Table 2. The rotational parameters involved in the derivation process of the look-up table for Dauphin twinning (twin element is {180, [0001]}) in -quartz.
| Symmetry operators S of point group 32 | Rotation matrices X = S R | Angleaxis pairs in O-a o b o c o {, u o} | Angleaxis pairs in O-abc {, u} | ||
|---|---|---|---|---|---|
|
|
{180, [001]} | {180, [0001]} | ||
|
|
{60, [001]} | {60, [0001]} | ||
|
|
{60, [00 ]} |
{60, [000]} |
||
|
|
{180,  [31/210]} |
{180, [100]} |
||
|
|
{180, [010]} | {180, [010]} |
||
|
|
{180, [
0]} |
{180, [100]} |
