Sphericon

A sphericon is the solid formed from a bicone with opening angle of (and therefore with ) obtained by slicing the solid with a plane containing the rotational axes resulting in a square cross section, then rotating the two pieces by and reconnecting them. It was constructed by Israeli game and toy inventor David Hirsch who patented the shape in Israel in 1984. It was given the name "sphericon" by Colin Roberts, who independently discovered the solid in the 1960s while attempting to carve a Möbius strip without a hole in the middle out of a block of wood.

The solid is not as widely known as it should be.

The above net shows another way the sphericon can be constructed. In this figure radians .

A sphericon has a single continuous face and rolls by wobbling along that face, resulting in straight-line motion. In addition, one sphericon can roll around another.

The sphericon with radius has surface area and volume

			(1)
			(2)

The centroid is at the origin, and the inertia tensor is given by

(3)