Rotope (EntityClass, 3)

From Hi.gher. Space

(Difference between revisions)
(Table of rotopes: fix shading, add rotopical index)
m (Table of rotopes: rotopical -> rotopic (rm double suffix))
Line 16: Line 16:
{|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="16%" style="background-color:#eeeeff; text-align:center;"|'''[[Rotopical index]]'''
+
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''[[Rotopic index]]'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''[[Group notation]]'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''[[Group notation]]'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''[[Digit notation]]'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''[[Digit notation]]'''

Revision as of 22:21, 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 Rotopic 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

Pages in this category (4)