One question that arises in phase equilibrium calculations and experiments is how many phases can be in equilibrium simultaneously, since this determines how many phases one should search for. Consider a one-component system. 

a. If only solid phases in different crystal forms are present, what is the maximum number of equilibrium solid phases that can coexist? 

b. If a liquid is present, what is the maximum number of solid phases that can also exist at equilibrium? 

c. If a vapor is present, what is the maximum number of solid phases that can also exist at equilibrium? 

d. If a vapor and a liquid are present, what is the maximum number of solid phases that can also exist at equilibrium?