Mathematical knots are severely restricted in the symmetries they can exhibit; they cannot assume the symmetries of the Platonic solids. An approach is presented that forms tubular knot sculptures that display in their overall structure the shapes of regular or semi-regular polyhedra: The knot strand passes along all the edges of such a polyhedron once or twice, so that an Eulerian circuit can be formed. Results are presented in the form of small 3D prints.