Table of kanichora (Meta, 11)

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This is a '''table of [[uniform polychora]]''' by their [[Kana mnemonic]].
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<[#ontology [kind meta] [cats 4D Uniform Polytope]]>
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This table shows the four-dimensional [[kanitope]]s arranged by their [[polytope family|family]] and [[Dx number]].
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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]].
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Variants enclosed in parentheses indicate it is a variant of the dual, rather than a variant of the parent.
{|cellpadding="2" cellspacing="1"
{|cellpadding="2" cellspacing="1"
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!bgcolor="#E0E0E0" rowspan="2" width="30"|[[Dx]]
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!bgcolor="#E0E0E0" rowspan="2" width="5%"|[[Dx]]
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!bgcolor="#E0E0E0" rowspan="2" width="80"|[[Coxeter-Dynkin|Coxeter-<br>Dynkin]]
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!bgcolor="#E0E0E0" rowspan="2" width="10%"|[[Coxeter-Dynkin|Coxeter-<br>Dynkin]]
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!bgcolor="#E0E0E0" colspan="4" width="40%"|[[Variance group]]
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!bgcolor="#E0E0E0" rowspan="2" width="15%"|[[Variant]]
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!bgcolor="#E0E0E0" rowspan="2"|Form
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!bgcolor="#E0E0E0" colspan="4" width="70%"|[[Symmetry group]]
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!bgcolor="#E0E0E0" colspan="4" width="40%"|[[Polychoric group]]
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|-
|-
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!bgcolor="#E0E0E0"|Standard
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!bgcolor="#E0E0E0"|Pyrochoric
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!bgcolor="#E0E0E0"|Krieger
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!bgcolor="#E0E0E0"|Staurochoric
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!bgcolor="#E0E0E0"|Conventional
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!bgcolor="#E0E0E0"|Xylochoric
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!bgcolor="#E0E0E0"|Alt. conv.
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!bgcolor="#E0E0E0"|Rhodochoric
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!bgcolor="#E0E0E0"|Pentachoric
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!bgcolor="#E0E0E0"|Hexadecachoric
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!bgcolor="#E0E0E0"|Icositetrachoric
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!bgcolor="#E0E0E0"|Hexacosichoric
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|-
|-
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|1||xooo||Parent||Parent||Parent||&nbsp;||-||[[ペン]] pen||[[テス]] tesu||[[コシ]] koshi||[[ヘカ]] heka
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|1||xooo||Parent||[[Pyrochoron|x3o3o3o]]||[[Geochoron|x4o3o3o]]||[[Xylochoron|x3o4o3o]]||[[Cosmochoron|x5o3o3o]]
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|-
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|2||oxoo||Rectate||Rectate||Hemicate||&nbsp;||-ミ -mi||[[ペンミ]] penmi||[[テスミ]] tesumi||[[コシミ]] koshimi||[[ヘカミ]] hekami
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|2||oxoo||[[Rectate]]||[[Pyrorectichoron|o3x3o3o]]||[[Georectichoron|o4x3o3o]]||[[Xylorectichoron|o3x4o3o]]||[[Cosmorectichoron|o5x3o3o]]
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|-
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|3||xxoo||Truncate||Truncate||Truncate||&nbsp;||-ト -to||[[ペント]] pento||[[テスト]] tesuto||[[コシト]] koshito||[[ヘカト]] hekato
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|3||xxoo||[[Truncate]]||[[Pyrotomochoron|x3x3o3o]]||[[Geotomochoron|x4x3x3o]]||[[Xylotomochoron|x3x4o3o]]||[[Cosmotomochoron|x5x3o3o]]
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|-
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|4||ooxo||---||---||Dual,hemic||&nbsp;||~ミ ~mi||([[ペンミ]] penmi)||([[コシ]] koshi)||([[コシミ]] koshimi)||[[サコミ]] sakomi
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|4||ooxo||(Rectate)||[[Pyrorectichoron|(o3x3o3o)]]||[[Xylochoron|''(x3o4o3o)'']]||[[Xylorectichoron|(o3x4o3o)]]||[[Hydrorectichoron|o3x3o5o]]
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|-
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|5||xoxo||Cantellate||sm Rhombi-||Omnihemate||&nbsp;||-ニミ -nimi||[[ペンニミ]] pennimi||[[テスニミ]] tesunimi||[[コシニミ]] koshinimi||[[ヘカニミ]] hekanimi
