Final answer:
Cyclic twinning is the type of twinning where two segments usually go extinct at different points with stage rotation, producing complex and symmetrical forms while being analyzed under polarized light. The correct answer is c) Cyclic twinning.
Step-by-step explanation:
The twinning type that results in two segments that usually go extinct at different points with stage rotation is cyclic twinning. Cyclic twinning occurs when three or more crystals share the same crystallographic axis and repeatedly adjoin each other in cyclic symmetry. This type of twinning can produce complex and symmetrical forms, as each segment in the twin tends to go extinct at different angles during stage rotation under polarized light in a microscope, a technique commonly used by geologists to analyze minerals. Other twinning types like simple twins, polysynthetic twinning, and penetration twins have different characteristics and do not typically exhibit this kind of behavior. The correct answer is c) Cyclic twinning.