Rotope (EntityClass, 3)

From Hi.gher. Space

(Difference between revisions)
m
(→Table of rotopes: reorder per rotopical indices, add the missing rotopes)
Line 36: Line 36:
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''1x1'''''
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''1x1'''''
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EE'''
|valign="top" width="20%" 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:#eeeeff; text-align:center;"|'''x<sup>y</sup>'''
 +
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''1<sup>1</sup>'''
 +
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''1~0'''''
 +
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ET'''
|-
|-
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Circle]]'''
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Circle]]'''
Line 42: Line 48:
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''2'''''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''2'''''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''EL'''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''EL'''
-
|-
 
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Triangle]]'''
 
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''x<sup>y</sup>'''
 
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''1<sup>1</sup>'''
 
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''1~0'''''
 
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ET'''
 
|-
|-
|valign="top" style="background-color:#bbbbff; text-align:center;" colspan="5"|'''3D Rotopes'''
|valign="top" style="background-color:#bbbbff; text-align:center;" colspan="5"|'''3D Rotopes'''
Line 56: Line 56:
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''1x1x1'''''
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''1x1x1'''''
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EEE'''
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EEE'''
-
|-
 
-
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Sphere]]'''
 
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(xyz)'''
 
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''3'''
 
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''3'''''
 
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ELL'''
 
