>Can you perfectly fill a 3 dimensional space with
>dodecahedrons? That depends on whether they are all the same size. If they are all the same size, then NO, because the angles where the faces meet are not pi/n (a requirement for several faces to fit together around a point without any cracks.
If they are allowed to be different sizes, then YES, of course. In fact you can fill space with any compact shape by just putting copies of the shape close together so they touch, and then putting smaller copies inthe cracks to fill them up, and then even smaller copies in the smaller cracks, etc. You end up with a fractal pattern filling the space. It requires an infinite number of copies of the shape, but you would need and infinite nubmer of copies even if they were all the same size, so this is really no worse. Of course, it is not as pleasing or pretty as tiling the space with same-size copies.
--Stuart Anderson