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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

#151
post #132

Earlier quoted context omitted.

Just as with the gömböc. Though the latter balances on only one unstable axis while a D6 die does so on 20 (12 edges and 8 vertices).

Vertices aren't axes! They have the wrong dimensionality.

Let's instead call the balance things in question "balance things".

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

#152

I wouldn't really call this a "shape" since the highly manipulated center of mass is what is actually doing the work here. I would call this an object or rigid body.

It’s both. To work you need a polyhedron constructed of a series of polygons, here triangles, and one of those triangles has to have its center of mass outside the base of the object in all orientations. Otherwise the weight will pin it down instead of tilt it over. That’s why in the one orientation it tips back before tipping sideways: the center of mass is inside the footprint of right edge of the tetrahedron but n…

The article does a good job of explaining that it's still a non-trivial problem even if you are allowed to distribute the weight unevenly, but I do agree that what is happening here is much more specific than a "shape," which is simply geometry without any density information.

Put another way, most things precisely constructed with that same exact shape (of the outer hull, which is usually what is meant by shape) would not exhibit this property.

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

#153

Earlier quoted context omitted.

I was expecting to see the photos, but the jpg are linked there instead of visible. IIRC you were using a self-made CMS for your blog, with more support for math formulas. Does it not allow images?

Everyone complains about how crap my website is, so in this case I've just exported a page from my internal zim-wiki. Yes, it can have photos, but it doesn't give any control over sizing or positioning, so I'm providing links for people to click through to. It's the middle of my working day and I'm in the middle of meetings, so I don't have time to do anything more right now.

Your site is fine, thank you very much, I was not able to able to save it in the internet archive though: https://web.archive.org/save/https://www.solipsys.co.uk/ZimE...

"Save Page Now could not capture this URL because it was unreachable. If the site is online, it may be blocking access from our service."

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

#154

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…

>useful as a tamper detector If anyone's actually looking for this, check out tilt and shock indicators made for fragile packages. https://www.uline.com/Cls_10/Damage-Indicators https://www.youtube.com/watch?v=M9hHHt-S9kY

If it's about intrusion detection of packaged goods lentils, beans or rice are very useful [0]. Cheap but great tamper detection.

[0]: https://dys2p.com/en/2021-12-tamper-evident-protection.html

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

#155
post #153

Earlier quoted context omitted.

Everyone complains about how crap my website is, so in this case I've just exported a page from my internal zim-wiki. Yes, it can have photos, but it doesn't give any control over sizing or positioning, so I'm providing links for people to click through to. It's the middle of my working day and I'm in the middle of meetings, so I don't have time to do anything more right now.

Your site is fine, thank you very much, I was not able to able to save it in the internet archive though: https://web.archive.org/save/https://www.solipsys.co.uk/ZimE... "Save Page Now could not capture this URL because it was unreachable. If the site is online, it may be blocking access from our service."

Interesting ... and baffling. I've simply exported that from the zim wiki, not doing anything special, so I have no idea why the internet archive would complain about it.

And it's the other part of my site that people complain bitterly about:

https://www.solipsys.co.uk/new/ColinsBlog.html?yf26hn

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

#157

Earlier quoted context omitted.

>useful as a tamper detector If anyone's actually looking for this, check out tilt and shock indicators made for fragile packages. https://www.uline.com/Cls_10/Damage-Indicators https://www.youtube.com/watch?v=M9hHHt-S9kY

These shock watches and tilt watchers are quite expensive. I wonder how much must be the package worth to be feasible to use this kind of protection

Problem is when transporting tilt watchers, you can’t tilt the package either.

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

#158

Earlier quoted context omitted.

>useful as a tamper detector If anyone's actually looking for this, check out tilt and shock indicators made for fragile packages. https://www.uline.com/Cls_10/Damage-Indicators https://www.youtube.com/watch?v=M9hHHt-S9kY

These shock watches and tilt watchers are quite expensive. I wonder how much must be the package worth to be feasible to use this kind of protection

These are pretty normal when shipping scientific equipment.

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

#159
post #84

Earlier quoted context omitted.

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.

Oops disregard this, by "has to be identical" I thought you were objecting to the non uniformity of the surface, not the incongruity of the sides' shapes, so that's where my comment was coming from.

The incongruity of the sides certainly makes it not a Platonic Solid, though the article doesn't actually assert that it is. It just uses some terrible phrasing that's bound to mislead. Their words with my clarification for how it could be parsed in a factually accurate way: "A tetrahedron is the simplest Platonic solid (when it's a regular tetrahedron). Mathematicians have now made one (a tetrahedron, not a Platonic solid)...".

It's a dumb phrasing, it's like saying "Tesla makes the world's fastest accelerating sports car. I bought one" and then revealing that the "one" refers to a Tesla Model 3, not the fastest accelerating sports car.

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