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

Comments

  1. Michael NelsonNovember 10, 2015 at 6:14 PM

    Well done!

    ReplyDelete
  2. John BaileyNovember 10, 2015 at 8:11 PM

    I 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?

    ReplyDelete
  3. John BaileyNovember 10, 2015 at 8:16 PM

    http://arxiv.org/abs/math/0202072 appears to bear a significant relationship to your paper.

    ReplyDelete
  4. Roice NelsonNovember 10, 2015 at 8:22 PM

    John 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.)

    http://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!

    ReplyDelete
  5. Math SolverNovember 11, 2015 at 12:52 AM

    Very interesting and informative work. Just I am reading it.

    ReplyDelete

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