Rotope (EntityClass, 3)

From Hi.gher. Space

(Difference between revisions)
(→Table of rotopes: reorder per rotopical indices, add the missing rotopes)
(→Table of rotopes: fix shading, add rotopical index)
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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%"
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''Name'''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''Name'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''[[Group Notation]]'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''[[Rotopical index]]'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''[[Digit Notation]]'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''[[Group notation]]'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''[[Product Notation]]'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''[[Digit notation]]'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''[[CSG Notation]]'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''[[Product notation]]'''
 +
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''[[CSG notation]]'''
|-
|-
-
|valign="top" style="background-color:#bbbbff; text-align:center;" colspan="5"|'''1D Rotopes'''
+
|valign="top" style="background-color:#bbbbff; text-align:center;" colspan="6"|'''0D rotopes'''
 +
|-
 +
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Point (object)|Point]]'''
 +
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''0'''
 +
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''''Empty string'''''
 +
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''''Empty string'''''
 +
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''0'''
 +
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''''Empty string'''''
 +
|-
 +
|valign="top" style="background-color:#bbbbff; text-align:center;" colspan="6"|'''1D rotopes'''
|-
|-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Line (object)|Line]]'''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Line (object)|Line]]'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''x'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''1'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''1'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''x'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''1'''''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''1'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''E'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''1'''
 +
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''E'''
|-
|-
-
|valign="top" style="background-color:#bbbbff; text-align:center;" colspan="5"|'''2D Rotopes'''
+
|valign="top" style="background-color:#bbbbff; text-align:center;" colspan="6"|'''2D rotopes'''
|-
|-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Square]]'''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Square]]'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''xy'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''2'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''11'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''xy'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''1x1'''''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''11'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EE'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''1x1'''
 +
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''EE'''
|-
|-
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Triangle]]'''
+
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Triangle]]'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''x<sup>y</sup>'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''3'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''1<sup>1</sup>'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''x<sup>y</sup>'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''1~0'''''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''1<sup>1</sup>'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ET'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''1~0'''
 +
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ET'''
|-
|-
-
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Circle]]'''
+
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Circle]]'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(xy)'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''4'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''2'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(xy)'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''2'''''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''2'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''EL'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''2'''
 +
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''EL'''
|-
|-
-
|valign="top" style="background-color:#bbbbff; text-align:center;" colspan="5"|'''3D Rotopes'''
+
|valign="top" style="background-color:#bbbbff; text-align:center;" colspan="6"|'''3D rotopes'''
|-
|-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Cube]]'''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Cube]]'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''xyz'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''5'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''111'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''xyz'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''1x1x1'''''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''111'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EEE'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''1x1x1'''
 +
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''EEE'''
|-
|-
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Square pyramid]]'''
+
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Square pyramid]]'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''xy<sup>z</sup>'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''6'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''11<sup>1</sup>'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''xy<sup>z</sup>'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''(1x1)~0'''''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''11<sup>1</sup>'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EET'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(1x1)~0'''
 +
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''EET'''
|-
|-
-
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Sphere]]'''
+
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Sphere]]'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(xyz)'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''7'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''3'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(xyz)'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''3'''''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''3'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ELL'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''3'''
 +
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ELL'''
|-
|-
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Triangular prism]]'''
+
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Triangular prism]]'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''x<sup>y</sup>z'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''8'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''1<sup>1</sup>1'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''x<sup>y</sup>z'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''(1~0)x1'''''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''1<sup>1</sup>1'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ETE'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(1~0)x1'''
 +
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ETE'''
|-
|-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Tetrahedron]]'''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Tetrahedron]]'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''x<sup>yz</sup>'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''9'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''1<sup>2</sup>'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''x<sup>yz</sup>'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''1~0~0'''''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''1<sup>2</sup>'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ETT'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''1~0~0'''
 +
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ETT'''
|-
|-
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Triangular torus]]'''
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Triangular torus]]'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(x<sup>y</sup>z)'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''10'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(1<sup>1</sup>1)'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(x<sup>y</sup>z)'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''2#(1~0)'''''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(1<sup>1</sup>1)'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ETQ'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''2#(1~0)'''
 +
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ETQ'''
|-
|-
-
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Cylinder]]'''
+
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Cylinder]]'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(xy)z'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''11'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''21'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(xy)z'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''2x1'''''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''21'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ELE'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''2x1'''
 +
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ELE'''
|-
|-
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Cone]]'''
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Cone]]'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(xy)<sup>z</sup>'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''12'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''2<sup>1</sup>'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(xy)<sup>z</sup>'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''2~0'''''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''2<sup>1</sup>'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ELT'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''2~0'''
 +
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ELT'''
|-
