Two 6×6 toroidal polyhedra join in a link, each one exactly filling the hole in its counterpart. The surface is patterned with a random arrangement (including position and rotation) of eight Truchet tiles. The tile colors on the two toroids are inverted with respect to each other. Each panel of the hull is unique, and the sculpture can be assembled in approximately 10²³ distinct arrangements.
The polygons comprising each toroid are all rectangles, trapezoids, or right triangles with integer dimensions, ranging from a 1×2 right triangle for the smallest panel, up to a 6×2 rectangle for the largest. There are exactly 3 unique dihedral angles between the faces and 4 unique face angles at the vertices of each polygon.

This piece was created in collaboration with Matt Zucker.
It will be displayed at the 2027 Joint Mathematics meeting in Chicago, IL.
