alt Hacker NewsWorst D-4 ever! But more seriously, I wonder how closely you could get to an non-uniform mass polyhedra which had 'knife edge' type balance. Which is to say;
1) Construct a polyhedra with uneven weight distribution which is stable on exactly two faces.
2) Make one of those faces much more stable than the other, so if it is on the limited stability face and disturbed, it will switch to the high stability face.
A structure like that would be useful as a tamper detector.
Replies
>useful as a tamper detector
The keyword is "mono-monostatic", and the Gömböc is an example of a non-polyhedra one: https://en.wikipedia.org/wiki/G%C3%B6mb%C3%B6c
Here's a 21 sided mono-monostatic polyhedra: https://arxiv.org/pdf/2103.13727v2
I imagine a dowel that is easily tipped over fits your description but I must be missing something.
If you're not limited to a polyhedron, a thin rod standing on end does the job.
A rod would fall over with a big clatter and bounce a few times. I wonder if there's a bistable polyhedron where the transition would be smooth enough that it wouldn't bounce. The original gomboc seemed to have its CG change smoothly enough that it wouldn't bounce under normal gravity.
Sort of like a mechanical binary state that passively "remembers" if it's been jostled
A solid tall cone is quite similar to what you want. I guess it can be tweaked to get a polyhedra.
> A structure like that would be useful as a tamper detector.
Why does it need to be a polyhedron?
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You jest, but I knew a DND player with a dice addicting that loved showing off his D-1 Mobius strip dice - https://www.awesomedice.com/products/awd101?variant=45578687...
For some reason he did not like my suggestion that he get a #1 billard ball.