Table of kanihedra (Meta, 11)
From Hi.gher. Space
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|width="80"|1||xoo||Parent||Parent||[[Tetrahedron|Kt1]]||[[Cube|Ko1]]||[[Dodecahedron|Ki1]] | |width="80"|1||xoo||Parent||Parent||[[Tetrahedron|Kt1]]||[[Cube|Ko1]]||[[Dodecahedron|Ki1]] | ||
|- | |- | ||
| - | |width="80"|2||oxo||Rectate||Rectate||[[Octahedron|( | + | |width="80"|2||oxo||Rectate||Rectate||[[Octahedron|''(Ko4)'']]||[[Cuboctahedron|Ko2]]||[[Icosidodecahedron|Ki2]] |
|- | |- | ||
|width="80"|3||xxo||Truncate||Truncate||[[Tetrahedral truncate|Kt3]]||[[Cubic truncate|Ko3]]||[[Dodecahedral truncate|Ki3]] | |width="80"|3||xxo||Truncate||Truncate||[[Tetrahedral truncate|Kt3]]||[[Cubic truncate|Ko3]]||[[Dodecahedral truncate|Ki3]] | ||
|- | |- | ||
| - | |width="80"|4||oox||Birectate||Dual||[[Tetrahedron|( | + | |width="80"|4||oox||Birectate||Dual||[[Tetrahedron|(Kt1)]]||[[Octahedron|Ko4]]||[[Icosahedron|Ki4]] |
|- | |- | ||
| - | |width="80"|5||xox||Cantellate||Rect,rect||[[Cuboctahedron|( | + | |width="80"|5||xox||Cantellate||Rect,rect||[[Cuboctahedron|''(Ko2)'']]||[[Cuboctahedral rectate|Ko5]]||[[Icosidodecahedral rectate|Ki5]] |
|- | |- | ||
| - | |width="80"|6||oxx||Bitruncate||Dual,trunc||[[Tetrahedral truncate|( | + | |width="80"|6||oxx||Bitruncate||Dual,trunc||[[Tetrahedral truncate|(Kt3)]]||[[Octahedral truncate|Ko6]]||[[Icosahedral truncate|Ki6]] |
|- | |- | ||
| - | |width="80"|7||xxx||Omnitruncate||Rect,trunc||[[Octahedral truncate|( | + | |width="80"|7||xxx||Omnitruncate||Rect,trunc||[[Octahedral truncate|''(Ko6)'']]||[[Cuboctahedral truncate|Ko7]]||[[Icosidodecahedral truncate|Ki7]] |
|- | |- | ||
| - | |width="80"|0||ooo||Snub||Snub||[[Icosahedron|( | + | |width="80"|0||ooo||Snub||Snub||[[Icosahedron|''(Ki4)'']]||[[Cubic snub|Ko0]]||[[Dodecahedral snub|Ki0]] |
|} | |} | ||
[[Category:Uniform polyhedra|$]] | [[Category:Uniform polyhedra|$]] | ||
Revision as of 16:29, 9 March 2011
This table shows the three-dimensional kanitopes arranged by their family and Dx number.
Forms enclosed in parentheses are non-canonical forms, which duplicate other cells of the table. In 3D, this only occurs in the tetrahedral family.
| Dx | Coxeter- Dynkin | Variance group | Polyhedral family | |||
|---|---|---|---|---|---|---|
| Standard | Conventional | Tetrahedral | Octahedral | Icosahedral | ||
| 1 | xoo | Parent | Parent | Kt1 | Ko1 | Ki1 |
| 2 | oxo | Rectate | Rectate | (Ko4) | Ko2 | Ki2 |
| 3 | xxo | Truncate | Truncate | Kt3 | Ko3 | Ki3 |
| 4 | oox | Birectate | Dual | (Kt1) | Ko4 | Ki4 |
| 5 | xox | Cantellate | Rect,rect | (Ko2) | Ko5 | Ki5 |
| 6 | oxx | Bitruncate | Dual,trunc | (Kt3) | Ko6 | Ki6 |
| 7 | xxx | Omnitruncate | Rect,trunc | (Ko6) | Ko7 | Ki7 |
| 0 | ooo | Snub | Snub | (Ki4) | Ko0 | Ki0 |