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|5||xoxo||[[Cantellate]]||[[Pyrocantichoron|x3o3x3o]]||[[Geocantichoron|x4o3x3o]]||[[Xylocantichoron|x3o4x3o]]||[[Cosmocantichoron|x5o3x3o]]
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|-
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|6||oxxo||Bitruncate||---||Rectate||&nbsp;||-レ/* -re/*||[[ペンレ]] penre||[[エス]] esu||[[コシレ]] koshire||[[サカ]] saka
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|6||oxxo||[[Mesotope]]||[[Pyromesochoron|o3x3x3o]]||[[Stauromesochoron|o4x3x3o]]||[[Xylomesochoron|o3x4x3o]]||[[Rhodomesochoron|o5x3x3o]]
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|7||xxxo||Cantitruncate||gr Rhombi-||Canticate||&nbsp;||-カ -ka||[[ペンカ]] penka||[[テスカ]] tesuka||[[コシカ]] koshika||[[ヘカカ]] hekaka
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|7||xxxo||[[Cantitruncate]]||[[Pyrocantitomochoron|x3x3x3o]]||[[Geocantitomochoron|x4x3x3o]]||[[Xylocantitomochoron|x3x4x3o]]||[[Cosmocantitomochoron|x5x3x3o]]
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|8||ooox||---||---||Dual||&nbsp;||~||([[ペン]] pen)||[[エク]] eku||([[コシ]] koshi)||[[サコ]] sako
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|8||ooox||[[Dual]]||[[Pyrochoron|(x3o3o3o)]]||[[Aerochoron|x3o3o4x]]||[[Xylochoron|(x3o4o3o)]]||[[Hydrochoron|x3o3o5o]]
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|-
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|9||xoox||Runcinate||---||Cantellate||Rect,rect||-ジレ/*レ -jire/*re||[[ペンジレ]] penjire||[[エスレ]] esure||[[コシジレ]] koshijire||[[サカレ]] sakare
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|9||xoox||[[Peritope]]||[[Pyroperichoron|x3o3o3x]]||[[Stauroperichoron|x4o3o3x]]||[[Xyloperichoron|x3o4o3x]]||[[Rhodoperichoron|x5o3o3x]]
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|-
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|10||oxox||---||---||Dual,omnihem||&nbsp;||~ニミ ~nimi||([[ペンニミ]] pennimi)||([[コシミ]] koshimi)||([[コシニミ]] koshinimi)||[[サコニミ]] sakonimi
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|10||oxox||(Cantellate)||[[Pyrocantichoron|(x3o3x3o)]]||[[Xylorectichoron|''(o3x4o3o)'']]||[[Xylocantichoron|(x3o4x3o)]]||[[Hydrocantichoron|x3o3x5o]]
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|-
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|11||xxox||Runcitruncate||---||Runcicate||&nbsp;||-ル -ru||[[ペンル]] penru||[[テスル]] tesuru||[[コシル]] koshiru||[[ヘカル]] hekaru
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|11||xxox||[[Runcitruncate]]||[[Pyroruncitomochoron|x3x3o3x]]||[[Georuncitomochoron|x4x3o3x]]||[[Xyloruncitomochoron|x3x4o3x]]||[[Cosmoruncitomochoron|x5x3o3x]]
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|12||ooxx||---||---||Dual,trunc||&nbsp;||~ト ~to||([[ペント]] pento)||[[エクト]] ekuto||([[コシト]] koshito)||[[サコト]] sakoto
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|12||ooxx||(Truncate)||[[Pyrotomochoron|(x3x3o3o)]]||[[Aerotomochoron|x3x3o4o]]||[[Xylotomochoron|(x3x4o3o)]]||[[Hydrotomochoron|x3x3o5o]]
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|-
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|13||xoxx||---||Prismatorh||Dual,runcic||&nbsp;||~ル ~ru||([[ペンル]] penru)||[[エクル]] ekuru||([[コシル]] koshiru)||[[サコル]] sakoru
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|13||xoxx||(Runcitruncate)||[[Pyroruncitomochoron|(x3x3o3x)]]||[[Aeroruncitomochoron|x3x3o4x]]||[[Xyloruncitomochoron|(x3x4o3x)]]||[[Hydroruncitomochoron|x3x3o5x]]
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|-
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|14||oxxx||---||---||Dual,cantic||&nbsp;||~カ ~ka||([[ペンカ]] penka)||([[コシト]] koshito)||([[コシカ]] koshika)||[[サコカ]] sakoka
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|14||oxxx||(Cantitruncate)||[[Pyrocantitomochoron|(x3x3x3o)]]||[[Xylocantitomochoron|''(x3x4o3o)'']]||[[Xylocantitomochoron|(x3x4x3o)]]||[[Hydrocantitomochoron|x3x3x5o]]
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|15||xxxx||Omnitruncate||---||Omnitruncate||Rect,trunc||*ト *to||[[ペンレト]] penreto||[[エスト]] esuto||[[コシレト]] koshireto||[[サカト]] sakato
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|15||xxxx||[[Pantome]]||[[Pyropantochoron|x3x3x3x]]||[[Stauropantochoron|x4x3x3x]]||[[Xylopantochoron|x3x4x3x]]||[[Rhodopantochoron|x5x3x3x]]
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|-
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|0||oooo||Snub||Snub||Snub||&nbsp;||-ス -su||---||---||[[コシス]] koshisu||---
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|}
|}
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;Form syntax
 
