Table of kanichora (Meta, 11)

From Hi.gher. Space

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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 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]].
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]].
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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"
!bgcolor="#E0E0E0" rowspan="2" width="5%"|[[Dx]]
!bgcolor="#E0E0E0" rowspan="2" width="5%"|[[Dx]]
!bgcolor="#E0E0E0" rowspan="2" width="10%"|[[Coxeter-Dynkin|Coxeter-<br>Dynkin]]
!bgcolor="#E0E0E0" rowspan="2" width="10%"|[[Coxeter-Dynkin|Coxeter-<br>Dynkin]]
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!bgcolor="#E0E0E0" rowspan="2" width="15%"|[[Mirror group]]
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!bgcolor="#E0E0E0" rowspan="2" width="15%"|[[Variant]]
!bgcolor="#E0E0E0" colspan="4" width="70%"|[[Symmetry group]]
!bgcolor="#E0E0E0" colspan="4" width="70%"|[[Symmetry group]]
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Revision as of 08:00, 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 pentachoric and icositetrachoric families due to them being self-dual, and in the hexadecachoric family due to the hexadecachoron 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