Table of kanihedra (Meta, 11)
From Hi.gher. Space
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This table shows the three-dimensional [[kanitope]]s arranged by their [[polytope family|family]] and [[Dx number]]. | This table shows the three-dimensional [[kanitope]]s arranged by their [[polytope family|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. | + | Forms enclosed in parentheses are non-canonical forms, which duplicate other cells of the table. In 3D, this only occurs in the tetrahedral family, due both to it being [[self-dual]] and to the tetrahedron being equivalent to the [[Demihypercube|demicube]]. |
{|cellpadding="2" cellspacing="1" | {|cellpadding="2" cellspacing="1" | ||
Revision as of 16:33, 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, due both to it being self-dual and to the tetrahedron being equivalent to the demicube.
| 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 |
