The distribution of the mapping points for the 235 bacterial genomes used in . A) The distribution of the mapping points in the reduced coordinate system (x, y, z) according to equation (3). The square (the side length = 2) corresponds to the projection of the regular tetrahedron onto the x-z coordinate plane. The bold and dotted circles correspond to projections of inscribe spheres with the correct radius length and wrongly calculated value 1/4, respectively. Based on the correct radius, in contrast to their conclusion that 45% of genomes have mapping points outside the inscribed sphere, none has the mapping point outside the inscribed sphere and none has an S value larger than 1/3. B) The distribution of the mapping points in the original coordinate system (X, Y, Z) according to equation (1). The square (the side length = ) corresponds to the projection of the regular tetrahedron onto the X-Z coordinate plane. Note that all mapping points are within the inscribed sphere, too, whose radius length is 1/4. The mistake of Elhaik et al. is the confusion of the original and reduced coordinate systems, and consequently, the neglect of the coordinate transform parameter . Refer to text for details.