|-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Torus]]'''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Torus]]'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''((xy)z)'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''13'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''(21)'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''((xy)z)'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''2#2'''''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(21)'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ELQ'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''2#2'''
 +
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ELQ'''
|-
|-
-
|valign="top" style="background-color:#bbbbff; text-align:center;" colspan="5"|'''4D Rotopes'''
+
|valign="top" style="background-color:#bbbbff; text-align:center;" colspan="6"|'''4D rotopes'''
|-
|-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Tesseract]]'''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Tesseract]]'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''xyzw'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''14'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''1111'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''xyzw'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''1x1x1x1'''''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''1111'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EEEE'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''1x1x1x1'''
 +
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''EEEE'''
|-
|-
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Cubic pyramid]]'''
+
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Cubic pyramid]]'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''xyz<sup>w</sup>'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''15'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''111<sup>1</sup>'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''xyz<sup>w</sup>'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''(1x1x1)~0'''''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''111<sup>1</sup>'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EEET'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(1x1x1)~0'''
 +
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''EEET'''
|-
|-
-
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Glome]]'''
+
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Glome]]'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(xyzw)'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''16'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''4'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(xyzw)'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''4'''''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''4'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ELLL'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''4'''
 +
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ELLL'''
|-
|-
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Square pyramid prism]]'''
+
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Square pyramid prism]]'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''xy<sup>z</sup>w'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''17'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''11<sup>1</sup>1'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''xy<sup>z</sup>w'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''((1x1)~0)x1'''''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''11<sup>1</sup>1'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EETE'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''((1x1)~0)x1'''
 +
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''EETE'''
|-
|-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Square dipyramid]]'''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Square dipyramid]]'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''xy<sup>zw</sup>'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''18'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''11<sup>2</sup>'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''xy<sup>zw</sup>'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''(1x1)~0~0'''''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''11<sup>2</sup>'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EETT'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(1x1)~0~0'''
 +
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''EETT'''
|-
|-
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Square pyramid torus]]'''
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Square pyramid torus]]'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(xy<sup>z</sup>w)'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''19'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(11<sup>1</sup>1)'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(xy<sup>z</sup>w)'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''((1x1)~0)#2'''''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(11<sup>1</sup>1)'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''EETQ'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''((1x1)~0)#2'''
 +
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''EETQ'''
|-
|-
-
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Spherinder]]'''
+
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Spherinder]]'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(xyz)w'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''20'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''31'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(xyz)w'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''3x1'''''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''31'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ELLE'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''3x1'''
 +
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ELLE'''
|-
|-
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Sphone]]'''
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Sphone]]'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(xyz)<sup>w</sup>'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''21'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''3<sup>1</sup>'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(xyz)<sup>w</sup>'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''3~0'''''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''3<sup>1</sup>'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ELLT'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''3~0'''
 +
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ELLT'''
|-
|-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Toraspherinder]]'''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Toraspherinder]]'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''((xyz)w)'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''22'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''(31)'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''((xyz)w)'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''3#2'''''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(31)'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ELLQ'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''3#2'''
 +
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ELLQ'''
|-
|-
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Triangular diprism]]'''
+
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Triangular diprism]]'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''x<sup>y</sup>zw'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''23'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''1<sup>1</sup>11'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''x<sup>y</sup>zw'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''(1~0)x1x1'''''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''1<sup>1</sup>11'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ETEE'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(1~0)x1x1'''
 +
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ETEE'''
|-
|-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Triangular prismidal pyramid]]'''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Triangular prismidal pyramid]]'''
-
|valign="top" width="20%" 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;"|'''24'''
-
|valign="top" width="20%" 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;"|'''x<sup>y</sup>z<sup>w</sup>'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''((1~0) x1)~0'''''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''1<sup>1</sup>1<sup>1</sup>'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ETET'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''((1~0) x1)~0'''
 +
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ETET'''
|-
|-
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Triangular diprismidal torus]]'''
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Triangular diprismidal torus]]'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(x<sup>y</sup>zw)'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''25'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(1<sup>1</sup>11)'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(x<sup>y</sup>zw)'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''2#((1~0) x1)'''''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(1<sup>1</sup>11)'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ETEQ'''
+
|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;"|'''ETEQ'''
|-
|-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Tetrahedral prism]]'''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Tetrahedral prism]]'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''x<sup>yz</sup>w'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''26'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''1<sup>2</sup>1'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''x<sup>yz</sup>w'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''(1~0~0) x1'''''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''1<sup>2</sup>1'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ETTE'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(1~0~0) x1'''
 +
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ETTE'''
|-
|-
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Pentachoron]]'''
+
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Pentachoron]]'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''x<sup>yzw</sup>'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''27'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''1<sup>3</sup>'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''x<sup>yzw</sup>'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''1~0~0~0'''''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''1<sup>3</sup>'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ETTT'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''1~0~0~0'''
 +
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ETTT'''
|-
|-
-
