We consider a novel representation of a DNA sequence representing the standard genetic code being based on coordinates restricted to a 3 x 3 x 3 part of 3-D Cartesian grid in which points represent nonoverlapping triplets of nucleotide bases. From the coordinates of triplets one derives the Euclidean distance matrix, ED, for the sequence, from which various structural invariants can be extracted. We particularly consider the row sums of ED and of additional matrices whose elements are the higher powers of individual elements of ED. Advantages of the novel approach are outlined by examining the exon I of the human beta-globin gene. (C) 2003 Elsevier B.V. All rights reserved.