nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpqknzsux7p6lzwzdedp3m8c3c92z0swzc0xyy5glvse58txj5e9ztqaufa4k (nprofile…fa4k) Yes! I just completed the cross-polytope calculations, and they agree with the prediction.
That is, for a cross-polytope in dimension d, the probability of the line containing two uniformly random points from the interior of the polytope intersecting any of the pairs of opposite faces is:
P(cross-polytope, d) = k_d / 2^d
where k_d = 4d/(d+1)
and we also have:
P(hypercube, d) = k_d / (2d)
Greg Egan
npub1qq…j5nhv
2025-08-25 14:25:44 UTC
in reply to nevent1q…2zfx
Author Public Key
npub1qqm7nu2qf25xd3mw6y6cyp4v2wr7ktf43ymp5wqz4u8jvz76ymtsjj5nhvPublished at
2025-08-25 14:25:44 UTCEvent JSON
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