Table of kanichora (Meta, 11)

From Hi.gher. Space

(Difference between revisions)
(Peritopes!)
(redo table with simplified mirror groups, updated names and short symbols)
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{|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%"|[[Mirror group]]
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!bgcolor="#E0E0E0" colspan="4" width="40%"|[[Polychoric group]]
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!bgcolor="#E0E0E0" colspan="4" width="70%"|[[Symmetry group]]
|-
|-
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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;||[[Pyrochoron|Kp1]]||[[Geochoron|Ke1]]||[[Xylochoron|Kk1]]||[[Cosmochoron|Ks1]]
+
|1||xooo||Parent||[[Pyrochoron|x3o3o3o]]||[[Geochoron|x4o3o3o]]||[[Xylochoron|x3o4o3o]]||[[Cosmochoron|x5o3o3o]]
|-
|-
-
|2||oxoo||Rectate||Rectate||Hemicate||&nbsp;||[[3-pyrotomochoron|Kp2]]||[[3-geotomochoron|Ke2]]||[[3-xylotomochoron|Kk2]]||[[3-cosmotomochoron|Ks2]]
+
|2||oxoo||Rectate||[[Rectified pyrochoron|o3x3o3o]]||[[Rectified geochoron|o4x3o3o]]||[[Rectified xylochoron|o3x4o3o]]||[[Rectified cosmochoron|o5x3o3o]]
|-
|-
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|3||xxoo||Truncate||Truncate||Truncate||&nbsp;||[[2-pyrotomochoron|Kp3]]||[[2-geotomochoron|Ke3]]||[[2-xylotomochoron|Kk3]]||[[2-cosmotomochoron|Ks3]]
+
|3||xxoo||Truncate||[[Truncated pyrochoron|x3x3o3o]]||[[Truncated geochoron|x4x3x3o]]||[[Truncated xylochoron|x3x4o3o]]||[[Truncated cosmochoron|x5x3o3o]]
|-
|-
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|4||ooxo||---||---||Dual,hemic||&nbsp;||[[3-pyrotomochoron|(Kp2)]]||[[Xylochoron|''(Kk1)'']]||[[3-xylotomochoron|(Kk2)]]||[[3-hydrotomochoron|Ks4]]
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|4||ooxo||(Rectate)||[[Rectified pyrochoron|(o3x3o3o)]]||[[Xylochoron|''(x3o4o3o)'']]||[[Rectified xylochoron|(o3x4o3o)]]||[[Rectified hydrochoron|o3x3o5o]]
|-
|-
-
|5||xoxo||Cantellate||sm Rhombi-||Cantellate||&nbsp;||[[Cantellated 5-cell|Kp5]]||[[Cantellated 8-cell|Ke5]]||[[Cantellated 24-cell|Kk5]]||[[Cantellated 120-cell|Ks5]]
+
|5||xoxo||Cantellate||[[Cantellated pyrochoron|x3o3x3o]]||[[Cantellated geochoron|x4o3x3o]]||[[Cantellated xylochoron|x3o4x3o]]||[[Cantellated cosmochoron|x5o3x3o]]
|-
|-
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|6||oxxo||Bitruncate||---||Rectate||&nbsp;||[[Pyromesochoron|Kp6]]||[[Stauromesochoron|Ke6]]||[[Xylomesochoron|Kk6]]||[[Rhodomesochoron|Ks6]]
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|6||oxxo||Mesotope||[[Pyromesochoron|o3x3x3o]]||[[Stauromesochoron|o4x3x3o]]||[[Xylomesochoron|o3x4x3o]]||[[Rhodomesochoron|o5x3x3o]]
|-
|-
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|7||xxxo||Cantitruncate||gr Rhombi-||Cantitruncate||&nbsp;||[[Cantitruncated 5-cell|Kp7]]||[[Cantitruncated 8-cell|Ke7]]||[[Cantitruncated 24-cell|Kk7]]||[[Cantitruncated 120-cell|Ks7]]
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|7||xxxo||Cantitruncate||[[Cantitruncated pyrochoron|x3x3x3o]]||[[Cantitruncated geochoron|x4x3x3o]]||[[Cantitruncated xylochoron|x3x4x3o]]||[[Cantitruncated cosmochoron|x5x3x3o]]
|-
|-
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|8||ooox||---||---||Dual||&nbsp;||[[Pyrochoron|(Kp1)]]||[[Aerochoron|Ke8]]||[[Xylochoron|(Kk1)]]||[[Hydrochoron|Ks8]]
