I'm confused about how  direction is determined for (100), (110) or (111) wafers. I found a book chapter which just confused me even more. From the image below, I understand how  is determined on the (110) wafer but not the other two. I'm also having a hard time understanding what different planes would look like on the (111) and (110) wafer. I would appreciate a resource for silicon wafers specifically (not necessarily crystallography). Here are things I'm not understanding.
How is the  direction determined and why is it different for each of the three wafers below? For the (110) wafer  is between x and y axis which makes sense. But for (100) it seems to go from z to y and for (111) it's between x and z. From my understanding  intercepts x and y axis at 1 and doesn't intercept z axis but that doesn't seem to be the case for (100) and (111) wafers.
Does the definition of x,y and z axis change when we're talking about (100), (111) or (110) wafers? I know that whichever wafer it is, that direction will be pointing out from the wafer surface but when I draw planes with respect to  and  (for (111) wafer), I don't know where the (100) plane should be. (110) plane would be perpendicular to the  direction and would be normal to the surface and (111) would be 35° from it. I can't find a drawing for it which makes me think we don't need to show the (100) plane? But if not then what if I need to align my mask to (100) plane on (111) wafer?
How would I define higher miller index planes on the 3 wafers? For example I need to align my mask to (122) or (411) plane, how would I start with it? I understand that this might become clear once I learn about the primary planes on the wafers.