|-
|-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Square pyramid]]'''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Square pyramid]]'''
Line 69: Line 63:
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EET'''
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EET'''
|-
|-
-
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Cylinder]]'''
+
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Sphere]]'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(xy)z'''
+
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(xyz)'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''21'''
+
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''3'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''2x1'''''
+
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''3'''''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ELE'''
+
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ELL'''
-
|-
+
-
|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="20%" style="background-color:#eeeeff; text-align:center;"|'''(21)'''
+
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''2#2'''''
+
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ELQ'''
+
-
|-
+
-
|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="20%" style="background-color:#ddddff; text-align:center;"|'''2<sup>1</sup>'''
+
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''2~0'''''
+
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ELT'''
+
|-
|-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Triangular prism]]'''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Triangular prism]]'''
Line 92: Line 74:
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''(1~0)x1'''''
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''(1~0)x1'''''
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ETE'''
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ETE'''
 +
|-
 +
|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="20%" style="background-color:#eeeeff; text-align:center;"|'''1<sup>2</sup>'''
 +
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''1~0~0'''''
 +
|valign="top" width="20%" 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]]'''
Line 99: Line 87:
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ETQ'''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ETQ'''
|-
|-
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Tetrahedron]]'''
+
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Cylinder]]'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''x<sup>yz</sup>'''
+
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(xy)z'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''1<sup>2</sup>'''
+
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''21'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''1~0~0'''''
+
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''2x1'''''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ETT'''
+
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ELE'''
 +
|-
 +
|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="20%" style="background-color:#ddddff; text-align:center;"|'''2<sup>1</sup>'''
 +
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''2~0'''''
 +
|valign="top" width="20%" 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:#eeeeff; text-align:center;"|'''((xy)z)'''
 +
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''(21)'''
 +
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''2#2'''''
 +
|valign="top" width="20%" 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="5"|'''4D Rotopes'''
Line 112: Line 112:
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''1x1x1x1'''''
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''1x1x1x1'''''
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EEEE'''
|valign="top" width="20%" 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:#eeeeff; text-align:center;"|'''xyz<sup>w</sup>'''
 +
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''111<sup>1</sup>'''
 +
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''(1x1x1)~0'''''
 +
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EEET'''
|-
|-
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Glome]]'''
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Glome]]'''
Line 119: Line 125:
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ELLL'''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ELLL'''
|-
|-
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Cubic pyramid]]'''
+
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Square pyramid prism]]'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''xyz<sup>w</sup>'''
+
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''xy<sup>z</sup>w'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''111<sup>1</sup>'''
+
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''11<sup>1</sup>1'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''(1x1x1)~0'''''
+
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''((1x1)~0)x1'''''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EEET'''
+
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EETE'''
 +
|-
 +
|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="20%" style="background-color:#eeeeff; text-align:center;"|'''11<sup>2</sup>'''
 +
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''(1x1)~0~0'''''
 +
|valign="top" width="20%" 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:#ddddff; text-align:center;"|'''(xy<sup>z</sup>w)'''
 +
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(11<sup>1</sup>1)'''
 +
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''((1x1)~0)#2'''''
 +
|valign="top" width="20%" 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:#ccccff; text-align:center;"|'''[[Spherinder]]'''
Line 130: Line 148:
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''3x1'''''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''3x1'''''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ELLE'''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ELLE'''
 +
|-
 +
|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="20%" style="background-color:#ddddff; text-align:center;"|'''3<sup>1</sup>'''
 +
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''3~0'''''
 +
|valign="top" width="20%" 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]]'''
Line 137: Line 161:
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ELLQ'''
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ELLQ'''
|-
|-
-
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Sphone]]'''
+
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Triangular diprism]]'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(xyz)<sup>w</sup>'''
+
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''x<sup>y</sup>zw'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''3<sup>1</sup>'''
+
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''1<sup>1</sup>11'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''3~0'''''
+
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''(1~0)x1x1'''''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ELLT'''
+
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ETEE'''
|-
|-
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Square pyramid prism]]'''
+
|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;"|'''xy<sup>z</sup>w'''
+
|valign="top" width="20%" 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;"|'''11<sup>1</sup>1'''
+
|valign="top" width="20%" 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;"|'''''((1x1)~0)x1'''''
+
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''((1~0) x1)~0'''''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EETE'''
+
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ETET'''
|-
|-
-
|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;"|'''[[Triangular diprismidal torus]]'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(xy<sup>z</sup>w)'''
+
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(x<sup>y</sup>zw)'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(11<sup>1</sup>1)'''
+
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(1<sup>1</sup>11)'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''((1x1)~0)#2'''''
+
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''2#((1~0) x1)'''''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''EETQ'''
+
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ETEQ'''
|-
|-
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Square dipyramid]]'''
+
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Tetrahedral prism]]'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''xy<sup>zw</sup>'''
+
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''x<sup>yz</sup>w'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''11<sup>2</sup>'''
+
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''1<sup>2</sup>1'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''(1x1)~0~0'''''
+
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''(1~0~0) x1'''''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EETT'''
+
|valign="top" width="20%" 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:#eeeeff; text-align:center;"|'''x<sup>yzw</sup>'''
 +
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''1<sup>3</sup>'''
 +
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''1~0~0~0'''''
 +
|valign="top" width="20%" style="background-color:#eeeeff; 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;"|'''(x<sup>yz</sup>w)'''
 +
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(1<sup>2</sup>1)'''
 +
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''2#(1~0~0)'''''
 +
|valign="top" width="20%" style="background-color:#ddddff; 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:#ddddff; text-align:center;"|'''(x<sup>y</sup>z)w'''
 +
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(1<sup>1</sup>1)1'''
 +
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''2#(1~0) x1'''''
 +
|valign="top" width="20%" 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;"|'''(x<sup>y</sup>z)<sup>w</sup>'''
 +
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(1<sup>1</sup>1)<sup>1</sup>'''
 +
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''(2#(1~0)) ~0'''''
 +
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ETQT'''
 +
|-
 +
|valign="top" width="20%" style="background-color:#ddddff; 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="20%" style="background-color:#eeeeff; text-align:center;"|'''((1<sup>1</sup>1)1)'''
 +
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''2#(2#(1~0))'''''
 +
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ETQQ'''
 +
|-
 +
|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="20%" 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="20%" 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:#eeeeff; text-align:center;"|'''(x<sup>y</sup>(zw))'''
 +
|valign="top" width="20%" 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="20%" style="background-color:#eeeeff; text-align:center;"|'''''Unknown'''''
|-
|-
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Cubinder]]'''
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Cubinder]]'''
Line 166: Line 232:
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''2x1x1'''''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''2x1x1'''''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ELEE'''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ELEE'''
-
|-
 
