In Coxeter’s “Regular Honeycombs in Hyperbolic Space”
on the Wayback Machine at:
https://web.archive.org/web/20160610043106/http://www.mathunion.org/ICM/ICM1954.3/Main/icm1954.3.0155.0169.ocr.pdf
Coxeter gives the edge length of this honeycomb to be 2φ where cosh^2 φ = 9/8, which I believe means the dot product between the Lorentzian unit timelike vectors corresponding to adjacent vertices should be:
–cosh(2 arccosh(3/(2√2)))
= –(2 cosh(arccosh(3/(2√2)))^2–1)
= –(9/4–1)
= –5/4
I’m posting this now in case I don’t get any further, but I ought to be able to figure out some more things that follow from this.
Greg Egan /
npub12c…gd38p
2024-04-22 13:41:30
in reply to nevent1q…v6as
Author Public Key
npub12cuzzqzv8e8y7na77a9zv47mx2v6pec60qs5h7takzmv5p0mw0fsmgd38pPublished at
2024-04-22 13:41:30Event JSON
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