A video is worth a thousand words of theory:

https://www.youtube.com/watch?v=-2jjgHsxEu4

Another nice puzzle:

A cube looks like a square from three orthogonal directions. A cylinder can look like a square from infinitely many directions, but they are all coplanar. Can you find a convex shape that looks like a square from more than three directions, without all of them being coplanar? In particular, can you find a convex shape that looks like a square from two distinct sets of three orthogonal directions? Can you find all such shapes?

Another interesting thing named after Prince Rupert is the Prince Rupert's drop for anyone interested: https://www.youtube.com/watch?v=k5MORochIDw

I knew of Prince Rupert’s drop before[1]. Reading about Prince Rupert’s cube sent me down the rabbit-hole of reading up on Prince Rupert himself.

Why do we no longer have Renaissance men/women today, contributing to the sciences, philosophy and the arts? What did we lose?

[1] https://en.m.wikipedia.org/wiki/Prince_Rupert%27s_Drop

Interesting that the optimal solution is not "slide it along the space diagonal" but rather "slide it parallel to a face".

Mathologer on Rupert's cube: https://www.youtube.com/watch?v=rAHcZGjKVvg

looks like a fun model to 3d-print

So, cubes have a margin of 6% play, if you need to pass any other cube through a given cube.

I reckon you could stretch this to a 30 minute whiteboard session to answer why (some) manhole covers are round.