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A new pyramid-like shape always lands the same side up

quantamagazine.org

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Re: A new pyramid-like shape always lands the same side up

#81

Post by cubefox »

gerdesj wrote: post #51
ortusdux wrote: post #39

Earlier quoted context omitted.

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.

Love it - any sphere will do. A ping pong ball would be great - the DM/GM could throw it at a player for effect without braining them! (billiard)

A sphere is bad, it rolls away. The shape from the article would be better, but it is too hard to manufacture. And weighting is cheating anyway. The best option for a D1 is probably the gömböc, which is mentioned in the article.

Re: A new pyramid-like shape always lands the same side up

#82

Post by jacquesm »

cbsks wrote: post #34
ChuckMcM wrote: post #16

Worst 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

Earthquake detector?

Re: A new pyramid-like shape always lands the same side up

#83

Post by zoky »

gerdesj wrote: post #58
hammock wrote: post #52

Earlier quoted context omitted.

Or any mobius strip

I think a spherical D1 is far more interesting than a Möbius strip in this case. Dn: after the Platonic solids, Dn generally has triangular facets and as n increases, the shape of the die tends towards a sphere made up of smaller and smaller triangular faces. A D20 is an icosahedron. I'm sure I remember a D30 and a D100. However, in the limit, as the faces tend to zero in area, you end up with a D1. Now do you get a…

> However, in the limit, as the faces tend to zero in area, you end up with a D1.

Not really. You end up with a D-infinity, i.e. a sphere. A theoretical sphere thrown randomly onto a plane is going to end up with one single point, or face, touching the plane, and the point or face directly opposite that pointing up. Since in the real world we are incapable of distinguishing between infinitesimally small points, we might just declare them all to be part of the same single face, but from a mathematical perspective a collection of infinitely many points that are all equidistant from a central point in 3-dimensional space is a sphere.

Re: A new pyramid-like shape always lands the same side up

#84

Post by peeters »

lynnharry wrote: post #77
Y_Y wrote: post #17

That's not a Platonic solid. Come on, like.

Yeah. I tried to google what's Platonic solid and each face of a platonic solid has to be identical.

It's a meaningless distinction. A solid is defined by a 3D shape enclosed by a surface. It doesn't require uniform density. Just imagine that the sides of this surface are infinitesimally thin so as to be invisible and porous to air, and you've filled the definition. Don't like this answer, then just imagine the same thing but with an actual thin shell like mylar. It makes no difference.

Re: A new pyramid-like shape always lands the same side up

#85

Post by waste_monk »

emporas wrote: post #79
boznz wrote: post #2

maybe they should build moon landers this shape :-)

They could do that, but a regular gomboc would be totally fine. There are no rules for spaceships that their corners cannot be rounded. Maybe exoskeletons for turtles could be more useful. Turtles with their short legs, require the bottom of their shell to be totally flat, and a gomboc has no flat surface. Vehicles that drive on slopes could benefit from that as well.

>There are no rules for spaceships that their corners cannot be rounded.

Someone should write to UNOOSA and get this fixed up.

Re: A new pyramid-like shape always lands the same side up

#86

Post by shalmanese »

cubefox wrote: post #81
gerdesj wrote: post #51

Earlier quoted context omitted.

Love it - any sphere will do. A ping pong ball would be great - the DM/GM could throw it at a player for effect without braining them! (billiard)

A sphere is bad, it rolls away. The shape from the article would be better, but it is too hard to manufacture. And weighting is cheating anyway. The best option for a D1 is probably the gömböc, which is mentioned in the article.

Technically, a gomboc is a D1.00…001.

Re: A new pyramid-like shape always lands the same side up

#88

Post by nextaccountic »

emporas wrote: post #79
boznz wrote: post #2

maybe they should build moon landers this shape :-)

They could do that, but a regular gomboc would be totally fine. There are no rules for spaceships that their corners cannot be rounded. Maybe exoskeletons for turtles could be more useful. Turtles with their short legs, require the bottom of their shell to be totally flat, and a gomboc has no flat surface. Vehicles that drive on slopes could benefit from that as well.

Note that a turtle's shell already approximate a Gömböc shape (the curved self-righting shape discovered by the same mathematician in the linked article)

https://en.wikipedia.org/wiki/G%C3%B6mb%C3%B6c#Relation_to_a...

But yeah a specially designed exoskeleton could perform better, kinda like the prosthetics of Oscar Pistorious

Re: A new pyramid-like shape always lands the same side up

#90

Post by fruitplants »

nextaccountic wrote: post #88
emporas wrote: post #79

Earlier quoted context omitted.

They could do that, but a regular gomboc would be totally fine. There are no rules for spaceships that their corners cannot be rounded. Maybe exoskeletons for turtles could be more useful. Turtles with their short legs, require the bottom of their shell to be totally flat, and a gomboc has no flat surface. Vehicles that drive on slopes could benefit from that as well.

Note that a turtle's shell already approximate a Gömböc shape (the curved self-righting shape discovered by the same mathematician in the linked article) https://en.wikipedia.org/wiki/G%C3%B6mb%C3%B6c#Relation_to_a... But yeah a specially designed exoskeleton could perform better, kinda like the prosthetics of Oscar Pistorious

Gábor Domokos (mentioned in the article) talked about this on one QI episode:

https://www.youtube.com/watch?v=ggUHo1BgTak

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