)'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''(ELE&EEL)R<sub>x</sub>[45°]S<sub>yz</sub>[2<sup>-1</sup>√2''']
+
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''(ELE&EEL)R<sub>x</sub>[45°]S<sub>yz</sub>[2<sup>-1</sup>√2]'''
|-
|-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Sphere]]'''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Sphere]]'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''21'''
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''21'''
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''[(<xy>z)w]'''
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''[(<xy>z)w]'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''Unknown'''''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''(ELE&EEL)R<sub>x</sub>[45°]S<sub>yz</sub>[2<sup>-1</sup>√2]E'''
|-
|-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Spherinder]]'''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Spherinder]]'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''[(xyz)w]'''
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''[(xyz)w]'''
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ELLE'''
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ELLE'''
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 +
<[xyz]w> bicubone?
 +
<[<xy>z]w> narrow bicubone*
 +
<[(xy)z]w> bicylone
 +
<[xy]zw> wide hexadecachoron*
 +
<xyzw> hexadecachoron
 +
<(xy)zw> dibicone
 +
<([xy]z)w> bicrone
 +
<(<xy>z)w> narrow bicrone*
 +
<(xyz)w> bisphone
 +
 +
|-
 +
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Cubic bipyramid]]?'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''N/A'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''23'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''<[xyz]w>'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EEED'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Narrow cubic bipyramid]]*'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''N/A'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''24'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''<[<xy>z]w>'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EDED'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Cylindrical bipyramid]]'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''N/A'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''25'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''<[(xy)z]w>'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ELE'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Wide hexadecachoron]]*'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''N/A'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''26'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''<[xy]zw>'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EEDD'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Hexadecachoron]]'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''N/A'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''27'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''<xyzw>'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EDDD'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Dibicone]]'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''N/A'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''28'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''<(xy)zw>'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ELDD'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Crindal bipyramid]]'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''N/A'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''29'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''<([xy]z)w>'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''(ELE&EEL)D'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Narrow crindal bipyramid]]*'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''N/A'''
 +
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''30'''
 +
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''<(<xy>z)w>'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''(ELE&EEL)R<sub>x</sub>[45°]S<sub>yz</sub>[2<sup>-1</sup>√2]D'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Bisphone]]'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''N/A'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''31'''
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|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''<(xyz)w>'''
 +
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ELLD'''
 +
|-
|}
|}

Revision as of 13:18, 18 June 2007

This is a list of bracketopes in dimensions from one to three.

Name Rotopic index Bracketopic index Bracket notation CSG notation
1D bracketopes
Line 1 1 [x] E
2D bracketopes
Square 2 2 [xy] EE
Diamond* N/A 3 <xy> ED
Circle 4 4 (xy) EL
3D bracketopes
Cube 5 5 [xyz] EEE
Cuboid* N/A 6 [<xy>z] EDE
Cylinder 11 7 [(xy)z] ELE
Wide octahedron* N/A 8 <[xy]z> EED
Octahedron N/A 9 <xyz> EDD
Bicone N/A 10 <(xy)z> ELD
Crind N/A 11 ([xy]z) ELE&EEL
Narrow crind* N/A 12 (<xy>z) (ELE&EEL)Rx[45°]Syz[2-1√2]
Sphere 7 13 (xyz) ELL
4D bracketopes
Tesseract 45 14 [xyzw] EEEE
Narrow tesseract* N/A 15 [<xy>zw] EDEE
Cubinder 34 16 [(xy)zw] ELEE
Wide octahedral prism* N/A 17 [<[xy]z>w] EEDE
Octahedral prism N/A 18 [<xyz>w] EDDE
Biconic prism N/A 19 [<(xy)z>w] ELDE
Crindal prism N/A 20 [([xy]z)w] (EL&LE)E
Narrow crindal prism* N/A 21 [(<xy>z)w] (ELE&EEL)Rx[45°]Syz[2-1√2]E
Spherinder 20 22 [(xyz)w] ELLE

<[xyz]w> bicubone? <[<xy>z]w> narrow bicubone* <[(xy)z]w> bicylone <[xy]zw> wide hexadecachoron* <xyzw> hexadecachoron <(xy)zw> dibicone <([xy]z)w> bicrone <(<xy>z)w> narrow bicrone* <(xyz)w> bisphone

Cubic bipyramid? N/A 23 <[xyz]w> EEED
Narrow cubic bipyramid* N/A 24 <[<xy>z]w> EDED
Cylindrical bipyramid N/A 25 <[(xy)z]w> ELE
Wide hexadecachoron* N/A 26 <[xy]zw> EEDD
Hexadecachoron N/A 27 <xyzw> EDDD
Dibicone N/A 28 <(xy)zw> ELDD
Crindal bipyramid N/A 29 <([xy]z)w> (ELE&EEL)D
Narrow crindal bipyramid* N/A 30 <(<xy>z)w> (ELE&EEL)Rx[45°]Syz[2-1√2]D
Bisphone N/A 31 <(xyz)w> ELLD
Retrieved from "http://hi.gher.space/wiki/List_of_bracketopes"