International symbols Inversion -1 ,(①) A x,y,z→-X,-y,-2 0 Reflection 1 m,o (Z=0 plane) 0 71 A 0 1(E) 0 01
1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 ij ij ij A A A − = − − = − = Inversion 1,(i) Reflection m, （Z=0 plane） 1(E) x y z x y z , , , , → − − − International symbols
Cube:48 symmetrical operations)(including 1 and 1,(i)) π 2，2 2π4π T 3’3 B 3*3=9 6*1=6 4*2=8 High symmetry demands more symmetrical operation
Cube: 48 symmetrical operations)(including 1 and ) 2 4 , 3 3 3 , , 2 2 4*2=8 π 3*3=9 6*1=6 1,(i) High symmetry demands more symmetrical operation
24 symmetrical operations
24 symmetrical operations
Possible ten symmetry elements for crystals B'A=nAB B'A=nAB 1,2,3,4,6 B'A'=AB(1-2cos0) 1,2,34,6 1-2c0s0=n c0s0:-1~+1 n=-1,0,1,2,3 0=0°，60°，90°，120°，180° XCH001031 1,2,3,4,6
1, 2, 3, 4, 6 1, 2, 3, 4, 6 Possible ten symmetry elements for crystals