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|8||ooox||Dual||[[Pyrochoron|(x3o3o3o)]]||[[Aerochoron|x3o3o4x]]||[[Xylochoron|(x3o4o3o)]]||[[Hydrochoron|x3o3o5o]]
|-
|-
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|9||xoox||Runcinate||---||Runcinate||Rect,rect||[[Pyroperichoron|Kp9]]||[[Stauroperichoron|Ke9]]||[[Xyloperichoron|Kk9]]||[[Rhodoperichoron|Ks9]]
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|9||xoox||Peritope||[[Pyroperichoron|x3o3o3x]]||[[Stauroperichoron|x4o3o3x]]||[[Xyloperichoron|x3o4o3x]]||[[Rhodoperichoron|x5o3o3x]]
|-
|-
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|10||oxox||---||---||Dual,cantel||&nbsp;||[[Cantellated 5-cell|(Kp5)]]||[[3-xylotomochoron|''(Kk2)'']]||[[Cantellated 24-cell|(Kk5)]]||[[Cantellated 600-cell|Ks10]]
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|10||oxox||(Cantellate)||[[Cantellated pyrochoron|(x3o3x3o)]]||[[Rectified xylochoron|''(o3x4o3o)'']]||[[Cantellated xylochoron|(x3o4x3o)]]||[[Cantellated hydrochoron|x3o3x5o]]
|-
|-
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|11||xxox||Runcitruncate||---||Runcitruncate||&nbsp;||[[Runcitruncated 5-cell|Kp11]]||[[Runcitruncated 8-cell|Ke11]]||[[Runcitruncated 24-cell|Kk11]]||[[Runcitruncated 120-cell|Ks11]]
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|11||xxox||Runcitruncate||[[Runcitruncated pyrochoron|x3x3o3x]]||[[Runcitruncated geochoron|x4x3o3x]]||[[Runcitruncated xylochoron|x3x4o3x]]||[[Runcitruncated cosmochoron|x5x3o3x]]
|-
|-
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|12||ooxx||---||---||Dual,trunc||&nbsp;||[[2-pyrotomochoron|(Kp3)]]||[[2-aerotomochoron|Ke12]]||[[2-xylotomochoron|(Kk3)]]||[[2-hydrotomochoron|Ks12]]
+
|12||ooxx||(Truncate)||[[Truncated pyrochoron|(x3x3o3o)]]||[[Truncated aerochoron|x3x3o4o]]||[[Truncated xylochoron|(x3x4o3o)]]||[[Truncated hydrochoron|x3x3o5o]]
|-
|-
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|13||xoxx||---||Prismatorh||Dual,runcic||&nbsp;||[[Runcitruncated 5-cell|(Kp11)]]||[[Runcitruncated 16-cell|Ke13]]||[[Runcitruncated 24-cell|(Kk11)]]||[[Runcitruncated 600-cell|Ks13]]
+
|13||xoxx||(Runcitruncate)||[[Runcitruncated pyrochoron|(x3x3o3x)]]||[[Runcitruncated aerochoron|x3x3o4x]]||[[Runcitruncated xylochoron|(x3x4o3x)]]||[[Runcitruncated hydrochoron|x3x3o5x]]
|-
|-
-
|14||oxxx||---||---||Dual,cantic||&nbsp;||[[Cantitruncated 5-cell|(Kp7)]]||[[2-xylotomochoron|''(Kk3)'']]||[[Cantitruncated 24-cell|(Kk7)]]||[[Cantitruncated 600-cell|Ks14]]
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|14||oxxx||(Cantitruncate)||[[Cantitruncated pyrochoron|(x3x3x3o)]]||[[Truncated xylochoron|''(x3x4o3o)'']]||[[Cantitruncated xylochoron|(x3x4x3o)]]||[[Cantitruncated hydrochoron|x3x3x5o]]
|-
|-
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|15||xxxx||Omnitruncate||---||Omnitruncate||Rect,trunc||[[Pyropantomochoron|Kp15]]||[[Stauropantomochoron|Ke15]]||[[Xylopantomochoron|Kk15]]||[[Rhodopantomochoron|Ks15]]
+
|15||xxxx||Pantome||[[Pyropantochoron|x3x3x3x]]||[[Stauropantochoron|x4x3x3x]]||[[Xylopantochoron|x3x4x3x]]||[[Rhodopantochoron|x5x3x3x]]
-
|-
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-
|0||oooo||Snub||Snub||Snub||&nbsp;||
+
|}
|}
[[Category:Uniform polychora|$]]
[[Category:Uniform polychora|$]]

Revision as of 22:35, 23 June 2013

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 		Mirror group 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
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