A New Geometric Shape?
A Relative of the Sphericon-Oloid Family

The Parabolicon

Sphericon Animation

Parabolicon Animation

David Hirsch named his new solid the PARABOLICON. It is a new member to the line segment bodies (solids whose surfaces are created by self-intersecting ruled surfaces that create closed 3D space). Like the sphericon and the oloid, co-members of this special family, its whole surface is made of a single smooth developable surface. Like the sphericon, and unlike the oloid, while rolling on a flat surface, its center of mass maintains constant altitude, so its motion is smooth. Unlike the sphericon and the oloid, the distance between any two parallel opposite planes that are tangent to its surface is constant, so that during all rolling duration its height doesn't change. It has 6 parabolic edges and 8 vertices, 6 of which, define a regular hexagon, which divides the PARABOLICON into two congruent parts. The PARABOLICON circumscribes a regular octahedron whose 6 vertices lie on the 6 PARABOLICON's edges.

David Hirsch also writes that the PARABOLICON is only one of an infinite number of shapes belonging to this new family of bodies. For example, a new shape made of six cone segments can be constructed to have a middle cross-section of a regular hexagon; thus, an appropriate name might be the HEXACON, a special case of the PARABOLICON. Other future possibilities include the Octacon, Decacon, etc.