Table of kanichora (Meta, 11)

From Hi.gher. Space

(Difference between revisions)

Latest revision as of 08:11, 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 pyrochoric and xylochoric families due to them being self-dual, and in the aerochoric family due to the aerochoron 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
Dx	Coxeter- Dynkin	Variant	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

@@ Line 1: / Line 1: @@
-This is a '''table of [[uniform polychora]]''' by their [[Kana mnemonic]].
+<[#ontology [kind meta] [cats 4D Uniform Polytope]]>
+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 pyrochoric and xylochoric families due to them being [[self-dual]], and in the aerochoric family due to the aerochoron being equivalent to the [[Demihypercube|demitesseract]].
-|[[Dx]]||width="80"|1||width="80"|2||width="80"|3||width="80"|4||width="80"|5||width="80"|6||width="80"|7||width="80"|8||width="80"|9||width="80"|10||width="80"|11||width="80"|12||width="80"|13||width="80"|14||width="80"|15||width="80"|0
+Variants enclosed in parentheses indicate it is a variant of the dual, rather than a variant of the parent.
+{|cellpadding="2" cellspacing="1"
+!bgcolor="#E0E0E0" rowspan="2" width="5%"|[[Dx]]
+!bgcolor="#E0E0E0" rowspan="2" width="10%"|[[Coxeter-Dynkin|Coxeter-<br>Dynkin]]
+!bgcolor="#E0E0E0" rowspan="2" width="15%"|[[Variant]]
+!bgcolor="#E0E0E0" colspan="4" width="70%"|[[Symmetry group]]
 |-
-|Cox-Dyn||xooo||oxoo||xxoo||ooxo||xoxo||oxxo||xxxo||ooox||xoox||oxox||xxox||ooxx||xoxx||oxxx||xxxx||oooo
+!bgcolor="#E0E0E0"|Pyrochoric
+!bgcolor="#E0E0E0"|Staurochoric
+!bgcolor="#E0E0E0"|Xylochoric
+!bgcolor="#E0E0E0"|Rhodochoric
 |-
-|Group (standard)||Parent||Rectate||Truncate||---||Cantellate||Bitruncate||Cantitruncate||---||Runcinate||---||Runcitruncate||---||---||---||Omnitruncate||Snub
+|1||xooo||Parent||[[Pyrochoron|x3o3o3o]]||[[Geochoron|x4o3o3o]]||[[Xylochoron|x3o4o3o]]||[[Cosmochoron|x5o3o3o]]
 |-
-|Group (Krieger)||Parent||Rectate||Truncate||---||sm Rhombi-||---||gr Rhombi-||---||---||---||---||---||Prismatorh||---||---||Snub
+|2||oxoo||[[Rectate]]||[[Pyrorectichoron|o3x3o3o]]||[[Georectichoron|o4x3o3o]]||[[Xylorectichoron|o3x4o3o]]||[[Cosmorectichoron|o5x3o3o]]
 |-
-|nowrap|Group (conventional)||Parent||Hemicate||Truncate||Dual,hemic||Omnihemate||Rectate||Canticate||Dual||Cantellate||Dual,omnihem||Runcicate||Dual,trunc||Dual,runcic||Dual,cantic||Omnitruncate||Snub
+|3||xxoo||[[Truncate]]||[[Pyrotomochoron|x3x3o3o]]||[[Geotomochoron|x4x3x3o]]||[[Xylotomochoron|x3x4o3o]]||[[Cosmotomochoron|x5x3o3o]]
-|Alternative conv.||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||Rect,rect||&nbsp;||&nbsp;||&nbsp;||&nbsp;||&nbsp;||Rect,trunc||&nbsp;
 |-
-|Form||-||-ﾐ -mi||-ﾄ -to||~ﾐ ~mi||-ﾆﾐ -nimi||-ﾚ/* -re/*||-ｶ -ka||~||-ｼﾞﾚ/*ﾚ -jire/*re||~ﾆﾐ ~nimi||-ﾙ -ru||~ﾄ ~to||~ﾙ ~ru||~ｶ ~ka||*ﾄ *to||-ｽ -su
+|4||ooxo||(Rectate)||[[Pyrorectichoron|(o3x3o3o)]]||[[Xylochoron|''(x3o4o3o)'']]||[[Xylorectichoron|(o3x4o3o)]]||[[Hydrorectichoron|o3x3o5o]]
 |-
