Table of kanichora (Meta, 11)
From Hi.gher. Space
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|5||xoxo||Cantellate||sm Rhombi-||Cantellate|| ||[[Cantellated 5-cell|Kp5]]||[[Cantellated 8-cell|Ke5]]||[[Cantellated 24-cell|Kk5]]||[[Cantellated 120-cell|Ks5]] | |5||xoxo||Cantellate||sm Rhombi-||Cantellate|| ||[[Cantellated 5-cell|Kp5]]||[[Cantellated 8-cell|Ke5]]||[[Cantellated 24-cell|Kk5]]||[[Cantellated 120-cell|Ks5]] | ||
|- | |- | ||
| - | |6||oxxo||Bitruncate||---||Rectate|| ||[[Pyromesochoron|Kp6]]||[[ | + | |6||oxxo||Bitruncate||---||Rectate|| ||[[Pyromesochoron|Kp6]]||[[Stauromesochoron|Ke6]]||[[Xylomesochoron|Kk6]]||[[Rhodomesochoron|Ks6]] |
|- | |- | ||
|7||xxxo||Cantitruncate||gr Rhombi-||Cantitruncate|| ||[[Cantitruncated 5-cell|Kp7]]||[[Cantitruncated 8-cell|Ke7]]||[[Cantitruncated 24-cell|Kk7]]||[[Cantitruncated 120-cell|Ks7]] | |7||xxxo||Cantitruncate||gr Rhombi-||Cantitruncate|| ||[[Cantitruncated 5-cell|Kp7]]||[[Cantitruncated 8-cell|Ke7]]||[[Cantitruncated 24-cell|Kk7]]||[[Cantitruncated 120-cell|Ks7]] | ||
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|14||oxxx||---||---||Dual,cantic|| ||[[Cantitruncated 5-cell|(Kp7)]]||[[2-xylotomochoron|''(Kk3)'']]||[[Cantitruncated 24-cell|(Kk7)]]||[[Cantitruncated 600-cell|Ks14]] | |14||oxxx||---||---||Dual,cantic|| ||[[Cantitruncated 5-cell|(Kp7)]]||[[2-xylotomochoron|''(Kk3)'']]||[[Cantitruncated 24-cell|(Kk7)]]||[[Cantitruncated 600-cell|Ks14]] | ||
|- | |- | ||
| - | |15||xxxx||Omnitruncate||---||Omnitruncate||Rect,trunc||[[Pyropantomochoron|Kp15]]||[[ | + | |15||xxxx||Omnitruncate||---||Omnitruncate||Rect,trunc||[[Pyropantomochoron|Kp15]]||[[Stauropantomochoron|Ke15]]||[[Xylopantomochoron|Kk15]]||[[Rhodopantomochoron|Ks15]] |
|- | |- | ||
|0||oooo||Snub||Snub||Snub|| || | |0||oooo||Snub||Snub||Snub|| || | ||
Revision as of 11:47, 11 March 2011
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.
| Dx | Coxeter- Dynkin | Variance group | Polychoric group | ||||||
|---|---|---|---|---|---|---|---|---|---|
| Standard | Krieger | Conventional | Alt. conv. | Pentachoric | Hexadecachoric | Icositetrachoric | Hexacosichoric | ||
| 1 | xooo | Parent | Parent | Parent | Kp1 | Ke1 | Kk1 | Ks1 | |
| 2 | oxoo | Rectate | Rectate | Hemicate | Kp2 | Ke2 | Kk2 | Ks2 | |
| 3 | xxoo | Truncate | Truncate | Truncate | Kp3 | Ke3 | Kk3 | Ks3 | |
| 4 | ooxo | --- | --- | Dual,hemic | (Kp2) | (Kk1) | (Kk2) | Ks4 | |
| 5 | xoxo | Cantellate | sm Rhombi- | Cantellate | Kp5 | Ke5 | Kk5 | Ks5 | |
| 6 | oxxo | Bitruncate | --- | Rectate | Kp6 | Ke6 | Kk6 | Ks6 | |
| 7 | xxxo | Cantitruncate | gr Rhombi- | Cantitruncate | Kp7 | Ke7 | Kk7 | Ks7 | |
| 8 | ooox | --- | --- | Dual | (Kp1) | Ke8 | (Kk1) | Ks8 | |
| 9 | xoox | Runcinate | --- | Runcinate | Rect,rect | Kp9 | Ke9 | Kk9 | Ks9 |
| 10 | oxox | --- | --- | Dual,cantel | (Kp5) | (Kk2) | (Kk5) | Ks10 | |
| 11 | xxox | Runcitruncate | --- | Runcitruncate | Kp11 | Ke11 | Kk11 | Ks11 | |
| 12 | ooxx | --- | --- | Dual,trunc | (Kp3) | Ke12 | (Kk3) | Ks12 | |
| 13 | xoxx | --- | Prismatorh | Dual,runcic | (Kp11) | Ke13 | (Kk11) | Ks13 | |
| 14 | oxxx | --- | --- | Dual,cantic | (Kp7) | (Kk3) | (Kk7) | Ks14 | |
| 15 | xxxx | Omnitruncate | --- | Omnitruncate | Rect,trunc | Kp15 | Ke15 | Kk15 | Ks15 |
| 0 | oooo | Snub | Snub | Snub | |||||
