The HexaSphericon belongs to an obscure family of shapes known as PolySphericons, which were inadvertently created just half a century ago. The HexaSphericon possesses some extraordinarily unique and fascinating mathematical properties, which allow it to roll around like a sphere (hence the name "sphere" -icon), but in its own unique meandering way.

The word "Sphericon" is credited to its discoverer, UK craftsman Colin Roberts, who in the late 1960s created the first Sphericon while trying to make a Möbius Strip. Israeli inventor, David Hirsch, independently created his own Sphericon in the late 1970's. Roberts' Sphericon was first introduced to the world by prominent science columnist and mathematician Ian Stewart in the October 1999 issue of Scientific American.

One of the most fascinating aspects of PolySphericons is with regard to their ability to roll. The center of mass of a Sphere or Cylinder travels in a straight line and maintains the same height while it rolls. A Cone's center of mass travels in a circle and also remains the same height while it rolls. A HexaSphericon's center of mass travels along a "meandering" path and remains the same height while it rolls. However, the average direction it rolls is still a straight line. Different Sphericons, different HexaSphericons, and different HexaSphericon twists roll along different types of meandering paths, but the general properties remain the same. The Solids of Constant Width, such as our Orbiform, do not "roll" in the same way since their center of mass oscillates in height.

There are three types of HexaSphericons, derived from a Hexagon (hence the Greek prefix Hexa). However, within these types, there are different variants, with different properties. For example, Point Type and Edge Type are chiral, meaning there are left handed and right handed versions. The Point Type HexaSphericon can roll infinitely, like a sphere, but the Edge Type HexaSphericon can only roll a fixed distance. The Hybrid HexaSphericon has two distinctly different variants, and interestingly it has both the ability to roll an infinite length (in a loop), and a finite length.

1. Point Type

• Revolution of a hexagon on its line of point symmetry.

• Infinite Straight line Rolling. (like a sphere)

• Chiral (left and right versions)

2. Edge Type

• Revolution of a hexagon on its line of edge symmetry.

• Finite Straight Line Rolling (like a sphere, which only can roll a fixed distance)

• Chiral (left and right versions)

3. Hybrid

• A combination of Point Type and Edge Type.

• Finite rolling and continuous loop rolling properties. Note: **Loop rolling means it follows a path, which ends where it starts, similar to a cone. It does not roll in a straight line like the Point Type.

• Two different, distinct versions