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Half of a {4,4,4} H³ Honeycomb

Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art
Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art
Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art
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Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art
Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art
Digital Preview

Not a Photo

Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art
Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art
Digital Preview

Not a Photo

Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art
Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art
Digital Preview

Not a Photo

Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art
Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art
Digital Preview

Not a Photo

Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art
Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art
Digital Preview

Not a Photo

Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art
Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art
Digital Preview

Not a Photo

Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art
Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art
Digital Preview

Not a Photo

Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art Pink Strong & Flexible Polished
Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art Pink Strong & Flexible Polished
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Not a Photo

Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art White Strong & Flexible Polished
Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art White Strong & Flexible Polished
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Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art Blue Strong & Flexible Polished
Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art Blue Strong & Flexible Polished
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Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art Purple Strong & Flexible Polished
Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art Purple Strong & Flexible Polished
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Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art Black Strong & Flexible
Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art Black Strong & Flexible
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Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art Red Strong & Flexible Polished
Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art Red Strong & Flexible Polished
Digital Preview

Not a Photo

Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art
Half of a {4,4,4} H³ Honeycomb 3d printed Sculptures Mathematical Art
Digital Preview

Not a Photo

About this Product

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
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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
 
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