76 Unique Honeycombs Last weekend, Tom Ruen and I hit the milestone of uploading to wikipedia at least one image for 9 families of compact, Wythoffian, uniform H3 honeycombs, a total of 76 unique honeycombs. http://en.wikipedia.org/wiki/Uniform_honeycombs_in_hyperbolic_space You can easily browse all the images on my wiki user page: http://commons.wikimedia.org/wiki/User:Roice3 - Compact means the cells are finite in extent. - Wythoffian means we can generate them using a kaleidoscopic construction, that is by reflecting in mirrors. - Uniform means they are vertex transitive and have uniform polyhedral cells. There may even be more honeycombs that meet all these criteria, I don't know. ( update: see Tom's comment below! ) I do know there are hundreds more which don't meet one or more of these criteria, many undiscovered. In fact, there are infinitely more because there are some infinite families of honeycombs. wendy krieger continues to discover and enumerate more...
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