More or less ok so far, except it could be more specific.chinglu said:M' is the primed frame origin.
C' is at $$(\frac{-vd'}{c},0,0)$$ in primed frame coordinates.
M is the origin of the unprimed frame.
So, there are only 2 frames.
And, 3 clocks are OK as long as they are in 2 frames.
Einstein's quote doesn't say there is a shared common x-axis. What do you think it means? Is this really just your intentional use of a confusing idea? You think Einstein says the stationary and moving frames "share a common x-axis", and any child can see that this cannot be true, they can only share a direction in which one of their dimensions is aligned "in common" with the other, which is I think what Einstein meant to say.And, there is a shared common x-axis. I already explained this to you with a quote from Einstein.
But of course, you need to apply your intentional abuse of meaning to keep the parade going, and if you can mangle what Einstein actually said, so much the better, you think. Any fool can see that you can't get a pair of cubes to share a common axis; you can slide one over the other so edges are parallel but at no time does this make them share anything except a common direction.