Does iPhone 13 Pro Max cases fit on iPhone 12 Pro Max?

The iPhone 13 Pro Max is exactly the same height and width as the iPhone 12 Pro Max, but the 12 Pro Max is thinner than 13 Pro Max. So an iPhone 13 Pro Max case will fit on 12 Pro Max, but the iPhone 12 Pro Max on a 13 Pro Max case may rattle when shaken.

If the dimensions are 'nearly’ the same, you will probably find that the answer is 'no’. You could find that the phone won't fit in the case, or will be a sloppy fit which could lead to the phone separating from the case if dropped. Surely your iPhone is worthy of a case that has been designed for it?