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
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 1: / Line 1: @@
-This is a '''table of [[uniform polychora]]''' by their [[Kana mnemonic]].
+This table shows the four-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 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]].
 {|cellpadding="2" cellspacing="1"
@@ Line 5: / Line 7: @@
 !bgcolor="#E0E0E0" rowspan="2" width="80"|[[Coxeter-Dynkin|Coxeter-<br>Dynkin]]
 !bgcolor="#E0E0E0" colspan="4" width="40%"|[[Variance group]]
-!bgcolor="#E0E0E0" rowspan="2"|Form
 !bgcolor="#E0E0E0" colspan="4" width="40%"|[[Polychoric group]]
 |-
@@ Line 17: / Line 18: @@
 !bgcolor="#E0E0E0"|Hexacosichoric
 |-
-|1||xooo||Parent||Parent||Parent||&nbsp;||-||[[ﾍﾟﾝ]] pen||[[ﾃｽ]] tesu||[[ｺｼ]] koshi||[[ﾍｶ]] heka
+|1||xooo||Parent||Parent||Parent||&nbsp;||[[Pyrochoron|Kp1]]||[[Geochoron|Ke1]]||[[Xylochoron|Kk1]]||[[Cosmochoron|Ks1]]
 |-
-|2||oxoo||Rectate||Rectate||Hemicate||&nbsp;||-ﾐ -mi||[[ﾍﾟﾝﾐ]] penmi||[[ﾃｽﾐ]] tesumi||[[ｺｼﾐ]] koshimi||[[ﾍｶﾐ]] hekami
+|2||oxoo||Rectate||Rectate||Hemicate||&nbsp;||[[3-pyrotomochoron|Kp2]]||[[3-geotomochoron|Ke2]]||[[3-xylotomochoron|Kk2]]||[[3-cosmotomochoron|Ks2]]
 |-
-|3||xxoo||Truncate||Truncate||Truncate||&nbsp;||-ﾄ -to||[[ﾍﾟﾝﾄ]] pento||[[ﾃｽﾄ]] tesuto||[[ｺｼﾄ]] koshito||[[ﾍｶﾄ]] hekato
+|3||xxoo||Truncate||Truncate||Truncate||&nbsp;||[[2-pyrotomochoron|Kp3]]||[[2-geotomochoron|Ke3]]||[[2-xylotomochoron|Kk3]]||[[2-cosmotomochoron|Ks3]]
 |-
-|4||ooxo||---||---||Dual,hemic||&nbsp;||~ﾐ ~mi||([[ﾍﾟﾝﾐ]] penmi)||([[ｺｼ]] koshi)||([[ｺｼﾐ]] koshimi)||[[ｻｺﾐ]] sakomi
+|4||ooxo||---||---||Dual,hemic||&nbsp;||[[3-pyrotomochoron|(Kp2)]]||[[Xylochoron|''(Kk1)'']]||[[3-xylotomochoron|(Kk2)]]||[[3-hydrotomochoron|Ks4]]
 |-
-|5||xoxo||Cantellate||sm Rhombi-||Cantellate||&nbsp;||-ｶ -ka||[[ﾍﾟﾝｶ]] penka||[[ﾃｽｶ]] tesuka||[[ｺｼｶ]] koshika||[[ﾍｶｶ]] hekaka
+|5||xoxo||Cantellate||sm Rhombi-||Cantellate||&nbsp;||[[Cantellated 5-cell|Kp5]]||[[Cantellated 8-cell|Ke5]]||[[Cantellated 24-cell|Kk5]]||[[Cantellated 120-cell|Ks5]]
 |-
-|6||oxxo||Bitruncate||---||Rectate||&nbsp;||-ﾚ/* -re/*||[[ﾍﾟﾝﾚ]] penre||[[ｴｽ]] esu||[[ｺｼﾚ]] koshire||[[ｻｶ]] saka
+|6||oxxo||Bitruncate||---||Rectate||&nbsp;||[[Pyromesochoron|Kp6]]||[[Geomesochoron|Ke6]]||[[Xylomesochoron|Kk6]]||[[Cosmomesochoron|Ks6]]
 |-
-|7||xxxo||Cantitruncate||gr Rhombi-||Cantitruncate||&nbsp;||-ﾄｶ -toka||[[ﾍﾟﾝﾄｶ]] pentoka||[[ﾃｽﾄｶ]] tesutoka||[[ｺｼﾄｶ]] koshitoka||[[ﾍｶﾄｶ]] hekatoka
+|7||xxxo||Cantitruncate||gr Rhombi-||Cantitruncate||&nbsp;||[[Cantitruncated 5-cell|Kp7]]||[[Cantitruncated 8-cell|Ke7]]||[[Cantitruncated 24-cell|Kk7]]||[[Cantitruncated 120-cell|Ks7]]
 |-
