Symmetry group (InstanceClass, 3)

From Hi.gher. Space

(Difference between revisions)

Revision as of 21:58, 2 March 2014

WIP

Three dimensions

2	3	4	5
C_s Plane
			C₅ Chiral rhodoaxial
C_2v Biaxial	C_3v Pyroaxial	C_4v Stauroaxial	C_5v Rhodoaxial
	D₃ Chiral pyroantiprismatic	D₄ Chiral stauroantiprismatic	D₅ Chiral rhodoantiprismatic
D_2d Biantiprismatic	D_3d Pyroantiprismatic	D_4d Stauroantiprismatic	D_5d Rhodoantiprismatic
D_2h Biprismatic (brick)	D_3h Pyroprismatic	D_4h Stauroprismatic	D_5h Rhodoprismatic
		O Chiral staurohedral	I Chiral rhodohedral
	T_d Pyrohedral	O_h Staurohedral	I_h Rhodohedral

Five symmetry groups are not seen in CRF polyhedra: C₁ (asymmetry), C_nh (chiral prismatic symmetry), S_n (S₂ being point symmetry), T (chiral pyrohedral symmetry), T_h (pyritohedral symmetry)

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Brick symmetry

@@ Line 5: / Line 5: @@
 !2!!3!!4!!5
 |-
-|Cs<br/>Plane
+|C<sub>s</sub><br/>[[Plane symmetry|Plane]]
 |
 |
@@ Line 13: / Line 13: @@
 |
 |
-|C5<br/>Chiral rhodoaxial
+|C<sub>5</sub><br/>[[Chiral rhodoaxial symmetry|Chiral rhodoaxial]]
 |-
-|C2v<br/>Biaxial
+|C<sub>2v</sub><br/>[[Biaxial symmetry|Biaxial]]
-|C3v<br/>Pyroaxial
+|C<sub>3v</sub><br/>[[Pyroaxial symmetry|Pyroaxial]]
-|C4v<br/>Stauroaxial
+|C<sub>4v</sub><br/>[[Stauroaxial symmetry|Stauroaxial]]
-|C5v<br/>Rhodoaxial
+|C<sub>5v</sub><br/>[[Rhodoaxial symmetry|Rhodoaxial]]
 |-
 |
-|D3<br/>Chiral pyroantiprismatic
+|D<sub>3</sub><br/>[[Chiral pyroantiprismatic symmetry|Chiral pyroantiprismatic]]
-|D4<br/>Chiral stauroantiprismatic
+|D<sub>4</sub><br/>[[Chiral stauroantiprismatic symmetry|Chiral stauroantiprismatic]]
-|D5<br/>Chiral rhodoantiprismatic
+|D<sub>5</sub><br/>[[Chiral rhodoantiprismatic symmetry|Chiral rhodoantiprismatic]]
 |-
-|D2d<br/>Biantiprismatic
+|D<sub>2d</sub><br/>[[Biantiprismatic symmetry|Biantiprismatic]]
-|D3d<br/>Pyroantiprismatic
+|D<sub>3d</sub><br/>[[Pyroantiprismatic symmetry|Pyroantiprismatic]]
-|D4d<br/>Stauroantiprismatic
+|D<sub>4d</sub><br/>[[Stauroantiprismatic symmetry|Stauroantiprismatic]]
-|D5d<br/>Rhodoantiprismatic
+|D<sub>5d</sub><br/>[[Rhodoantiprismatic symmetry|Rhodoantiprismatic]]
 |-
-|D2h<br/>Biprismatic (brick)
+|D<sub>2h</sub><br/>[[Biprismatic symmetry|Biprismatic (brick)]]
-|D3h<br/>Pyroprismatic
+|D<sub>3h</sub><br/>[[Pyroprismatic symmetry|Pyroprismatic]]
-|D4h<br/>Stauroprismatic
+|D<sub>4h</sub><br/>[[Stauroprismatic symmetry|Stauroprismatic]]
-|D5h<br/>Rhodoprismatic
+|D<sub>5h</sub><br/>[[Rhodoprismatic symmetry|Rhodoprismatic]]
 |-
 |
 |
-|O<br/>Chiral staurohedral
+|O<br/>[[Chiral staurohedral symmetry|Chiral staurohedral]]
-|I<br/>Chiral rhodohedral
+|I<br/>[[Chiral rhodohedral symmetry|Chiral rhodohedral]]
 |-
 |
-|Td<br/>Pyrohedral
+|T<sub>d</sub><br/>[[Pyrohedral symmetry|Pyrohedral]]
-|Oh<br/>Staurohedral
+|O<sub>h</sub><br/>[[Staurohedral symmetry|Staurohedral]]
-|Ih<br/>Rhodohedral
+|I<sub>h</sub><br/>[[Rhodohedral symmetry|Rhodohedral]]
 |}
-Five symmetry groups are not seen in CRF polyhedra: C1 (asymmetry), Cnh (chiral n-gonal prismatic symmetry), Sn (S2 being point symmetry), T (chiral pyrohedral symmetry), Th (pyritohedral symmetry)
+Five symmetry groups are not seen in CRF polyhedra: C<sub>1</sub> ([[asymmetry]]), C<sub>''n''h</sub> ([[chiral prismatic symmetry]]), S<sub>''n''</sub> (S<sub>2</sub> being [[point symmetry]]), T ([[chiral pyrohedral symmetry]]), T<sub>h</sub> ([[pyritohedral symmetry]])