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Did you know it's possible to cut a hole in a cube such that an identical cube can fit inside it? Really! It's called "Rupert's Property." *All Platonic solids are Rupert!* Except one new shape, which *cannot* fit inside itself. This eldritch polygon is called a Noperthedron!

arxiv.org/pdf/2508.18475

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in reply to Cory Doctorow

naturally, this only works in that same ideal/purely theoretical sense (ask any carpenter or mechanic) in which all cows are orbs for Physicists. =)

It's not that Mathematicians don't have a sense of humor, it's just that most of it is not perceivable by humans, such as - say - that of Astrophysicists.

in reply to Cory Doctorow

I think the term they coined is "Noperthedron". Like "Ru_pert", but not ;)

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in reply to Cory Doctorow

A small correction to this description— this new polyhedron is convex, not platonic. All platonics ARE Rupert; this new solid disproves the conjecture that all CONVEX 3d polyhedra are Rupert.

And I agree, Noperthedron is a great name for it. I wouldn’t have noticed the name if you hadn’t pointed it out.

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in reply to Matt Diamond

@matt_diamond A second correction (sorry):

Rupert’s property is that an identical cube can •pass through• the hole, not •fit inside• it.

(The latter would is trivially true if we read it as “at least some of it can fit inside the hole” — just remove any point on the surface — and would clearly be impossible if we read it as “fitting fully inside the hole” unless we allow the “hole” to consist of the entire polyhedron’s volume.)

The more formal definition of Rupert’s property is that there there are two different isometric 2D projections of a cube such that one of the resulting 2D shapes is a subset of the other.

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@Cory Doctorow
Oh good heavens, now we know: the Gallifreyans got their physics from Rupert. Who knew. Who knew?