In quantum physics lectures, half-integer spins are generally introduced as "objects that do not come back to their original state after one full turn but that do after two." As a consequence, students often consider this behavior to be purely quantum mechanical. However, spin-1/2 is above all a geometrical property of the rotations group and can, therefore, also have practical consequences at the macroscopic scale. To illustrate this, we introduce and describe in this work a new pedagogical tool named the spinorial ball. It allows students to concretely manipulate a macroscopic 1/2-spin, which helps them to build intuition as to how the latter behaves under rotations. This object can also be used to introduce several general concepts from the theory of Lie groups, such as group homomorphism and homotopy classes of loops through the example of the groups SU(2) and SO(3). The spinorial ball provides a macroscopic visualization of all these concepts, which are ubiquitous in quantum physics.