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
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
Wow, that looks amazing! Can I buy one?
ReplyDeleteYes, but as luck would have it, you don't need to :) They accidentally sent me two of these, so I have an extra with your name on it. Shoot me an email with a mailing address, and I'll drop it in the mail this week. (I don't have an extra lighted base, however - those are available at http://www.lasercrystalawards.com/catalog/presentation-bases.html)
ReplyDeleteFor anyone else interested, these can be purchased from www.lasercrystalawards.com for a little under $40. You can upload a dummy model file during checkout and leave a note pointing them to the (large) stl file here: http://www.gravitation3d.com/lasercrystal/H3_336.stl
ReplyDeleteTrying to upload this large file to their servers fails, which is the reason for the dummy model file.
Roice Nelson Thanks so much! I'll email you my address. Someone needs to do a Shapeways for crystal engraving...
ReplyDeleteVery nice! How the STL file is rendered? As the vertices of triangles or do they generate some new dots?
ReplyDeleteFantastic. If it's not too much trouble, I'd love to see a video where the camera moves around the cube!
ReplyDeleteVladimir Bulatov, the rendering is the result of many tiny dot microfractures in the glass. The stl I made is just triangles though (about 1.3 million of them). Laser crystal awards does the rest. I know Bathsheba has made her own special algorithms for her engraved crystals controlling exactly where dots go, but I haven't found this necessary.
ReplyDeletehttp://www.bathsheba.com/crystal/process/
I will say that on the {3,3,6} model, only the surface gets turned into dots, and this does have a little bit of a downside near the really crowded vertices (leading to small voids), so that is potentially improvable if I tried to control the dots myself.
By the way, this is the third model I've had engraved, and all have been very pleasing. Here's some pics of another:
https://lh3.googleusercontent.com/hdkOy3am_6Ao8sOgilX1Fl98c_QIuK42FEs999VRVg4ANPZ5Zb18YRd995T3Erd8rSnsVPHrRSOjv4fg_nobvGwDgLUwiHn_v00=s0
The last was a portion of a 120-cell, but it was a gift and unfortunately I didn't take pics before giving it.
Allen Knutson, I just made a video for you. All I have to record is my phone, and things are a little blurry, but hopefully it gives a view like you were hoping :)
ReplyDelete{3,3,6} H3 Honeycomb
Vladimir Bulatov, sorry, I misunderstood your question earlier, so edited my previous response. In short, they generate new dots (it is not just triangle vertices that are rendered).
ReplyDeleteThis may be of interest to you Mark Bruce, perhaps you could have your bust in optical crystal by this means.
ReplyDeleteDON,T UNDERSTAND A WORD BUT LOVE THE PICTURE OF YOU AND SARAH SEND ME ONE AND THE CHRYSTAL IS BEAUTIFUL LOVE GRANDMA
ReplyDeleteLooks cool. Maybe I will try to 3d print this stereolithography file on the rapid prototype machine at work. :)
ReplyDeleteRoice Nelson I'm told that the package has arrived in Oklahoma, I'm looking forward to seeing it in person!
ReplyDelete