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Geometrical Interpretation of the Symmetry Operations of the 3D Point Groups


SymbolSymmetry Operations (in Seitz notation )
1 1
-11; -1
21; 2010
m1; m010
2/m1; 2010; -1; m010
2221; 2001; 2010; 2100
mm21; 2001; m010; m100
mmm1; 2001; 2010; 2100; -1; m001; m010; m100
41; 2001; 4+001; 4-001
-41; 2001; -4+001; -4-001
4/m1; 2001; 4+001; 4-001; -1; m001; -4+001; -4-001
4221; 2001; 4+001; 4-001; 2010; 2100; 2110; 21-10
4mm1; 2001; 4+001; 4-001; m010; m100; m110; m1-10
-42m1; 2001; -4+001; -4-001; 2010; 2100; m110; m1-10
4/mmm1; 2001; 4+001; 4-001; 2010; 2100; 2110; 21-10; -1; m001; -4+001; -4-001; m010; m100; m110; m1-10
31; 3+001; 3-001
-31; 3+001; 3-001; -1; -3+001; -3-001
3211; 3+001; 3-001; 21-10; 2120; 2210; 1; 3+001; 3-001; 2110; 2100; 2010
3m11; 3+001; 3-001; m1-10; m120; m210; 1; 3+001; 3-001; m110; m100; m010
-3m11; m1-10; m120; m210; 3+001; 3-001; 21-10; 2120; 2210; -1; -3+001; -3-001; 1; m110; m100; m010; 3+001; 3-001; 2110; 2100; 2010; -1; -3+001; -3-001
61; 3+001; 3-001; 2001; 6-001; 6+001
-61; 3+001; 3-001; m001; -6-001; -6+001
6/m1; 3+001; 3-001; 2001; 6-001; 6+001; -1; -3+001; -3-001; m001; -6-001; -6+001
6221; 3+001; 3-001; 2001; 6-001; 6+001; 2110; 2100; 2010; 21-10; 2120; 2210
6mm1; 3+001; 3-001; 2001; 6-001; 6+001; m110; m100; m010; m1-10; m120; m210
-6m21; 21-10; 2120; 2210; 3+001; 3-001; m001; -6-001; -6+001; m110; m100; m010
6/mmm1; 3+001; 3-001; 2001; 6-001; 6+001; 2110; 2100; 2010; 21-10; 2120; 2210; -1; -3+001; -3-001; m001; -6-001; -6+001; m110; m100; m010; m1-10; m120; m210
231; 2001; 2010; 2100; 3+111; 3+-11-1; 3+1-1-1; 3+-1-11; 3-111; 3-1-1-1; 3--1-11; 3--11-1
m-31; 2001; 2010; 2100; 3+111; 3+-11-1; 3+1-1-1; 3+-1-11; 3-111; 3-1-1-1; 3--1-11; 3--11-1; -1; m001; m010; m100; -3+111; -3+-11-1; -3+1-1-1; -3+-1-11; -3-111; -3-1-1-1; -3--1-11; -3--11-1
4321; 2001; 2010; 2100; 3+111; 3+-11-1; 3+1-1-1; 3+-1-11; 3-111; 3-1-1-1; 3--1-11; 3--11-1; 2110; 21-10; 4-001; 4+001; 4-100; 2011; 201-1; 4+100; 4+010; 2101; 4-010; 2-101
-43m1; 2001; 2010; 2100; 3+111; 3+-11-1; 3+1-1-1; 3+-1-11; 3-111; 3-1-1-1; 3--1-11; 3--11-1; m1-10; m110; -4+001; -4-001; m01-1; -4+100; -4-100; m011; m-101; -4-010; m101; -4+010
m-3m1; 2001; 2010; 2100; 3+111; 3+-11-1; 3+1-1-1; 3+-1-11; 3-111; 3-1-1-1; 3--1-11; 3--11-1; 2110; 21-10; 4-001; 4+001; 4-100; 2011; 201-1; 4+100; 4+010; 2101; 4-010; 2-101; -1; m001; m010; m100; -3+111; -3+-11-1; -3+1-1-1; -3+-1-11; -3-111; -3-1-1-1; -3--1-11; -3--11-1; m110; m1-10; -4-001; -4+001; -4-100; m011; m01-1; -4+100; -4+010; m101; -4-010; m-101


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