-
|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="20%" style="background-color:#eeeeff; text-align:center;"|'''(211)'''
 
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''2#3'''''
 
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ELEQ'''
 
|-
|-
|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]]'''
Line 179: Line 239:
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ELET'''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ELET'''
|-
|-
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Torinder]]'''
+
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Toracubinder]]'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''((xy)z)w'''
+
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''((xy)zw)'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''(21)1'''
+
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''(211)'''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''(2#2)x1'''''
+
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''2#3'''''
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ELQE'''
+
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ELEQ'''
-
|-
+
-
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Tetratorus]]'''
+
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(((xy)z)w)'''
+
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''((21)1)'''
+
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''(2#2)#2'''''
+
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ELQQ'''
+
-
|-
+
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Toroidal pyramid]]'''
+
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''((xy)z)<sup>w</sup>'''
+
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''(21)<sup>1</sup>'''
+
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''(2#2)~0'''''
+
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ELQT'''
+
|-
|-
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Coninder]]'''
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Coninder]]'''
Line 202: Line 250:
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''(2~0)x1'''''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''(2~0)x1'''''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ELTE'''
|valign="top" width="20%" 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;"|'''(xy)<sup>zw</sup>'''
 +
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''2<sup>2</sup>'''
 +
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''2~0~0'''''
 +
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ELTT'''
|-
|-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Conindral torus]]'''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Conindral torus]]'''
Line 209: Line 263:
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ELTQ'''
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ELTQ'''
|-
|-
-
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Circular dipyramid]]'''
+
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Torinder]]'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(xy)<sup>zw</sup>'''
+
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''((xy)z)w'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''2<sup>2</sup>'''
+
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''(21)1'''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''2~0~0'''''
+
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''(2#2)x1'''''
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ELTT'''
+
|valign="top" width="20%" 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:#eeeeff; text-align:center;"|'''((xy)z)<sup>w</sup>'''
 +
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''(21)<sup>1</sup>'''
 +
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''(2#2)~0'''''
 +
|valign="top" width="20%" style="background-color:#eeeeff; 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;"|'''(((xy)z)w)'''
 +
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''((21)1)'''
 +
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''(2#2)#2'''''
 +
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ELQQ'''
|-
|-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Duocylinder]]'''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Duocylinder]]'''
Line 226: Line 292:
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''(2x2)#2'''''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''(2x2)#2'''''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''Unknown'''''
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''Unknown'''''
-
|-
 
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Triangular diprism]]'''
 
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''x<sup>y</sup>zw'''
 
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''1<sup>1</sup>11'''
 
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''(1~0)x1x1'''''
 
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ETEE'''
 
-
|-
 
-
|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="20%" style="background-color:#ddddff; text-align:center;"|'''(1<sup>1</sup>11)'''
 
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''2#((1~0) x1)'''''
 
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ETEQ'''
 
-
|-
 
-
|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="20%" 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;"|'''''((1~0) x1)~0'''''
 
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ETET'''
 
-
|-
 
-
|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="20%" style="background-color:#ddddff; text-align:center;"|'''(1<sup>1</sup>1)1'''
 
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''2#(1~0) x1'''''
 
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ETQE'''
 
-
|-
 
-
|valign="top" width="20%" style="background-color:#ddddff; 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="20%" style="background-color:#eeeeff; text-align:center;"|'''((1<sup>1</sup>1)1)'''
 
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''2#(2#(1~0))'''''
 
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ETQQ'''
 
-
|-
 
-
|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;"|'''(x<sup>y</sup>z)<sup>w</sup>'''
 
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(1<sup>1</sup>1)<sup>1</sup>'''
 
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''(2#(1~0)) ~0'''''
 
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ETQT'''
 