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Tetrahedral torus]]'''
+
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Tetrahedral torus]]'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(x<sup>yz</sup>w)'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''28'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(1<sup>2</sup>1)'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(x<sup>yz</sup>w)'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''2#(1~0~0)'''''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(1<sup>2</sup>1)'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ETTQ'''
+
|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;"|'''ETTQ'''
|-
|-
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Triangular toroidal prism]]'''
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Triangular toroidal prism]]'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(x<sup>y</sup>z)w'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''29'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(1<sup>1</sup>1)1'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(x<sup>y</sup>z)w'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''2#(1~0) x1'''''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(1<sup>1</sup>1)1'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ETQE'''
+
|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:#ccccff; text-align:center;"|'''[[Triangular toroidal pyramid]]'''
+
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Triangular toroidal pyramid]]'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(x<sup>y</sup>z)<sup>w</sup>'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''30'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(1<sup>1</sup>1)<sup>1</sup>'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(x<sup>y</sup>z)<sup>w</sup>'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''(2#(1~0)) ~0'''''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(1<sup>1</sup>1)<sup>1</sup>'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ETQT'''
+
|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:#ddddff; text-align:center;"|'''[[Triangular ditorus]]'''
+
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Triangular ditorus]]'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''((x<sup>y</sup>z)w)'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''31'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''((1<sup>1</sup>1)1)'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''((x<sup>y</sup>z)w)'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''2#(2#(1~0))'''''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''((1<sup>1</sup>1)1)'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ETQQ'''
+
|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="20%" style="background-color:#ddddff; text-align:center;"|'''''Unknown shape'''''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''x<sup>y</sup>(zw)'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''32'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''1<sup>1</sup>2'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''x<sup>y</sup>(zw)'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''Unknown'''''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''1<sup>1</sup>2'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''Unknown'''''
+
|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:#ddddff; text-align:center;"|'''''Unknown shape'''''
+
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''''Unknown shape'''''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''(x<sup>y</sup>(zw))'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''33'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''(1<sup>1</sup>2)'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(x<sup>y</sup>(zw))'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''Unknown'''''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(1<sup>1</sup>2)'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''Unknown'''''
+
|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:#ccccff; text-align:center;"|'''[[Cubinder]]'''
+
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Cubinder]]'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(xy)zw'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''34'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''211'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(xy)zw'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''2x1x1'''''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''211'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ELEE'''
+
|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="20%" style="background-color:#ccccff; text-align:center;"|'''[[Cylindrical pyramid]]'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(xy)z<sup>w</sup>'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''35'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''21<sup>1</sup>'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(xy)z<sup>w</sup>'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''(2x1)~0'''''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''21<sup>1</sup>'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ELET'''
+
|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="20%" style="background-color:#ddddff; text-align:center;"|'''[[Toracubinder]]'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''((xy)zw)'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''36'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''(211)'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''((xy)zw)'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''2#3'''''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(211)'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ELEQ'''
+
|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="20%" style="background-color:#ccccff; text-align:center;"|'''[[Coninder]]'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(xy)<sup>z</sup>w'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''37'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''2<sup>1</sup>1'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(xy)<sup>z</sup>w'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''(2~0)x1'''''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''2<sup>1</sup>1'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ELTE'''
+
|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:#ccccff; text-align:center;"|'''[[Circular dipyramid]]'''
+
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Circular dipyramid]]'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(xy)<sup>zw</sup>'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''38'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''2<sup>2</sup>'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(xy)<sup>zw</sup>'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''2~0~0'''''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''2<sup>2</sup>'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ELTT'''
+
|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:#ddddff; text-align:center;"|'''[[Conindral torus]]'''
+
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Conindral torus]]'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''((xy)<sup>z</sup>w)'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''39'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''(2<sup>1</sup>1)'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''((xy)<sup>z</sup>w)'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''2#(2~0)'''''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(2<sup>1</sup>1)'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ELTQ'''
+
|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="20%" style="background-color:#ddddff; text-align:center;"|'''[[Torinder]]'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''((xy)z)w'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''40'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''(21)1'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''((xy)z)w'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''(2#2)x1'''''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(21)1'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ELQE'''
+
|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:#ddddff; text-align:center;"|'''[[Toroidal pyramid]]'''
+
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Toroidal pyramid]]'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''((xy)z)<sup>w</sup>'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''41'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''(21)<sup>1</sup>'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''((xy)z)<sup>w</sup>'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''(2#2)~0'''''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(21)<sup>1</sup>'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ELQT'''
+
|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:#ccccff; text-align:center;"|'''[[Tetratorus]]'''
+
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Tetratorus]]'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(((xy)z)w)'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''42'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''((21)1)'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(((xy)z)w)'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''(2#2)#2'''''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''((21)1)'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ELQQ'''
+
|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:#ddddff; text-align:center;"|'''[[Duocylinder]]'''
+
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Duocylinder]]'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''(xy)(zw)'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''43'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''22'''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(xy)(zw)'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''2x2'''''
+
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''22'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EL*EL'''
+
|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:#ccccff; text-align:center;"|'''[[Tiger]]'''
+
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Tiger]]'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''((xy)(zw))'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''44'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(22)'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''((xy)(zw))'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''(2x2)#2'''''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(22)'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''Unknown'''''
+
|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 22:09, 16 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.

