New things: Hyperbolic honeycombs.

Originally shared by Henry Segerman

New things: Hyperbolic honeycombs. These sculptures are joint work with Roice Nelson and show various tilings of 3-dimensional hyperbolic space.
http://www.youtube.com/watch?v=YzzJGeiucNg

Comments

  1. Eduard BaumannDecember 10, 2013 at 5:46 AM

    Perfect presentation!

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  2. wendy kriegerDecember 21, 2013 at 12:19 AM

    At the back one sees {6,3,4}, and in the front, {4,3,5} and its dual {5,3,4}.  The {4,3,5} contains the vertices of the {5,3,4}, but the cubes are the same size as one might inscribe in the dodecahedra of {5,3,4}.  The order of resolution is about 16.

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  3. Roice NelsonDecember 27, 2013 at 6:09 PM

    Hi Wendy. The one in the back is a {6,3,3}.  I'm curious, what do you mean by "the order of resolution"?

    ReplyDelete
  4. wendy kriegerDecember 27, 2013 at 7:22 PM

    You'e right about {6,3,3}. The order of resolution is a measure of the edge detail, something to do with the mean horocyclic diameter squared, in terms of sextants. They're ideas from my Hyperbolic geometry without the tears.

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  5. Roice NelsonDecember 29, 2013 at 12:57 PM

    Thanks, can you point me to your hyperbolic geometry without the tears?

    ReplyDelete
  6. wendy kriegerDecember 29, 2013 at 2:13 PM

    At the moment, no. It,s based on the idea that if you use a euclidean ruler in hyperbolic space, you can do euclidean geometry. But the intersect between euclidean and hyperbolic geometries is a circle. So most of the trick is to draw a chain of circles. The actual rulers measure the square of distances, which greatly simplifies the maths.

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