-|Pentachoric||[[ﾍﾟﾝ]] pen||[[ﾍﾟﾝﾐ]] penmi||[[ﾍﾟﾝﾄ]] pento||([[ﾍﾟﾝﾐ]] penmi)||[[ﾍﾟﾝﾆﾐ]] pennimi||[[ﾍﾟﾝﾚ]] penre||[[ﾍﾟﾝｶ]] penka||([[ﾍﾟﾝ]] pen)||[[ﾍﾟﾝｼﾞﾚ]] penjire||([[ﾍﾟﾝﾆﾐ]] pennimi)||[[ﾍﾟﾝﾙ]] penru||([[ﾍﾟﾝﾄ]] pento)||([[ﾍﾟﾝﾙ]] penru)||([[ﾍﾟﾝｶ]] penka)||[[ﾍﾟﾝﾚﾄ]] penreto||---
+|5||xoxo||[[Cantellate]]||[[Pyrocantichoron|x3o3x3o]]||[[Geocantichoron|x4o3x3o]]||[[Xylocantichoron|x3o4x3o]]||[[Cosmocantichoron|x5o3x3o]]
 |-
-|Hexadecachoric||[[ﾃｽ]] tesu||[[ﾃｽﾐ]] tesumi||[[ﾃｽﾄ]] tesuto||([[ｺｼ]] koshi)||[[ﾃｽﾆﾐ]] tesunimi||[[ｴｽ]] esu||[[ﾃｽｶ]] tesuka||[[ｴｸ]] eku||[[ｴｽﾚ]] esure||([[ｺｼﾐ]] koshimi)||[[ﾃｽﾙ]] tesuru||[[ｴｸﾄ]] ekuto||[[ｴｸﾙ]] ekuru||([[ｺｼﾄ]] koshito)||[[ｴｽﾄ]] esuto||---
+|6||oxxo||[[Mesotope]]||[[Pyromesochoron|o3x3x3o]]||[[Stauromesochoron|o4x3x3o]]||[[Xylomesochoron|o3x4x3o]]||[[Rhodomesochoron|o5x3x3o]]
 |-
-|Icositetrachoric||[[ｺｼ]] koshi||[[ｺｼﾐ]] koshimi||[[ｺｼﾄ]] koshito||([[ｺｼﾐ]] koshimi)||[[ｺｼﾆﾐ]] koshinimi||[[ｺｼﾚ]] koshire||[[ｺｼｶ]] koshika||([[ｺｼ]] koshi)||[[ｺｼｼﾞﾚ]] koshijire||([[ｺｼﾆﾐ]] koshinimi)||[[ｺｼﾙ]] koshiru||([[ｺｼﾄ]] koshito)||([[ｺｼﾙ]] koshiru)||([[ｺｼｶ]] koshika)||[[ｺｼﾚﾄ]] koshireto||[[ｺｼｽ]] koshisu
+|7||xxxo||[[Cantitruncate]]||[[Pyrocantitomochoron|x3x3x3o]]||[[Geocantitomochoron|x4x3x3o]]||[[Xylocantitomochoron|x3x4x3o]]||[[Cosmocantitomochoron|x5x3x3o]]
 |-
-|Hexacosichoric||[[ﾍｶ]] heka||[[ﾍｶﾐ]] hekami||[[ﾍｶﾄ]] hekato||[[ｻｺﾐ]] sakomi||[[ﾍｶﾆﾐ]] hekanimi||[[ｻｶ]] saka||[[ﾍｶｶ]] hekaka||[[ｻｺ]] sako||[[ｻｶﾚ]] sakare||[[ｻｺﾆﾐ]] sakonimi||[[ﾍｶﾙ]] hekaru||[[ｻｺﾄ]] sakoto||[[ｻｺﾙ]] sakoru||[[ｻｺｶ]] sakoka||[[ｻｶﾄ]] sakato||---
+|8||ooox||[[Dual]]||[[Pyrochoron|(x3o3o3o)]]||[[Aerochoron|x3o3o4x]]||[[Xylochoron|(x3o4o3o)]]||[[Hydrochoron|x3o3o5o]]
+|-
+|9||xoox||[[Peritope]]||[[Pyroperichoron|x3o3o3x]]||[[Stauroperichoron|x4o3o3x]]||[[Xyloperichoron|x3o4o3x]]||[[Rhodoperichoron|x5o3o3x]]
+|-
+|10||oxox||(Cantellate)||[[Pyrocantichoron|(x3o3x3o)]]||[[Xylorectichoron|''(o3x4o3o)'']]||[[Xylocantichoron|(x3o4x3o)]]||[[Hydrocantichoron|x3o3x5o]]
+|-
+|11||xxox||[[Runcitruncate]]||[[Pyroruncitomochoron|x3x3o3x]]||[[Georuncitomochoron|x4x3o3x]]||[[Xyloruncitomochoron|x3x4o3x]]||[[Cosmoruncitomochoron|x5x3o3x]]
+|-
+|12||ooxx||(Truncate)||[[Pyrotomochoron|(x3x3o3o)]]||[[Aerotomochoron|x3x3o4o]]||[[Xylotomochoron|(x3x4o3o)]]||[[Hydrotomochoron|x3x3o5o]]
+|-
+|13||xoxx||(Runcitruncate)||[[Pyroruncitomochoron|(x3x3o3x)]]||[[Aeroruncitomochoron|x3x3o4x]]||[[Xyloruncitomochoron|(x3x4o3x)]]||[[Hydroruncitomochoron|x3x3o5x]]
+|-
+|14||oxxx||(Cantitruncate)||[[Pyrocantitomochoron|(x3x3x3o)]]||[[Xylocantitomochoron|''(x3x4o3o)'']]||[[Xylocantitomochoron|(x3x4x3o)]]||[[Hydrocantitomochoron|x3x3x5o]]
+|-
+|15||xxxx||[[Pantome]]||[[Pyropantochoron|x3x3x3x]]||[[Stauropantochoron|x4x3x3x]]||[[Xylopantochoron|x3x4x3x]]||[[Rhodopantochoron|x5x3x3x]]
 |}
-Form syntax:
-* "-" means the parent mneumonic
-* "*" means the rectate mneumonic
-* "~" means the dual mneumonic
-* Where a / occurs, self-duals take the left form and non-self-duals take the right form.
-[[Category:Uniform polychora|$]]