I wondered how silly you could get with sonobe, and had a bash at a buckyball, which is a fullerene (technically a truncated isocahedron; you can see a simple model here). It's twelve pentagons—each surrounded by 5 hexagons (20 in total)—making a football shape in England or a soccer ball shape in the USA.
It's made of 32 different colours; in total, it is 180 sonobe units.
I have used the same colour scheme as the coloured dodecahedron (with the pentagonal faces the same colours as the dodecahedron pictured here). This is a black pentagonal based face surrounded by 5 hexagonal based face.
Anyone wanting to build—firstly, you've gotta be slightly mad; secondly, draw a graph and it is almost exactly the same as the dodecahedron (i.e. you always put a flap in the pocket of a similar colour).
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9 Comments
Looks great! I've built the simpler 90 unit version with "instructions" here. But yours is cool how you can actually do a face coloring. Also using smaller units is definitely the way to go because otherwise the shape gets a little flimsy. I'm impressed. So awesome.
I hadn't really clicked that you could do it with 90 units - will have to give it a go. I am not sure you could make it much more complicated with that sort of compound in the above - it's not convex enough (or should that be concave?) The more complicated the model the higher the angle made by two faces and the sonobe need to be more crushed up - or at least thats how it feels when putting together
I'm pretty sure that when you go to "higher-order" buckyballs this wouldn't actually change since you would just insert more hexagons which don't change the curvature...so my point is that it can't get less curved than a flat plane and you're already making those whenever you make a hexagon.
Actually just thinking about this it probably means that you couldn't do negative curvature with these units. Rings of more than 6 wouldn't probably work too well. I haven't tried that with a regular sonobe before either...hmmm.... interesting.
You're dead right about adding more hexagons and that the hexagon is a plane (with equilaterals) - but the angle between the larger "faces" ie the pentagon and hexagons increases when you add more faces; and I am not sure that you could easily build it. Looking carefully the sonobe bridging between a pentagonal face and a hexagonal face is fatter than that between two hexagonal faces. Anyway - the next iteration of fulerene is just too complicated
Ah. You're right. My thinking was too simple.
Imatfaal, you're awesome... I've been working on a quilt, which is pretty time consuming. As soon as I'm finished I'm going to tackle some of these more complex models. Looks beautiful.
Cheers - I needed to catch up on some music and really relax. I tried to make a stop-motion video of the build - but manged to chew through two battery packs before I got to the actual build - oops. Gonna do another one and be more careful with battery use! Quilting just isn't common in my part of the world - very much an American pastime I think - is it a square pattern or irregular? I have always wanted a Piet Mondrian quilt - gonna have to learn...
Would love to see the video. It's my first quilt, and it's really simple. Just squares. Japanese woven fabric that differs on slightly from the other squares in hue / value. I want to make some origami for christmas presents, though, so I better get on it!
That would be an awesome quilt. Cool idea. I should put up a template for a Mondrian pattern on a sphere for an ornament.
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