English: We notice the one W codon and three X codons are homologous and in a prime 1:3 degeneracy ratio, suggesting the stop codons “point at” W.

Therefore, using three perpendicular isotropic axes, we require W to be at a vertex with the three X codons adjacent. W is at a vertex (coplanar and) adjacent to XXX ugg requires 3 vectors, 2 beginning or ending with g, and 1 beginning or ending with u, thus, u and g must be at opposite ends of each vector: g _ _ u or u _ _ g From the 2nd and 3rd codon positions of W and X, [g, a] are adjacent: g a _ u or u _ a g Only c remains: g a c u or u c a g By convention we select gacu, affirming there is a second mirror solution, and by isotropy, we construct all three axes of the cube using gacu.

We observe this topology: 1) Segregates wobble by [g, a] and [c, u]. 2) Makes all three Isoleucine codons colinear and adjacent. 3) Groups the 4 + 2 degeneracy of R and L as adjacent lines.

In terms of physical chemistry, parallel planes ngn, nan, ncn, and nun group codons by hydropathy and molar volume. nan is hydrophilic, ntn is hydrophobic, ncn is tightly packed in molar volume / hydropathy space, and ngn sweeps outliers in hydropathy / molar volume space. Serine is the only amino acid in two such planes: ngn and ncn. Similarly, the 4 + 2 codon degeneracy of serine is not adjacent, whereas the 6-degenarate 4 + 2 codons for R and L are each adjacent. We speculate this topology uses the least number of connectors between degenerate codons and is closest packed.

.