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