In their book Turtle Geometry, Abelson and diSessa formulate and prove the POLY Closing Theorem, which gives an exact condition for when a path produced by the POLY program closes (initial and final turtle position are equal) properly (initial and final turtle heading are equal). The POLY program repeats a translation (Move command) followed by a rotation (Turn command). Their Looping Lemma states that any repeated turtle program is rotation-symmetry equivalent to a POLY program. The POLY Closing Theorem and Looping Lemma are useful in understanding and creating artistic motifs because repeating the same turtle program so that it closes properly, leads to a rotationally symmetric path. In this article, we generalize their result to 3D. A surprising corollary is that when repeating a non-closed non-proper turtle program, its path is closed if and only if it is proper.