Visualizing Hyperbolic Honeycombs
Visualizing Hyperbolic Honeycombs
I'm super excited about this, as it is the first time I've contributed to a submitted paper!
Pick any three integers (larger than 2), and we describe how to draw a picture of a corresponding {p,q,r} honeycomb, up to and including {∞,∞,∞}.
Originally shared by Henry Segerman
New paper with Roice Nelson, "Visualizing Hyperbolic Honeycombs". http://arxiv.org/abs/1511.02851
I'm super excited about this, as it is the first time I've contributed to a submitted paper!
Pick any three integers (larger than 2), and we describe how to draw a picture of a corresponding {p,q,r} honeycomb, up to and including {∞,∞,∞}.
Originally shared by Henry Segerman
New paper with Roice Nelson, "Visualizing Hyperbolic Honeycombs". http://arxiv.org/abs/1511.02851
Well done!
ReplyDeleteI have been collecting articles on closed topologies for the universe. This seems to add a ton more possibilities. Jeffrey Weeks name mean anything to you?
ReplyDeletehttp://arxiv.org/abs/math/0202072 appears to bear a significant relationship to your paper.
ReplyDeleteJohn Bailey, Yes! Jeffrey's book The Shape of Space had a big influence on me. It was the inspiration for a program I wrote called MagicTile, which was the way I was able to dip my toes into learning about hyperbolic geometry. (I'm still dipping my toes.)
ReplyDeletehttp://www.gravitation3d.com/magictile/
He and I exchanged a couple emails about MagicTile (the limit of our interaction), and I've watched some of his online lectures. I think Henry knows him better.
Most of these honeycombs have a fundamental region with infinite volume, so I'm not sure how/if they can apply to the shape of space. Of course, I would love it if they could!
Very interesting and informative work. Just I am reading it.
ReplyDelete