This is joint work with Henry Segerman (www.shapeways.com/shops/henryseg). It models a regular space-filling tessellation of hyperbolic space (one of eleven exotic tessellations that have infinite cells and/or vertex figures). In this case, the cell is a tiling of squares, and the model is face-centered. Four cells meet at every edge, and an infinite number of cells meet at every vertex (the vertex figure is a tiling of squares too). For more details, see Coxeter's paper, "Regular Honeycombs in Hyperbolic Space"

Dimensions

IN: 3.94 w x 3.94 d x 2.091 h
CM: 10.008 w x 10.008 d x 5.312 h

Comments

Sign In or Join to comment.
 
Hi @lilys. I made it with custom software I wrote that can generate edges of hyperbolic honeycombs as STL shells. If you'd like to know a little more about hyperbolic honeycombs, see this: http://roice3.blogspot.com/2013/09/the-dual-534-and-435.html This particular model also relied on Shapeway's AbFab3D library: http://abfab3d.com/ AbFab3D was necessary to union all the separate shells because the output of my software produces a separate shell for every one of the edges in this model (over a thousand of them). I hope that gives a general idea, but I'm happy to answer more specific questions too, if you have them.
July 23, 2014, 3:08 am
Wow how did you create this?
July 23, 2014, 2:20 am
 
Logo

Hello.

We're sorry to inform you that we no longer support this browser and can't confirm that everything will work as expected. For the best Shapeways experience, please use one of the following browsers:

Click anywhere outside this window to continue.