Rotope (EntityClass, 3)

From Hi.gher. Space

(Difference between revisions)
m (Rotopes moved to Rotope: depluralizing article title)
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A tapertope is an object formed by tapering another object to a point. It has been suggested that tapertopes be limited to only include the line and objects formed by extruding or tapering other objects.
A tapertope is an object formed by tapering another object to a point. It has been suggested that tapertopes be limited to only include the line and objects formed by extruding or tapering other objects.
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== Table of rotopes ==
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== Finding rotopes ==
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{|style="border: 1px solid; border-color:#808080; border-collapse: collapse;" cellpadding="2" width="100%"
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There are currently two main methods for finding rotopes:
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''Name'''
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*[[List of rotopes]]
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''[[Rotopic index]]'''
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*[[Rotope construction chart]]
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''[[Group notation]]'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''[[Digit notation]]'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''[[Product notation]]'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''[[CSG notation]]'''
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|-
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|valign="top" style="background-color:#bbbbff; text-align:center;" colspan="6"|'''0D rotopes'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Point (object)|Point]]'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''0'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''''Empty string'''''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''''Empty string'''''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''0'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''''Empty string'''''
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|-
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|valign="top" style="background-color:#bbbbff; text-align:center;" colspan="6"|'''1D rotopes'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Line (object)|Line]]'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''1'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''x'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''1'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''1'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''E'''
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|-
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|valign="top" style="background-color:#bbbbff; text-align:center;" colspan="6"|'''2D rotopes'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Square]]'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''2'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''xy'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''11'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''1x1'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''EE'''
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|-
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|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Triangle]]'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''3'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''x<sup>y</sup>'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''1<sup>1</sup>'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''1~0'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ET'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Circle]]'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''4'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(xy)'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''2'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''2'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''EL'''
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|-
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|valign="top" style="background-color:#bbbbff; text-align:center;" colspan="6"|'''3D rotopes'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Cube]]'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''5'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''xyz'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''111'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''1x1x1'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''EEE'''
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|-
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|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Square pyramid]]'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''6'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''xy<sup>z</sup>'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''11<sup>1</sup>'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(1x1)~0'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''EET'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Sphere]]'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''7'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(xyz)'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''3'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''3'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ELL'''
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|-
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|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Triangular prism]]'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''8'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''x<sup>y</sup>z'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''1<sup>1</sup>1'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(1~0)x1'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ETE'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Tetrahedron]]'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''9'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''x<sup>yz</sup>'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''1<sup>2</sup>'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''1~0~0'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ETT'''
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|-
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|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Triangular torus]]'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''10'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(x<sup>y</sup>z)'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(1<sup>1</sup>1)'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''2#(1~0)'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ETQ'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Cylinder]]'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''11'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(xy)z'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''21'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''2x1'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ELE'''
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|-
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|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Cone]]'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''12'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(xy)<sup>z</sup>'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''2<sup>1</sup>'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''2~0'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ELT'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Torus]]'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''13'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''((xy)z)'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(21)'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''2#2'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ELQ'''
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|-
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|valign="top" style="background-color:#bbbbff; text-align:center;" colspan="6"|'''4D rotopes'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Tesseract]]'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''14'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''xyzw'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''1111'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''1x1x1x1'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''EEEE'''
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|-
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|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Cubic pyramid]]'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''15'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''xyz<sup>w</sup>'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''111<sup>1</sup>'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(1x1x1)~0'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''EEET'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Glome]]'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''16'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(xyzw)'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''4'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''4'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ELLL'''
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|-
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|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Square pyramid prism]]'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''17'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''xy<sup>z</sup>w'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''11<sup>1</sup>1'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''((1x1)~0)x1'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''EETE'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Square dipyramid]]'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''18'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''xy<sup>zw</sup>'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''11<sup>2</sup>'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(1x1)~0~0'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''EETT'''
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|-
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|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Square pyramid torus]]'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''19'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(xy<sup>z</sup>w)'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(11<sup>1</sup>1)'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''((1x1)~0)#2'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''EETQ'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Spherinder]]'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''20'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(xyz)w'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''31'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''3x1'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ELLE'''
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|-
