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Henry Segerman's recent shapeways model of the {3,3,6} H3 honeycomb inspired me to make a similar model using...

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Henry Segerman's recent shapeways model of the {3,3,6} H3 honeycomb inspired me to make a similar model using different media... laser engraved crystal.  I took the tessellation a few levels deeper and rendered edges with proper thicknesses in the Poincare ball model.

The print has a very ghostly feel to it, which is quite nice for including lots of tetrahedra and still being able to see the the cells living towards the interior of the ball.  I think it would work well with even more cells added.  Lighting has a big effect on how things look!

The {3,3,6} is one of 15 regular honeycombs in hyperbolic 3-space.  It is one of 11 that have infinite cells and/or vertex figures.  For more info, see:

Henry's video about his shapeways model:
Regular triangulation of H³

Coxeter's paper, "Regular Honeycombs in Hyperbolic Space":
http://www.mathunion.org/ICM/ICM1954.3/Main/icm1954.3.0155.0169.ocr.pdf