Platonicons are a hybrid of two very different families of solids; one ancient - the family of Platonic solids, the other new, named only recently - the developable rollers. A developable roller is a convex solid whose surface is one continuous developable face. Being polyhedra, the Platonic solids have flat faces that provide a stable base. The shape of the faces is simple and uniform, and spatial symmetry makes the solids look the same when viewed from different angles. They possess simplicity, stability, order and permanence. The single, twisted face of a developable roller makes it unstable. Any deviation from a delicate equilibrium causes it to start rolling. The curved and unbounded surface creates a sense of no beginning or end. The special shape of the surface also endows surprising meandering motion. They are dynamic, unpredictable and unstable.

In 2017, I asked if it was possible to create bodies that combine the qualities of these two different families. The simple, uniform structure of the Platonic bodies provided me with the key to resolving this question, specifically the regularity of the edges meeting at each vertex. I could fit to the vertices parts of identical cones and then join them to form one surface, a ‘tight garment’ wrapping the entire polyhedron. The ‘sewing’ process was challenging because there are many possible ways to join the surface parts and most do not give the desired result (one continuous face). Even after solving the problem geometrically, I still found it difficult to visualize the result. Only when 3D-printed models were in my hands could I grasp their unique and complex structure. My original question was answered positively. The Platonicons find a balance between the qualities of the two original families. They preserve the vertex system of the Platonic solids so one can identify in each body the polyhedron it circumscribes. On the other hand, they have the dynamic and mysterious qualities attributed to developable rollers.