In the context of double-helical DNA, the periodic image distance refers to the distance between one strand and its periodic image, which is a copy of the strand wrapped around the circumference of the cylinder formed by the DNA double helix. If the periodic image distance is zero, it means that the two strands are perfectly superimposed on each other and that there is no change in the relative orientation or position of the two strands as you move along the cylinder.

This result can occur if the DNA double helix has a uniform structure throughout its length, with no twists or writhes, and if the two strands are perfectly complementary and form a stable base pairing. In such a case, the periodic image distance would be expected to be zero.

It's important to note that in most real-life cases, the periodic image distance of DNA is not zero but rather is a small non-zero value that reflects the presence of structural variations and irregularities along the length of the DNA molecule.