-
|-
 
-
|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="20%" style="background-color:#eeeeff; text-align:center;"|'''1<sup>2</sup>1'''
 
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''(1~0~0) x1'''''
 
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ETTE'''
 
-
|-
 
-
|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Tetrahedral torus]]'''
 
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(x<sup>yz</sup>w)'''
 
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''(1<sup>2</sup>1)'''
 
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''2#(1~0~0)'''''
 
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''ETTQ'''
 
-
|-
 
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Pentachoron]]'''
 
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''x<sup>yzw</sup>'''
 
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''1<sup>3</sup>'''
 
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''1~0~0~0'''''
 
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ETTT'''
 
|}
|}
[[Category:Rotopes|*]]
[[Category:Rotopes|*]]

Revision as of 21:38, 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 Group Notation Digit Notation Product Notation CSG Notation
1D Rotopes
Line x 1 1 E
2D Rotopes
Square xy 11 1x1 EE
Triangle xy 11 1~0 ET
Circle (xy) 2 2 EL
3D Rotopes
Cube xyz 111 1x1x1 EEE
Square pyramid xyz 111 (1x1)~0 EET
Sphere (xyz) 3 3 ELL
Triangular prism xyz 111 (1~0)x1 ETE
Tetrahedron xyz 12 1~0~0 ETT
Triangular torus (xyz) (111) 2#(1~0) ETQ
Cylinder (xy)z 21 2x1 ELE
Cone (xy)z 21 2~0 ELT
Torus ((xy)z) (21) 2#2 ELQ
4D Rotopes
Tesseract xyzw 1111 1x1x1x1 EEEE
Cubic pyramid xyzw 1111 (1x1x1)~0 EEET
Glome (xyzw) 4 4 ELLL
Square pyramid prism xyzw 1111 ((1x1)~0)x1 EETE
Square dipyramid xyzw 112 (1x1)~0~0 EETT
Square pyramid torus (xyzw) (1111) ((1x1)~0)#2 EETQ
Spherinder (xyz)w 31 3x1 ELLE
Sphone (xyz)w 31 3~0 ELLT
Toraspherinder ((xyz)w) (31) 3#2 ELLQ
Triangular diprism xyzw 1111 (1~0)x1x1 ETEE
Triangular prismidal pyramid xyzw 1111 ((1~0) x1)~0 ETET
Triangular diprismidal torus (xyzw) (1111) 2#((1~0) x1) ETEQ
Tetrahedral prism xyzw 121 (1~0~0) x1 ETTE
Pentachoron xyzw 13 1~0~0~0 ETTT
Tetrahedral torus (xyzw) (121) 2#(1~0~0) ETTQ
Triangular toroidal prism (xyz)w (111)1 2#(1~0) x1 ETQE
Triangular toroidal pyramid (xyz)w (111)1 (2#(1~0)) ~0 ETQT
Triangular ditorus ((xyz)w) ((111)1) 2#(2#(1~0)) ETQQ
Unknown shape xy(zw) 112 Unknown Unknown
Unknown shape (xy(zw)) (112) Unknown Unknown
Cubinder (xy)zw 211 2x1x1 ELEE
Cylindrical pyramid (xy)zw 211 (2x1)~0 ELET
Toracubinder ((xy)zw) (211) 2#3 ELEQ
Coninder (xy)zw 211 (2~0)x1 ELTE
Circular dipyramid (xy)zw 22 2~0~0 ELTT
Conindral torus ((xy)zw) (211) 2#(2~0) ELTQ
Torinder ((xy)z)w (21)1 (2#2)x1 ELQE
Toroidal pyramid ((xy)z)w (21)1 (2#2)~0 ELQT
Tetratorus (((xy)z)w) ((21)1) (2#2)#2 ELQQ
Duocylinder (xy)(zw) 22 2x2 EL*EL
Tiger ((xy)(zw)) (22) (2x2)#2 Unknown
Retrieved from "http://hi.gher.space/wiki/Rotope"

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