Don't forget the cube with quadratic sides. In general these are called platonic solids [1] and there are only 5 of them.
Why only 5 ? It has to do with angles and how you can unfold such a solid. (so it's somewhat caused by getting something from 3d-space into the 2d-plane)
I feel bad for the poor heptagon, which has neither a flat tiling nor a solid. At least on the hyperbolic plane everyone gets to take part in a tiling.
Comments
This reminds me of Roger Penrose's spacetime diagrams.
http://copaseticflow.blogspot.co.uk/2014/07/nine-notes-about...
Mesmerizing. I wish I could stop the spinning though.
Sure. Download the index.html and run it locally. Comment out line 259: //setInterval( animate, 20 );
in the inspector,
or, in this case,
works
I appreciated the "what the heck am I looking at?" section. Very smooth.
So, I can only create perfect solids with some numbers of sides (3 and 5). Why is that? Some symmetry caused by having 3 dimensions?
Don't forget the cube with quadratic sides. In general these are called platonic solids [1] and there are only 5 of them. Why only 5 ? It has to do with angles and how you can unfold such a solid. (so it's somewhat caused by getting something from 3d-space into the 2d-plane)
[1] http://en.wikipedia.org/wiki/Platonic_solid
Also, it's not just about the angles. It's about the number of connections between vertices too. There just aren't any other solutions.
To convince yourself, here's a fun game you can try with pencil and paper: http://ferkeltongs.livejournal.com/28364.html (disclosure: that's my blog)
I feel bad for the poor heptagon, which has neither a flat tiling nor a solid. At least on the hyperbolic plane everyone gets to take part in a tiling.
Very nice!