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Bad parallelism and good thickness, what can be common...

Hi all.
Situation: I have a round thin part, and on each side I measure 6 points on 3 radii exactly opposite each other. Next, I measure the thickness of this part between them. As well as its flatness and parallelism between the planes built from these points.
Please help me understand how this can happen and why. I understand the difference between flatness and parallelism, but here I can’t explain why, with such an even thickness over the entire surface of the parts, we have such poor parallelism. I would be very grateful if this was depicted visually, so that the explanation would be just for dummies.

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