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

(www.quantamagazine.org)
600 points robinhouston | 3 comments | 25 Jun 25 20:01 UTC | HN request time: 0.774s | source
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kazinator ◴[25 Jun 25 21:21 UTC] No.44381940[source]▶
This is categorically different from the Gömböc, because it doesn't have uniform density. Most of its mass is concentrated in the base plate.
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Nevermark ◴[25 Jun 25 22:13 UTC] No.44382275[source]▶
> 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.

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1. kazinator ◴[25 Jun 25 23:29 UTC] No.44382765[source]▶
If the constraints are that an object has to be of uniform density, convex, and not containing any voids, then you cannot choose where its centre of mass will be, other than by changing it shape.
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2. Nevermark ◴[26 Jun 25 04:50 UTC] No.44384273[source]▶
That isn't true.

Look at the pictures. It has the same outer shape, that is all that is required for the geometry.

And for center of mass, you set the positions for the bars, any variations in their thickness, then size and place the flat facet, in order to achieve the same center of mass as for a filled uniform density object of the same geometry.

As the article says:

> carefully calibrated center of mass

Unless an object has internal interactions, for purposes of center of mass you can achieve the uniform-density-equivalent any way you want. It won't change the behavior.

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3. gus_massa ◴[26 Jun 25 14:34 UTC] No.44387853[source]▶
> Unless an object has internal interactions, for purposes of center of mass you can achieve the uniform-density-equivalent any way you want. It won't change the behavior.

That is true, but they are using a very heavy material for a small part and very light material for the other. So in this case the center of mass is almost on one of the faces of the polyhedron.