Polyhedral symmetries play an important role in mathematics, physics, chemistry, art and architecture. Despite the rich bibliography on this subject, little is known, to the non-expert, on the use of symmetric constructions in specialized scientific applications. We present a short review showing the influence of the geometry of polyhedra in the design of multi-detector systems employed in nuclear physics studies. In detection systems with a small number of detectors, designs based on Platonic and Archimedean solids have been used. On the other hand, in order to accommodate a large number of detector modules, highly segmented shell-like structures have been created. These constructions are based on a geodesic breakdown of an icosahedron and resemble architectural dome structures.