File:Parabolicon construction.gif

English: The Parabolicon is a new member to the line segment bodies (solids whose surfaces are created by self-intersecting ruled surfaces that create closed 3D space). its whole surface is made of a single smooth developable surface. While rolling on a flat surface, its center of mass maintains constant altitude, so its motion is smooth. The distance between any two opposite parallel 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.