Table of rotopes

Name Rotopical index Group notation Digit notation Product notation CSG notation
0D rotopes
Point 0 Empty string Empty string 0 Empty string
1D rotopes
Line 1 x 1 1 E
2D rotopes
Square 2 xy 11 1x1 EE
Triangle 3 xy 11 1~0 ET
Circle 4 (xy) 2 2 EL
3D rotopes
Cube 5 xyz 111 1x1x1 EEE
Square pyramid 6 xyz 111 (1x1)~0 EET
Sphere 7 (xyz) 3 3 ELL
Triangular prism 8 xyz 111 (1~0)x1 ETE
Tetrahedron 9 xyz 12 1~0~0 ETT
Triangular torus 10 (xyz) (111) 2#(1~0) ETQ
Cylinder 11 (xy)z 21 2x1 ELE
Cone 12 (xy)z 21 2~0 ELT
Torus 13 ((xy)z) (21) 2#2 ELQ
4D rotopes
Tesseract 14 xyzw 1111 1x1x1x1 EEEE
Cubic pyramid 15 xyzw 1111 (1x1x1)~0 EEET
Glome 16 (xyzw) 4 4 ELLL
Square pyramid prism 17 xyzw 1111 ((1x1)~0)x1 EETE
Square dipyramid 18 xyzw 112 (1x1)~0~0 EETT
Square pyramid torus 19 (xyzw) (1111) ((1x1)~0)#2 EETQ
Spherinder 20 (xyz)w 31 3x1 ELLE
Sphone 21 (xyz)w 31 3~0 ELLT
Toraspherinder 22 ((xyz)w) (31) 3#2 ELLQ
Triangular diprism 23 xyzw 1111 (1~0)x1x1 ETEE
Triangular prismidal pyramid 24 xyzw 1111 ((1~0) x1)~0 ETET
Triangular diprismidal torus 25 (xyzw) (1111) 2#((1~0) x1) ETEQ
Tetrahedral prism 26 xyzw 121 (1~0~0) x1 ETTE
Pentachoron 27 xyzw 13 1~0~0~0 ETTT
Tetrahedral torus 28 (xyzw) (121) 2#(1~0~0) ETTQ
Triangular toroidal prism 29 (xyz)w (111)1 2#(1~0) x1 ETQE
Triangular toroidal pyramid 30 (xyz)w (111)1 (2#(1~0)) ~0 ETQT
Triangular ditorus 31 ((xyz)w) ((111)1) 2#(2#(1~0)) ETQQ
Unknown shape 32 xy(zw) 112 Unknown Unknown
Unknown shape 33 (xy(zw)) (112) Unknown Unknown
Cubinder 34 (xy)zw 211 2x1x1 ELEE
Cylindrical pyramid 35 (xy)zw 211 (2x1)~0 ELET
Toracubinder 36 ((xy)zw) (211) 2#3 ELEQ
Coninder 37 (xy)zw 211 (2~0)x1 ELTE
Circular dipyramid 38 (xy)zw 22 2~0~0 ELTT
Conindral torus 39 ((xy)zw) (211) 2#(2~0) ELTQ
Torinder 40 ((xy)z)w (21)1 (2#2)x1 ELQE
Toroidal pyramid 41 ((xy)z)w (21)1 (2#2)~0 ELQT
Tetratorus 42 (((xy)z)w) ((21)1) (2#2)#2 ELQQ
Duocylinder 43 (xy)(zw) 22 2x2 EL*EL
Tiger 44 ((xy)(zw)) (22) (2x2)#2 Unknown
Retrieved from "http://hi.gher.space/wiki/Rotope"

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