What is a Sphericon?

In gemotery, sphericon are solids with a continuous developable surface, 2 curved edges and 4 vertices.
They are special kind of roller solids that, while being rolled on a flat surface, bring all the points of their surface to contact with the surface they are rolling on.
The original one is a derivative of square and was discovered in 1969.

Due to his nature, the sphericon has a really strange way to move when rolled on a surface.

It's really fascinating how much the mathematics behave in the real world.

How it's made?

Using figures with an even nuber of sides, let say nSide, is possible to create other complex sphericons: revolving the figure on one of its diagonal we obtaine a primitive solid (a bicone, starting from a square). Cutting the solid with a midplane, then rotating one half by 360/nSide deg, we have the sphericon.

And the other rollers?

Using figures with odd number of sides, or taking a revolving axis of the startng figure different from the diagonal, we obtain other interesting solids.
I call them semi-sphericon, being the final solid surface not exactly continuous.
They too are truly special rollers.