In December The utilization characteristics to describe the selection of variants of twinning in the magnesium alloy AZ31 . On the basis of orientation maps are currently suitable algorithms that enable the calculation of how much and what share of the twins at the turn of micro-section created by rotation around the respective crystallographic axis a_i an angle of 86 degrees for the twinning { 10-12 } < 10-11 > and 56 degrees for twinning { 10 -11 } < 10-1-2 > . In the case of twinning { 10-12 } < 10-11 > , we can distinguish the following six options : (10-12) [ -1011 ] (01-12 ) [ 0-111 ] ( -1102 ) [ 1-101 ] ( -1012 ) [ 10-11 ] , ( 0-112 ) [ 01-11 ] and ( 1-102 ) [ -1101 ] . These variants can be obtained from the mother through the appropriate orientation of the rotation counter-clockwise by an angle of 86 degrees relative to the crystallographic axis following : a2 ,- a1 , a3 -a2 , a1 - a3 . By choosing an appropriate subset of the set of symmetry operators for hexagonal networks ( permutation of {9 , 7, 4, 2 , 1, 6} in the standard set of these operators ) is multiplied sixfold unit vector { 1,0,0 } crystallite by a left multiplication by the operator and another multiplication by the transpose of the matrix orientation g due to the expression of this system versor sample. The creation of the twin orientation is carried out by calculating the rotation around the active matrix crystallite versors propagated , and then recombining it and multiplying by the matrix of left-sided g is due to the fact that if f : C' - > C , and g : S- > C, gf ^ T : S- > C ' .