Umbilic Rolling Link



This is a dynamic piece: The deltoid umbilic torus rolls through the dual cardioid umbilic torus and vice-versa, each piece free to turn. The umbilic refers to the deltoid as a hypocycloid of three cusps; the cardioid as an epicycloid of one cusp.

Each torus is the dual of the other, an outside-in instantiation: The compactification of the exterior of one is topologically the interior of the other.

Each is the inside out of the other
Each is the outside in of the other
Together they form a yin-yang pair;
yang is the deltoid torus, and
yin is cardioid torus.
As solid tori they can be viewed as an instantiation of a three-sphere.

Umbilic Rolling Link: A dynamic mathematical sculpture in action from Helaman Ferguson on Vimeo.