The three twin types
Contact twins meet at a flat composition plane — the famous Japan-law quartz twin sits two quartz prisms at exactly 84°33'. Penetration twins interpenetrate so that each crystal appears to grow through the other — staurolite's St. Andrew's cross, iron-cross pyrite. Polysynthetic twins repeat in alternating thin lamellae — albite striations on plagioclase, calcite e-twin lamellae visible under the microscope.
Famous habits
Japan-law quartz, swallow-tail gypsum, butterfly calcite, fishtail gypsum, sixling tourmaline, cyclic twin aragonite (Spanish sputnik), heart-shaped chrysoberyl, knee-twin rutile (six-fold sixling rosettes), iron-cross pyrite. Each is so distinctive that the twin itself becomes the species' most-wanted form.
What twinning reveals
Twinning records the temperature, pressure, and growth speed of crystallization. Aragonite's cyclic twins suggest rapid growth from supersaturated solution. Plagioclase's polysynthetic albite twinning tracks shear stress in the surrounding rock. For a collector, a clean twin is worth several times the price of two random crystals of the same combined size.