The fundamental role of symmetry in the genetic code is to decrease disorder between codons and to preserve the integrity of system. The Standard Genetic Code (SGC) table is structured alphabetically in a horizontal and vertical array of U-C-A-G bases only with aesthetic symmetry. We postulate "the symmetry theory of genetic code" which is based on the unique physicochemical purine - pyrimidine symmetry net between codons of our Supersymmetry genetic code (SSyGC) table. The common purine - pyrimidine symmetry net as "the golden rule" and a core of the SSyGC table is universal, remaining unchanged during all of evolution. It is identical for more than 30 known genetic codes including those that will be discovered in the future, as well as for all RNA and DNA species. The unique SSyGC table has five physicochemical symmetries between bases, codons, and amino acids: 1) purine - pyrimidine symmetry on the principle of the Watson - Crick pairing (A↔U, C↔G), 2) direct - complement symmetry between codons, 3) mirror symmetry between bases and codons, 4) A + T rich and C + G rich symmetry between codons, and 5) symmetry between position of amino acids. Opposite to the SGC table where the third base is inactive, in the SSyGC table the role of the third base in codons is dominant in creation of symmetries. There are also present for the first time the symmetric positions of all boxes with amino acids. Opposite of the SGC table, the SSyGC code table contains three sextets for Serine, Arginine, and Leucine, each with six codons, positioned in continuity. Multi - facet symmetries of the SSyGC table as a natural law exclude the individual random creation of amino acids even in primitive life form. Accordingly, we hypothesize that the contemporary life arose due to common activity of all natural amino acids. With discovery of the unique physicochemical Supersymmetry genetic code table, the new light is shed on the symmetry of the genetic code.