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* "-" means the parent mneumonic
 
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* "*" means the rectate mneumonic
 
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* "~" means the dual mneumonic
 
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[[Category:Uniform polychora|$]]
 

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
Pyrochoric Staurochoric Xylochoric Rhodochoric
1xoooParentx3o3o3ox4o3o3ox3o4o3ox5o3o3o
2oxooRectateo3x3o3oo4x3o3oo3x4o3oo5x3o3o
3xxooTruncatex3x3o3ox4x3x3ox3x4o3ox5x3o3o
4ooxo(Rectate)(o3x3o3o)(x3o4o3o)(o3x4o3o)o3x3o5o
5xoxoCantellatex3o3x3ox4o3x3ox3o4x3ox5o3x3o
6oxxoMesotopeo3x3x3oo4x3x3oo3x4x3oo5x3x3o
7xxxoCantitruncatex3x3x3ox4x3x3ox3x4x3ox5x3x3o
8oooxDual(x3o3o3o)x3o3o4x(x3o4o3o)x3o3o5o
9xooxPeritopex3o3o3xx4o3o3xx3o4o3xx5o3o3x
10oxox(Cantellate)(x3o3x3o)(o3x4o3o)(x3o4x3o)x3o3x5o
11xxoxRuncitruncatex3x3o3xx4x3o3xx3x4o3xx5x3o3x
12ooxx(Truncate)(x3x3o3o)x3x3o4o(x3x4o3o)x3x3o5o
13xoxx(Runcitruncate)(x3x3o3x)x3x3o4x(x3x4o3x)x3x3o5x
14oxxx(Cantitruncate)(x3x3x3o)(x3x4o3o)(x3x4x3o)x3x3x5o
15xxxxPantomex3x3x3xx4x3x3xx3x4x3xx5x3x3x