Message #2320

From: Andrey <>
Subject: [MC4D] Re: Hyperbolic Honeycomb {7,3,3}
Date: Fri, 06 Jul 2012 10:07:08 -0000

> Ah okay, it took me a few minutes to realize the significance of that.
> That tells me that if we started with a {3,3} cell of the {3,3,7}
> (which is what I was assuming)
> we will NOT get a regular hexagon
> (since the dihedral angle of that cell is exactly 2*pi/7),
> in fact we will not get a regular hexagon
> when starting with any {3,3,n}
> (since the dihedral angle of the cell would be 2*pi/n).
> That’s disappointing.
> So when starting with {3,3,7}, the hexagon isn’t regular…
> but I’m still not sure which edges are longer and which are shorter.
> (And I guess whichever it is for {3,3,7},
> it will be the opposite for all {3,3,n>=8}, since the switchover
> is somewhere between 2*pi/8 and 2*pi/7…
> assuming some kind of monotonicity, which seems likely.)

I think that for {3,3,7} cutting edges will be shorter. Because when we take {3,3,6}, its {3} faces have parallel sides (i.e. they meet at infinity) and distance between them is zero. While we decrease angle below zero, distance will increase, but in {3,3,7} it will be still small enough.