garden of quasiperiodic rhombus tilings

January 8, 2012 6:37 AM

Need some quasiperiodic tilings? Alan Schoen has a smorgasbord of tilings of rhombuses with pentagonal, heptagonal, and nonagonal symmetry that come in many flavors. Be sure to check out his page on triply periodic minimal surfaces and the other curios at his Geometry Garret.
posted by oonh (9 comments total)

These guys are such squares...
posted by Fizz at 6:54 AM on January 8, 2012

Pretty cool. I can cross my eyes to get most of the stereo images on the triply periodic minimal surfaces link to resolve into 3D. Unfortunately, in doing so I seem to have opened a slipstream gateway to a cyclopean dimension and am presently being bodily consumed by a host of unfathomable congeries.

Take heed.
posted by Edogy at 7:37 AM on January 8, 2012 [1 favorite]

oooh, tilings.
posted by EricGjerde at 7:59 AM on January 8, 2012 [1 favorite]

I want actual tiles, or CAD files to get from some 3D printer in ceramic -- tiles I can actually use at home; got a hole where a hearth used to be that would fill nicely with those. Anyone?
posted by hank at 10:17 AM on January 8, 2012

Yeah, I did need some quasiperiodic tilings, thanks.

Years ago, I wrote a Ruby program that used Ammann-bar forcing rules to generate PostScript tilings. I wish I had time to work on it.

I sank a lot of money into Zometool too, building Danzer tiles.

I also dream of actual ceramic tiles. It's just a kite and a dart...
posted by Rat Spatula at 10:20 AM on January 8, 2012

I want actual tiles, or CAD files to get from some 3D printer in ceramic -- tiles I can actually use at home; got a hole where a hearth used to be that would fill nicely with those. Anyone?

It's been done before, so I don't see why not. You shouldn't need 3d printing or anything - just someone who will spend all day cutting rhombusses for you.
posted by Popular Ethics at 10:37 AM on January 8, 2012 [1 favorite]

> just someone who will spend all day cutting rhombusses

I'm not rich enough for that method, so I'm hoping for a technofix.

(Just printing out the outlines of the shapes would work, in a 3D printer using one of the ceramic or metal materials; lay that down, then fill the holes with colored concrete, cloisonne-like.
posted by hank at 11:34 AM on January 8, 2012

(but, yes, there's a good example here using fairly large tiles in two colors: -- and that took 40 hours with a tile saw, they say). Thanks for the pointer, I hadn't seen that one with the actual time info.
posted by hank at 11:37 AM on January 8, 2012

Need some 15th century quasiperiodic tilings? (Girih tiles are really great).
posted by ecmendenhall at 9:37 AM on January 9, 2012 [1 favorite]