Eric Weinstein

Okay.

So what's going on is that, for example, is that Neil can't figure out, well, where did this come from?

So what it is is...

spheres of radius root two at the eight vertices of a cube passing through each other but closing off an octahedral cavity with positively curved triangles inside that's what I needed you for well

But the all shape is a different thing.

Because in this case, in order to do this, what he did is he said...

I'm going to make mathematical spheres.

They're going to start to intersect each other, right?

And the intersections are going to be ignored because it's made out of fictitious math material until they close off the holes in the cubical lattice structure, leaving octahedral voids with this kind of curvature.

To make what he calls the all shape, you do something very different.

You'd start off with a tetrahedron, which is distinguished among the five platonic solids as being self-dual.

That is, there are four vertices and there are four faces, and you can interchange faces with vertices.

And in fact, I don't know if you guys have these things.

You have this?

No.

So this is an engineering feat.

So if you think platonic solids are old, a guy named Chuck Haberman figured out how to take the self-duality of a tetrahedron, and you can change the color of the sphere...

by throwing it up.

And effectively, if you think about the four dots on the surface of one of these, in between them are four triangles.

And he figured out a mechanism.