Table of kanichora (Meta, 11)
From Hi.gher. Space
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Forms enclosed in parentheses are non-canonical forms, which duplicate other cells of the table. In 4D, this occurs in the pentachoric and icositetrachoric families due to them being [[self-dual]], and in the hexadecachoric family due to the hexadecachoron being equivalent to the [[Demihypercube|demitesseract]]. | Forms enclosed in parentheses are non-canonical forms, which duplicate other cells of the table. In 4D, this occurs in the pentachoric and icositetrachoric families due to them being [[self-dual]], and in the hexadecachoric family due to the hexadecachoron being equivalent to the [[Demihypercube|demitesseract]]. | ||
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+ | Variants enclosed in parentheses indicate it is a variant of the dual, rather than a variant of the parent. | ||
{|cellpadding="2" cellspacing="1" | {|cellpadding="2" cellspacing="1" | ||
!bgcolor="#E0E0E0" rowspan="2" width="5%"|[[Dx]] | !bgcolor="#E0E0E0" rowspan="2" width="5%"|[[Dx]] | ||
!bgcolor="#E0E0E0" rowspan="2" width="10%"|[[Coxeter-Dynkin|Coxeter-<br>Dynkin]] | !bgcolor="#E0E0E0" rowspan="2" width="10%"|[[Coxeter-Dynkin|Coxeter-<br>Dynkin]] | ||
- | !bgcolor="#E0E0E0" rowspan="2" width="15%"|[[ | + | !bgcolor="#E0E0E0" rowspan="2" width="15%"|[[Variant]] |
!bgcolor="#E0E0E0" colspan="4" width="70%"|[[Symmetry group]] | !bgcolor="#E0E0E0" colspan="4" width="70%"|[[Symmetry group]] | ||
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Revision as of 08:00, 11 February 2014
This table shows the four-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 4D, this occurs in the pentachoric and icositetrachoric families due to them being self-dual, and in the hexadecachoric family due to the hexadecachoron being equivalent to the demitesseract.
Variants enclosed in parentheses indicate it is a variant of the dual, rather than a variant of the parent.
Dx | Coxeter- Dynkin | Variant | Symmetry group | |||
---|---|---|---|---|---|---|
Pyrochoric | Staurochoric | Xylochoric | Rhodochoric | |||
1 | xooo | Parent | x3o3o3o | x4o3o3o | x3o4o3o | x5o3o3o |
2 | oxoo | Rectate | o3x3o3o | o4x3o3o | o3x4o3o | o5x3o3o |
3 | xxoo | Truncate | x3x3o3o | x4x3x3o | x3x4o3o | x5x3o3o |
4 | ooxo | (Rectate) | (o3x3o3o) | (x3o4o3o) | (o3x4o3o) | o3x3o5o |
5 | xoxo | Cantellate | x3o3x3o | x4o3x3o | x3o4x3o | x5o3x3o |
6 | oxxo | Mesotope | o3x3x3o | o4x3x3o | o3x4x3o | o5x3x3o |
7 | xxxo | Cantitruncate | x3x3x3o | x4x3x3o | x3x4x3o | x5x3x3o |
8 | ooox | Dual | (x3o3o3o) | x3o3o4x | (x3o4o3o) | x3o3o5o |
9 | xoox | Peritope | x3o3o3x | x4o3o3x | x3o4o3x | x5o3o3x |
10 | oxox | (Cantellate) | (x3o3x3o) | (o3x4o3o) | (x3o4x3o) | x3o3x5o |
11 | xxox | Runcitruncate | x3x3o3x | x4x3o3x | x3x4o3x | x5x3o3x |
12 | ooxx | (Truncate) | (x3x3o3o) | x3x3o4o | (x3x4o3o) | x3x3o5o |
13 | xoxx | (Runcitruncate) | (x3x3o3x) | x3x3o4x | (x3x4o3x) | x3x3o5x |
14 | oxxx | (Cantitruncate) | (x3x3x3o) | (x3x4o3o) | (x3x4x3o) | x3x3x5o |
15 | xxxx | Pantome | x3x3x3x | x4x3x3x | x3x4x3x | x5x3x3x |