Distribution of mapping points of 20 amino acids in the tetrahedral space

Based on the genetic codes and a simple theorem for the geometrical property of the regular tetrahedron, each amino acid is mapped onto a unique point in a 3-dimensional tetrahedral space. The distribution of the 20 mapping points for 20 amino acids is studied in detail. It is found that the mapping points for the hydrophobic and hydrophilic amino acids are distributed at distinct regions in the 3-dimensional space. A plane separating the two kinds of points satisfactorily based on the Fisher's algorithm has been calculated. It is shown that the codons coding for the hydrophobic amino acids are constituted dominantly by the bases of keto group, i.e., G and T. While the codons coding for the hydrophilic amino acids are constituted dominantly by the bases of amino group, i.e., A and C. The biological implication of the mapping points and the separating plane has been discussed in some details.