List of rotopes (no ontology)
From Hi.gher. Space
This is a list of rotopes in dimensions from zero to four.
| 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 segment | 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 pyramidal prism | 17 | xyzw | 1111 | ((1x1)~0)x1 | EETE |
| Square dipyramid | 18 | xyzw | 112 | (1x1)~0~0 | EETT |
| Square pyramidal torus | 19 | (xyzw) | (1111) | ((1x1)~0)#2 | EETQ |
| Spherinder | 20 | (xyz)w | 31 | 3x1 | ELLE |
| Sphone | 21 | (xyz)w | 31 | 3~0 | ELLT |
| Torisphere | 22 | ((xyz)w) | (31) | 3#2 | ELLQ |
| Triangular diprism | 23 | xyzw | 1111 | (1~0)x1x1 | ETEE |
| Triangular prismic pyramid | 24 | xyzw | 1111 | ((1~0) x1)~0 | ETET |
| Triangular prismic 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 toric prism | 29 | (xyz)w | (111)1 | 2#(1~0) x1 | ETQE |
| Triangular toric pyramid | 30 | (xyz)w | (111)1 | (2#(1~0)) ~0 | ETQT |
| Triangular ditorus | 31 | ((xyz)w) | ((111)1) | 2#(2#(1~0)) | ETQQ |
| Cyltrianglinder | 32 | xy(zw) | 112 | Unknown | Unknown |
| Cyltrianglintigroid | 33 | (xy(zw)) | (112) | Unknown | Unknown |
| Cubinder | 34 | (xy)zw | 211 | 2x1x1 | ELEE |
| Cylindrical pyramid | 35 | (xy)zw | 211 | (2x1)~0 | ELET |
| Spheritorus | 36 | ((xy)zw) | (211) | 2#3 | ELEQ |
| Coninder | 37 | (xy)zw | 211 | (2~0)x1 | ELTE |
| Dicone | 38 | (xy)zw | 22 | 2~0~0 | ELTT |
| Conic torus | 39 | ((xy)zw) | (211) | 2#(2~0) | ELTQ |
| Torinder | 40 | ((xy)z)w | (21)1 | (2#2)x1 | ELQE |
| Toric pyramid | 41 | ((xy)z)w | (21)1 | (2#2)~0 | ELQT |
| Ditorus | 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 |
