Table of kanihedra (Meta, 11)

From Hi.gher. Space

(Difference between revisions)

Latest revision as of 22:44, 11 February 2014

This table shows the three-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 3D, this only occurs in the tetrahedral family, due both to it being self-dual and to the tetrahedron being equivalent to the demicube.

Dx	Coxeter- Dynkin	Mirror group	Symmetry family
Dx	Coxeter- Dynkin	Mirror group	Pyrohedral	Staurohedral	Rhodohedral
1	xoo	Parent	x3o3o	x4o3o	x5o3o
2	oxo	Mesotope	(x3o4o)	o4x3o	o5x3o
3	xxo	Truncate	x3x3o	x4x3o	x5x3o
4	oox	Dual	(x3o3o)	x3o4o	x3o5o
5	xox	Peritope	(o4x3o)	x4o3x	x5o3x
6	oxx	(Truncate)	(x3x3o)	x3x4o	x3x5o
7	xxx	Pantome	(x3x4o)	x4x3x	x5x3x
0	ooo	Snub	(x3o5o)	s4s3s	s5s3s

@@ Line 1: / Line 1: @@
+<[#ontology [kind meta] [cats 3D Uniform Polytope]]>
 This table shows the three-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 3D, this only occurs in the tetrahedral family.
+Forms enclosed in parentheses are non-canonical forms, which duplicate other cells of the table. In 3D, this only occurs in the tetrahedral family, due both to it being [[self-dual]] and to the tetrahedron being equivalent to the [[Demihypercube|demicube]].
 {|cellpadding="2" cellspacing="1"
-!bgcolor="#E0E0E0" rowspan="2" width="30"|[[Dx]]
+!bgcolor="#E0E0E0" rowspan="2" width="10%"|[[Dx]]
-!bgcolor="#E0E0E0" rowspan="2" width="80"|[[Coxeter-Dynkin|Coxeter-<br>Dynkin]]
+!bgcolor="#E0E0E0" rowspan="2" width="15%"|[[Coxeter-Dynkin|Coxeter-<br>Dynkin]]
-!bgcolor="#E0E0E0" colspan="2" width="30%"|[[Variance group]]
+!bgcolor="#E0E0E0" rowspan="2" width="15%"|[[Mirror group]]
-!bgcolor="#E0E0E0" colspan="3" width="40%"|[[Polyhedral family]]
+!bgcolor="#E0E0E0" colspan="3" width="60%"|[[Symmetry family]]
 |-
-!bgcolor="#E0E0E0"|Standard
+!bgcolor="#E0E0E0"|Pyrohedral
-!bgcolor="#E0E0E0"|Conventional
+!bgcolor="#E0E0E0"|Staurohedral
-!bgcolor="#E0E0E0"|Tetrahedral
+!bgcolor="#E0E0E0"|Rhodohedral
-!bgcolor="#E0E0E0"|Octahedral
-!bgcolor="#E0E0E0"|Icosahedral
 |-
-|width="80"|1||xoo||Parent||Parent||[[Tetrahedron|Kt1]]||[[Cube|Ko1]]||[[Dodecahedron|Ki1]]
+|width="80"|1||xoo||Parent||[[Tetrahedron|x3o3o]]||[[Cube|x4o3o]]||[[Dodecahedron|x5o3o]]
 |-
-|width="80"|2||oxo||Rectate||Rectate||[[Octahedron|(Kt2)]]||[[Cuboctahedron|Ko2]]||[[Icosidodecahedron|Ki2]]
+|width="80"|2||oxo||[[Mesotope]]||[[Octahedron|''(x3o4o)'']]||[[Stauromesohedron|o4x3o]]||[[Rhodomesohedron|o5x3o]]
 |-
-|width="80"|3||xxo||Truncate||Truncate||[[Tetrahedral truncate|Kt3]]||[[Cubic truncate|Ko3]]||[[Dodecahedral truncate|Ki3]]
+|width="80"|3||xxo||[[Truncate]]||[[Tetrahedral truncate|x3x3o]]||[[Cubic truncate|x4x3o]]||[[Dodecahedral truncate|x5x3o]]
 |-
-|width="80"|4||oox||Birectate||Dual||[[Tetrahedron|(Kt4)]]||[[Octahedron|Ko4]]||[[Icosahedron|Ki4]]
+|width="80"|4||oox||[[Dual]]||[[Tetrahedron|(x3o3o)]]||[[Octahedron|x3o4o]]||[[Icosahedron|x3o5o]]
 |-
-|width="80"|5||xox||Cantellate||Rect,rect||[[Cuboctahedron|(Kt5)]]||[[Cuboctahedral rectate|Ko5]]||[[Icosidodecahedral rectate|Ki5]]
+|width="80"|5||xox||[[Peritope]]||[[Stauromesohedron|''(o4x3o)'']]||[[Stauroperihedron|x4o3x]]||[[Rhodoperihedron|x5o3x]]
 |-
-|width="80"|6||oxx||Bitruncate||Dual,trunc||[[Tetrahedral truncate|(Kt6)]]||[[Octahedral truncate|Ko6]]||[[Icosahedral truncate|Ki6]]
+|width="80"|6||oxx||(Truncate)||[[Tetrahedral truncate|(x3x3o)]]||[[Octahedral truncate|x3x4o]]||[[Icosahedral truncate|x3x5o]]
 |-
-|width="80"|7||xxx||Omnitruncate||Rect,trunc||[[Octahedral truncate|(Kt7)]]||[[Cuboctahedral truncate|Ko7]]||[[Icosidodecahedral truncate|Ki7]]
+|width="80"|7||xxx||[[Pantome]]||[[Octahedral truncate|''(x3x4o)'']]||[[Stauropantohedron|x4x3x]]||[[Rhodopantohedron|x5x3x]]
 |-
-|width="80"|0||ooo||Snub||Snub||[[Icosahedron|(Kt0)]]||[[Cubic snub|Ko0]]||[[Dodecahedral snub|Ki0]]
+|width="80"|0||ooo||[[Snub]]||[[Icosahedron|''(x3o5o)'']]||[[Snub staurohedron|s4s3s]]||[[Snub rhodohedron|s5s3s]]
 |}
-[[Category:Uniform polyhedra|$]]