In the isometric system, the most common types of twins are the Spinel Law (twin plane, parallel to an octahedron) <111>, where the twin axis is perpendicular to an octahedral face, and the Iron Cross <001>, which is the interpenetration of two pyritohedrons, a subtype of dodecahedron.
In the hexagonal system, calcite shows the contact twin laws {0001} and {0112}. Quartz shows the Brazil Law {1120}, and Dauphiné Law <0001>, which are penetration twins caused by transformation, and Japan Law {1122}, which is often caused by accidents during growth.
In the tetragonal system, cyclical contact twins are the most commonly observed type of twin, such as in rutile titanium dioxide and cassiterite tin oxide.
In the orthorhombic system, crystals usually twin on planes parallel to the prism face, where the most common is a {110} twin, which produces cyclical twins, such as in aragonite, chrysoberyl, and cerussite.
In the monoclinic system, twins occur most often on the planes {100} and {001} by the Manebach Law {001}, Carlsbad Law [001], Baveno Law {021} in orthoclase, and the Swallow Tail Twins (Manebach law) {001} in gypsum.
In the triclinic system, the most commonly twinned crystals are the feldspar minerals plagioclase and microcline. These minerals show the Albite and Pericline Laws.
The most common twin operations by crystal system are tabulated below. This list is not exhaustive, particularly for the crystal systems of lowest symmetry, such as the triclinic system.