-|8||ooox||---||---||Dual||&nbsp;||~||([[ﾍﾟﾝ]] pen)||[[ｴｸ]] eku||([[ｺｼ]] koshi)||[[ｻｺ]] sako
+|8||ooox||---||---||Dual||&nbsp;||[[Pyrochoron|(Kp1)]]||[[Aerochoron|Ke8]]||[[Xylochoron|(Kk1)]]||[[Hydrochoron|Ks8]]
 |-
-|9||xoox||Runcinate||---||Runcinate||Rect,rect||-ｷﾚ/*ﾚ -kire/*re||[[ﾍﾟﾝｷﾚ]] penkire||[[ｴｽﾚ]] esure||[[ｺｼｷﾚ]] koshikire||[[ｻｶﾚ]] sakare
+|9||xoox||Runcinate||---||Runcinate||Rect,rect||[[Runcinated 5-cell|Kp9]]||[[Runcinated 8-cell|Ke9]]||[[Runcinated 24-cell|Kk9]]||[[Runcinated 120-cell|Ks9]]
 |-
-|10||oxox||---||---||Dual,cantel||&nbsp;||~ｶ ~ka||([[ﾍﾟﾝｶ]] penka)||([[ｺｼﾐ]] koshimi)||([[ｺｼｶ]] koshika)||[[ｻｺｶ]] sakoka
+|10||oxox||---||---||Dual,cantel||&nbsp;||[[Cantellated 5-cell|(Kp5)]]||[[3-xylotomochoron|''(Kk2)'']]||[[Cantellated 24-cell|(Kk5)]]||[[Cantellated 600-cell|Ks10]]
 |-
-|11||xxox||Runcitruncate||---||Runcitruncate||&nbsp;||-ﾄﾙ -toru||[[ﾍﾟﾝﾄﾙ]] pentoru||[[ﾃｽﾄﾙ]] tesutoru||[[ｺｼﾄﾙ]] koshitoru||[[ﾍｶﾄﾙ]] hekatoru
+|11||xxox||Runcitruncate||---||Runcitruncate||&nbsp;||[[Runcitruncated 5-cell|Kp11]]||[[Runcitruncated 8-cell|Ke11]]||[[Runcitruncated 24-cell|Kk11]]||[[Runcitruncated 120-cell|Ks11]]
 |-
-|12||ooxx||---||---||Dual,trunc||&nbsp;||~ﾄ ~to||([[ﾍﾟﾝﾄ]] pento)||[[ｴｸﾄ]] ekuto||([[ｺｼﾄ]] koshito)||[[ｻｺﾄ]] sakoto
+|12||ooxx||---||---||Dual,trunc||&nbsp;||[[2-pyrotomochoron|(Kp3)]]||[[2-aerotomochoron|Ke12]]||[[2-xylotomochoron|(Kk3)]]||[[2-hydrotomochoron|Ks12]]
 |-
-|13||xoxx||---||Prismatorh||Dual,runcic||&nbsp;||~ﾄﾙ ~toru||([[ﾍﾟﾝﾄﾙ]] pentoru)||[[ｴｸﾄﾙ]] ekutoru||([[ｺｼﾄﾙ]] koshitoru)||[[ｻｺﾄﾙ]] sakotoru
+|13||xoxx||---||Prismatorh||Dual,runcic||&nbsp;||[[Runcitruncated 5-cell|(Kp11)]]||[[Runcitruncated 16-cell|Ke13]]||[[Runcitruncated 24-cell|(Kk11)]]||[[Runcitruncated 600-cell|Ks13]]
 |-
-|14||oxxx||---||---||Dual,cantic||&nbsp;||~ﾄｶ ~toka||([[ﾍﾟﾝﾄｶ]] pentoka)||([[ｺｼﾄ]] koshito)||([[ｺｼﾄｶ]] koshitoka)||[[ｻｺﾄｶ]] sakotoka
+|14||oxxx||---||---||Dual,cantic||&nbsp;||[[Cantitruncated 5-cell|(Kp7)]]||[[2-xylotomochoron|''(Kk3)'']]||[[Cantitruncated 24-cell|(Kk7)]]||[[Cantitruncated 600-cell|Ks14]]
 |-
-|15||xxxx||Omnitruncate||---||Omnitruncate||Rect,trunc||*ﾄ *to||[[ﾍﾟﾝﾚﾄ]] penreto||[[ｴｽﾄ]] esuto||[[ｺｼﾚﾄ]] koshireto||[[ｻｶﾄ]] sakato
+|15||xxxx||Omnitruncate||---||Omnitruncate||Rect,trunc||[[Pyropantomochoron|Kp15]]||[[Geopantomochoron|Ke15]]||[[Xylopantomochoron|Kk15]]||[[Cosmopantomochoron|Ks15]]
 |-
-|0||oooo||Snub||Snub||Snub||&nbsp;||-ｽ -su||---||---||[[ｺｼｽ]] koshisu||---
+|0||oooo||Snub||Snub||Snub||&nbsp;||
 |}
-;Form syntax
-* "-" means the parent mneumonic
-* "*" means the rectate mneumonic
-* "~" means the dual mneumonic
-* Where "/" separates two forms, self-duals take the left form and non-self-duals take the right form.
 [[Category:Uniform polychora|$]]