Table of kanihedra (Meta, 11)

From Hi.gher. Space

(Difference between revisions)

Revision as of 16:08, 9 March 2011

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.

Dx	Coxeter- Dynkin	Variance group		Polyhedral family
Dx	Coxeter- Dynkin	Standard	Conventional	Tetrahedral	Octahedral	Icosahedral
1	xoo	Parent	Parent	Kt1	Ko1	Ki1
2	oxo	Rectate	Rectate	(Kt2)	Ko2	Ki2
3	xxo	Truncate	Truncate	Kt3	Ko3	Ki3
4	oox	Birectate	Dual	(Kt4)	Ko4	Ki4
5	xox	Cantellate	Rect,rect	(Kt5)	Ko5	Ki5
6	oxx	Bitruncate	Dual,trunc	(Kt6)	Ko6	Ki6
7	xxx	Omnitruncate	Rect,trunc	(Kt7)	Ko7	Ki7
0	ooo	Snub	Snub	(Kt0)	Ko0	Ki0

@@ Line 1: / Line 1: @@
-This is a '''table of [[uniform polyhedra]]''' by their [[Kana mnemonic]].
+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.
 {|cellpadding="2" cellspacing="1"
@@ Line 5: / Line 7: @@
 !bgcolor="#E0E0E0" rowspan="2" width="80"|[[Coxeter-Dynkin|Coxeter-<br>Dynkin]]
 !bgcolor="#E0E0E0" colspan="2" width="30%"|[[Variance group]]
-!bgcolor="#E0E0E0" rowspan="2" width="80"|Form
+!bgcolor="#E0E0E0" colspan="3" width="40%"|[[Polyhedral family]]
-!bgcolor="#E0E0E0" colspan="3" width="40%"|[[Polyhedral group]]
 |-
 !bgcolor="#E0E0E0"|Standard
@@ Line 14: / Line 15: @@
 !bgcolor="#E0E0E0"|Icosahedral
 |-
-|width="80"|1||xoo||Parent||Parent||-||[[ﾃ]] te||[[ｷｭ]] kyu||[[ﾄﾞ]] do
+|width="80"|1||xoo||Parent||Parent||[[Tetrahedron|Kt1]]||[[Cube|Ko1]]||[[Dodecahedron|Ki1]]
 |-
-|width="80"|2||oxo||Rectate||Rectate||*||([[ｵｸ]] oku)||[[ｺ]] ko||[[ｲﾄﾞ]] ido
+|width="80"|2||oxo||Rectate||Rectate||[[Octahedron|(Kt2)]]||[[Cuboctahedron|Ko2]]||[[Icosidodecahedron|Ki2]]
 |-
-|width="80"|3||xxo||Truncate||Truncate||-ﾄ -to||[[ﾃﾄ]] teto||[[ｷｭﾄ]] kyuto||[[ﾄﾞﾄ]] doto
+|width="80"|3||xxo||Truncate||Truncate||[[Tetrahedral truncate|Kt3]]||[[Cubic truncate|Ko3]]||[[Dodecahedral truncate|Ki3]]
 |-
-|width="80"|4||oox||Birectate||Dual||~||([[ﾃ]] te)||[[ｵｸ]] oku||[[ｲｺ]] iko
+|width="80"|4||oox||Birectate||Dual||[[Tetrahedron|(Kt4)]]||[[Octahedron|Ko4]]||[[Icosahedron|Ki4]]
 |-
-|width="80"|5||xox||Cantellate||Rect,rect||*ﾚ *re||([[ｺ]] ko)||[[ｺﾚ]] kore||[[ｲﾄﾞﾚ]] idore
+|width="80"|5||xox||Cantellate||Rect,rect||[[Cuboctahedron|(Kt5)]]||[[Cuboctahedral rectate|Ko5]]||[[Icosidodecahedral rectate|Ki5]]
 |-
-|width="80"|6||oxx||Bitruncate||Dual,trunc||~ﾄ ~to||([[ﾃﾄ]] teto)||[[ｵｸﾄ]] okuto||[[ｲｺﾄ]] ikoto
+|width="80"|6||oxx||Bitruncate||Dual,trunc||[[Tetrahedral truncate|(Kt6)]]||[[Octahedral truncate|Ko6]]||[[Icosahedral truncate|Ki6]]
 |-
-|width="80"|7||xxx||Omnitruncate||Rect,trunc||*ﾄ *to||([[ｵｸﾄ]] okuto)||[[ｺﾄ]] koto||[[ｲﾄﾞﾄ]] idoto
+|width="80"|7||xxx||Omnitruncate||Rect,trunc||[[Octahedral truncate|(Kt7)]]||[[Cuboctahedral truncate|Ko7]]||[[Icosidodecahedral truncate|Ki7]]
 |-
-|width="80"|0||ooo||Snub||Snub||~ｽ ~su||([[ｲｺ]] iko)||[[ｷｭｽ]] kyusu||[[ﾄﾞｽ]] dosu
+|width="80"|0||ooo||Snub||Snub||[[Icosahedron|(Kt0)]]||[[Cubic snub|Ko0]]||[[Dodecahedral snub|Ki0]]
 |}
-;Form syntax
-* "-" means the parent mneumonic
-* "*" means the rectate mneumonic
-* "~" means the dual mneumonic
 [[Category:Uniform polyhedra|$]]