{infinity,3,3}

Hyperbolic tesselation

Category:

Science & Technology

Tags:

• Hyperbolic
• geometry

[mgoerner]

I have uploaded {3,3,infinity}. I hope the explanation there helps.

Also, yes, you have just proven that random walk in hyperbolic space is non-recurrent.

[AlephNeil]

Would {3,3,infinity} be impossible? (Thinking aloud: if the vertices are points within the space then the vicinity of a point looks like sphere, and so for {a,b,c} we need 1/b + 1/c > 1/2. Does the 'vicinity' of a point at infinity looks like an infinite Euclidean plane, so that we need 1/b + 1/c = 1/2? I think so...)

[AlephNeil]

They're all awesome but there's something almost scary about this one... the thought "once you go down one of those branches, you can never return unless you come back the way you came"