Table of kanichora (Meta, 11)

From Hi.gher. Space

(Difference between revisions)

Revision as of 18:30, 24 August 2012

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
Dx	Coxeter- Dynkin	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

@@ Line 34: / Line 34: @@
 |8||ooox||---||---||Dual||&nbsp;||[[Pyrochoron|(Kp1)]]||[[Aerochoron|Ke8]]||[[Xylochoron|(Kk1)]]||[[Hydrochoron|Ks8]]
 |-
-|9||xoox||Runcinate||---||Runcinate||Rect,rect||[[Runcinated 5-cell|Kp9]]||[[Runcinated 8-cell|Ke9]]||[[Runcinated 24-cell|Kk9]]||[[Runcinated 120-cell|Ks9]]
+|9||xoox||Runcinate||---||Runcinate||Rect,rect||[[Pyroperichoron|Kp9]]||[[Stauroperichoron|Ke9]]||[[Xyloperichoron|Kk9]]||[[Rhodoperichoron|Ks9]]
 |-
 |10||oxox||---||---||Dual,cantel||&nbsp;||[[Cantellated 5-cell|(Kp5)]]||[[3-xylotomochoron|''(Kk2)'']]||[[Cantellated 24-cell|(Kk5)]]||[[Cantellated 600-cell|Ks10]]