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)
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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)