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|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Sphone]]'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''21'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(xyz)<sup>w</sup>'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''3<sup>1</sup>'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''3~0'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ELLT'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Toraspherinder]]'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''22'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''((xyz)w)'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(31)'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''3#2'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ELLQ'''
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|-
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|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Triangular diprism]]'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''23'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''x<sup>y</sup>zw'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''1<sup>1</sup>11'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(1~0)x1x1'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ETEE'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Triangular prismidal pyramid]]'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''24'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''x<sup>y</sup>z<sup>w</sup>'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''1<sup>1</sup>1<sup>1</sup>'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''((1~0) x1)~0'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ETET'''
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|-
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|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Triangular diprismidal torus]]'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''25'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(x<sup>y</sup>zw)'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(1<sup>1</sup>11)'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''2#((1~0) x1)'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ETEQ'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Tetrahedral prism]]'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''26'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''x<sup>yz</sup>w'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''1<sup>2</sup>1'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(1~0~0) x1'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ETTE'''
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|-
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|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Pentachoron]]'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''27'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''x<sup>yzw</sup>'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''1<sup>3</sup>'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''1~0~0~0'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ETTT'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Tetrahedral torus]]'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''28'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(x<sup>yz</sup>w)'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(1<sup>2</sup>1)'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''2#(1~0~0)'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ETTQ'''
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|-
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|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Triangular toroidal prism]]'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''29'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(x<sup>y</sup>z)w'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(1<sup>1</sup>1)1'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''2#(1~0) x1'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ETQE'''
+
-
|-
+
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Triangular toroidal pyramid]]'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''30'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(x<sup>y</sup>z)<sup>w</sup>'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(1<sup>1</sup>1)<sup>1</sup>'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(2#(1~0)) ~0'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ETQT'''
+
-
|-
+
-
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Triangular ditorus]]'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''31'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''((x<sup>y</sup>z)w)'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''((1<sup>1</sup>1)1)'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''2#(2#(1~0))'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ETQQ'''
+
-
|-
+
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''Unknown shape'''''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''32'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''x<sup>y</sup>(zw)'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''1<sup>1</sup>2'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''''Unknown'''''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''''Unknown'''''
+
-
|-
+
-
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''''Unknown shape'''''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''33'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(x<sup>y</sup>(zw))'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(1<sup>1</sup>2)'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''''Unknown'''''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''''Unknown'''''
+
-
|-
+
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Cubinder]]'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''34'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(xy)zw'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''211'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''2x1x1'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ELEE'''
+
-
|-
+
-
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Cylindrical pyramid]]'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''35'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(xy)z<sup>w</sup>'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''21<sup>1</sup>'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(2x1)~0'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ELET'''
+
-
|-
+
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Toracubinder]]'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''36'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''((xy)zw)'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(211)'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''2#3'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ELEQ'''
+
-
|-
+
-
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Coninder]]'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''37'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(xy)<sup>z</sup>w'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''2<sup>1</sup>1'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(2~0)x1'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ELTE'''
+
-
|-
+
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Circular dipyramid]]'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''38'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(xy)<sup>zw</sup>'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''2<sup>2</sup>'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''2~0~0'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ELTT'''
+
-
|-
+
-
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Conindral torus]]'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''39'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''((xy)<sup>z</sup>w)'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(2<sup>1</sup>1)'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''2#(2~0)'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ELTQ'''
+
-
|-
+
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Torinder]]'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''40'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''((xy)z)w'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(21)1'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(2#2)x1'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ELQE'''
+
-
|-
+
-
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Toroidal pyramid]]'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''41'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''((xy)z)<sup>w</sup>'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(21)<sup>1</sup>'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(2#2)~0'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ELQT'''
+
-
|-
+
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Tetratorus]]'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''42'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(((xy)z)w)'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''((21)1)'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(2#2)#2'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ELQQ'''
+
-
|-
+
-
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Duocylinder]]'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''43'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(xy)(zw)'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''22'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''2x2'''
+
-
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''EL*EL'''
+
-
|-
+
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Tiger]]'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''44'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''((xy)(zw))'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(22)'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(2x2)#2'''
+
-
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''''Unknown'''''
+
-
|}
+
[[Category:Rotopes|*]]
[[Category:Rotopes|*]]

Revision as of 00:13, 17 June 2007

Sets of rotopes

Rotopes are combinations of rotatopes, toratopes and tapertopes. A rotope may be any combination of these, with the exception that a toratope may never be a tapertope and vice versa. There are also rotopes that are none of these. An example is the torinder. The number of non-tapertopes in any dimension is always twice the number of toratopes. In the table below, 'x' denotes the cartesian product, '#' denotes the torus product and '~' denotes tapering. Note that the CSG Notation column shows the notation for a completely solid form of the object.

Rotatopes

A rotatope, invented by Garrett Jones is an object formed by linear extensions or rotations about the origin.

Toratopes

Toratopes were coined by Paul Wright, and invented by him and Marek14. A toratope is an object formed by spheration, i.e. putting a new k-sphere at every point in an object. This is also called the "torus product", #. A#B is the result of replacing every point in A with a copy of B, oriented along the normal space of A.

Tapertopes

Tapertopes were coined by Keiji, and invented by him and Paul Wright. A tapertope is an object formed by tapering another object to a point. It has been suggested that tapertopes be limited to only include the line and objects formed by extruding or tapering other objects.

Finding rotopes

There are currently two main methods for finding rotopes:

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

Pages in this category (4)