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The groups of symmetry of regular polyhedra are considered. It is shown that a total number and types of gauge bosons in the Grand Unified Theory with the group SU(5) can be deduced from the structure of the cube rotation group. Possible connections of fundamental fermions with the icosahedral symmetry are discussed.
Context in source publication
Context 1
... we know, in a three-dimensional space there are only five such polyhedra ( Fig. 1): a tetrahedron (it has four faces), a cube (six), an octahedron (eight), a dodecahedron (twelve) and an icosahedron (twenty). They are called Platonic bodies, since mathematicians, close to Plato's Academy, first studied their entire set. Ancient Greek natural philosophers connected the first four bodies to four elements (fire, air, ...
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