The genetic code is a mapping of 64 codons to 22 actions, including polypeptide chain initiation, termination, and incorpora- tion of the twenty amino acids. The standard tabular representation is useful for looking up which amino acid is encoded by a particular codon, but says little about functional relationships in the code. The possibility of making sense of the code rather than simply enumerating its codon-to-action pairings therefore is appealing, and many have attempted to find geometric representations of the code that illuminate its functional organization. Here, I show that a regular tetrahedron with each of its four faces divided into sixteen equilateral triangles (for a total of 64 triangular ‘cells’) is a particularly apt geometry for representing the code. I apply five principles of symmetry and balance in order to assign codons to the triangular cells of the tetrahedral faces. These principles draw on various aspects of the genetic code and the twenty amino acids, making the final construct a positional balance of the amino acids and their functions rather than a re-analysis of them. The potential signifi- cance of this exercise, and others like it, is that this way of organizing the biological facts may provide new insights into them.