Instead of (or in addition to) the common vector diagram with cones, we propose to visualize the
peculiarities of quantum mechanical angular momentum by a completely quantized 3D model. It
spotlights the discrete eigenvalues and noncommutativity of components of angular momentum and
corresponds to outcomes of measurements—real or computer-simulated. The latter can be easily
realized by an interactive worksheet of a suitable program package of algebraic calculations. The
proposed complementary method of visualization helps undergraduate students to better understand the
counterintuitive properties of this quantum mechanical observable.