The sphericon is a three-dimensional solid with one side and two edges. It was first introduced by the Israeli game and toy inventor David Haran Hirsch who patented it in Israel in 1980. It was given its name by Colin Roberts, of Hertfordshire, England, who also explored it.

It may be constructed from a bicone (a double cone) with an apex of 90 degrees, by splitting the bicone along a plane through both apexes, rotating one of the two halves by 90 degrees, and reattaching the two halves.

Generalizing this construction to a regular 2n-sided polygon (square, hexagon, octogon ...), will give access to a set of other 3D solids with the same properties as sphericons when rolling on themselves they cover their whole surface.

order 2 & 4 are shown in action here: http://youtu.be/8OgA3UW9Adc

the offered parameters you can play with are:

sphericon_order : this defines the number of sides of the polygon = 2 * sphericon_order

sphericon_diameter : this is the diameter in mm of the sphere in which is included the sphericon

full_sphericon : [yes,no] if you want a full sphericon check "yes", but if you prefer to print it in half, check "no"

sphericon_angular_offset : if you have checked "yes" for full sphericon, this parameter allows to rotate the two halves by 1 to n sides

If you've printed the sphericon in two pieces, a set of cylindrical holes are foreseen to help aligning the two parts. Playing with pin_height and diameter allows either to insert small cylindrical magnets or pieces of plastic filament...
(pin_height and pin_diameter)

edit : I don't know why, the order 4 sphericon once genrated cannot be sliced by slic3r. It is needed to repear it with netfabb.
A repeared version has been posted here.