Table of kanichora (Meta, 11)
From Hi.gher. Space
(Difference between revisions)
Revision as of 16:32, 9 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 |