So, like my Vans?
A new pyramid-like shape always lands the same side up
31–40 of 175 posts
Re: A new pyramid-like shape always lands the same side up
#32[flagged]
Re: A new pyramid-like shape always lands the same side up
#33Worst 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 struc…
[flagged]
Re: A new pyramid-like shape always lands the same side up
#34Worst 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 struc…
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
Re: A new pyramid-like shape always lands the same side up
#35This is categorically different from the Gömböc, because it doesn't have uniform density. Most of its mass is concentrated in the base plate.
[flagged]
Re: A new pyramid-like shape always lands the same side up
#36Re: A new pyramid-like shape always lands the same side up
#37Earlier quoted context omitted.
Did they actual prove this?
They didn't need to, because it was proven in 1969 (J. H. Conway and R. K. Guy, _Stability of polyhedra_, SIAM Rev. 11, 78–82)
That article doesn't prove what you say that it does. It just proves because a perpetuum mobile is impossible, it is trivial that a polyhedron must always eventually come to rest on one
face. It doesn't assert that the face-down face is always the same face (unistable/monostable). It goes on to query whether or not a uniformly dense object can be constructed so as to be unistable, although if I understand correctly Guy himself had already constructed a 19-faced one in 1968 and knew the answer to be true.
Re: A new pyramid-like shape always lands the same side up
#38This is categorically different from the Gömböc, because it doesn't have uniform density. Most of its mass is concentrated in the base plate.
> This tetrahedron, which is mostly hollow and has a carefully calibrated center of mass
Uniform density isn't an issue for rigid bodies.
If you make sure the center of mass is in the same place, it will behave the same way.
Re: A new pyramid-like shape always lands the same side up
#39Worst 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 struc…
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.
Re: A new pyramid-like shape always lands the same side up
#40Somewhat disappointing that it won’t work with uniform density. More surprising it needed such massive variation in density and couldn’t just be 3d printed from one material with holes in.
Yeah isn’t this just like those toys with a heavy bottom that always end up standing straight up.
The main difference, and it matters a lot, is that all the surfaces are flat.