I've encountered quite a few interesting solids during my time. Some of them, are the sphericons. They are taken by rotating a regular polygon around an axis, and twisting the resulting figure to reach a snaking appearance. I'd like to explore higher dimensional analogs, since I feel that you could use a polyhedron instead of a polygon to create a 4d version. On another note, I've noticed their similarities to slices of coiloids though this may only be superficial.
http://www.mathias.org/steve/sphericons/series.htm
Here are some pictures of sphericons.