
Symmetry Groups for the Crystal Systems
 Practical Electron Microscopy and Database 
 An Online Book 

https://www.globalsino.com/EM/

This book (Practical Electron Microscopy and Database) is a reference for TEM and SEM students, operators, engineers, technicians, managers, and researchers.

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Table 3545a. Symmetry groups for the crystal systems.
System 
Essential symmetry 
Lattice symmetry 
Diffraction (Laue) symmetry 
Point Groups (Hermann–Mauguin notation) 
Triclinic 
None 


1, 1 
Monoclinic 

2/m 
2/m 
2, m, 2/m 
Orthorhombic 
222 or 2mm

mmm

mmm 
222, mm2, mmm 
Tetragonal 

4/mmm

4/m

4, 4, 4/m 
4/mmm 
422, 42m, 4mm, 4/mmm 
Trigonal 


3 
3, 3 
3m1 
321, 3m1, 3m1 
31m 
312, 31m, 31m 
Hexagonal 

6/mmm

6/m 
6, 6, 6/m 
6/mmm 
622, 62m, 6mm, 6/mmm 
Cubic 
23 
m3m

m3 
23, m3 
m3m 
432, 43m, m3m 
Table 3545b. Minimum number of symmetry elements.
System 
Minimum number of symmetry elements 
Triclinic 
None 
Monoclinic 
One 2fold rotation or rotoinversion,
axis parallel to yaxis 
Orthorhombic 
Three 2fold rotation or rotoinversion,
axes parallel to x,y,zaxes 
Tetragonal 
One 4fold rotation or rotoinversion,
axis parallel to zaxis 
Rhombohedral (Trigonal) 
One 3fold rotation or rotoinversion, axis parallel to zaxis 
Hexagonal 
One 6fold rotation or rotoinversion,
axis parallel to zaxis 
Cubic 
Four 3fold rotation or rotoinversion,
axes parallel to body diagonals 
















Nonpyroelectric 




Nonferroelectric 
Figure 3545. Schematic illustration of the different classes of crystal systems and their properties.

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