Calcite (Calcium carbonate) is a very common mineral, but fascinating in the vast variety of crystal forms it assumes, including some beautiful symmetries produced by the phenomenon of crystal twinning ( http://lifeartearth.blogspot.com/2013/10/calcite-twinning-four-classes.html ).

Four distinct classes of calcite twin have long been recognized, depending on the orientation of the c-axis of each member of the crystal twin relative to the other and the orientation of the twin contact plane. In addition to these cases where adjacent twin members meet at a composition surface approximating a plane, penetration twins also occur (illustrated by examples from Kazakhstan below).

Click on the first image below for a summary of the four twin laws.