On geometric representation of regular tetrahedron's rotation group

In this paper, we construct a geometric graph for the A4 group different from Cayley’s graph. We also explore its geometric representation and calculate the representation’s spectrum. The irreducible components of this spectrum are representations of the A4 group by rotations of a regular tetrahedron. In fact, we suggest an algorithm for construction of a polyhedron in Euclid space with a given rotation group.