Jason (jcreed) wrote,
Jason
jcreed

Quick and somewhat naïve question to any of you out there who know things about polytopes:

Is there a known simple criterion for whether a given lattice is the face lattice of some polytope?

Ideally a criterion that is subjectively "finite"-feeling, something combinatorial rather than about convex subsets of huge infinite things like Rn.

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Hmm this paper (mentioned at mathoverflow under a similar question) suggests that it is NP-hard to answer this question already with 4-dimensional polytopes. I was kind of hoping it would be decidable at least, but I'm not sure if that question is open or not. In other words, I don't know whether the mathematical community at large knows how to reliably know whether a given lattice is a face lattice. That's three knowings! That's a lot, unless perhaps you're a complexity theorist, in which case you have to deal with this kind of nonsense all the time.
Tags: math, polytopes
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  • (no subject)

    Saw Mike Birbiglia's "Thank God for Jokes" with K in a little theater on bleeker. Funny show. I highly recommend his show "My girlfriend's boyfriend"…

  • (no subject)

    Second city yesterday was really funny. We got shoved in a front-row seat and picked on to provide detailed improv prompts for a big log improv…

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    It was a shitty rainy night so we stayed in and ate italian and watched " Dress to Kill", which was pretty excellent. I already kind of knew most the…