knot tiling triangle-faced polyhedra


A single shape tiles the faces of all three equilateral triangle-faced regular polyhedra with knots. Only the bend angle of the shape changes between the solids. The knot also tiles the plane.

Notice that the knot on the tetrahedron appears to be interlocked triangles; squares for the octahedron; and pentagons for the dodecahedron. Hexagons are reserved for the 2-dimensional version of this knot.