I should think so. It sounds like a rigid transformation. Rotating a billiard ball with two different measuring systems.
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well,it sounded isometric by the description and isometric transformations are rigid and rigid transformations preserves size and shape.
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I agree with Stephen Paul KIng. Nothing in your description indicated anything that was other than a fancy billiard ball. It’s easy to work with as you can use many shortcuts.
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I’m not critiquing your direction. Rather, it’s a pedagogical truism.
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