The common term is triplex DNA, also called triple-stranded DNA or a DNA triple helix.
In this structure, a third oligonucleotide associates with an existing DNA duplex, usually in its major groove. The extra strand forms Hoogsteen or reverse-Hoogsteen hydrogen bonds rather than the ordinary Watson–Crick pairs that hold the original duplex together. Because three strands participate, the resulting arrangement is called a triplex.
Triplex formation is favored by particular sequence patterns, especially homopurine–homopyrimidine stretches, and its stability can depend on pH, metal ions, and DNA supercoiling. Intramolecular forms, including H-DNA, can arise when part of a DNA molecule folds back onto itself; intermolecular triplexes use a separate third strand, sometimes called a triplex-forming oligonucleotide.
The alternatives describe different DNA structures. Z-DNA is a left-handed duplex, A-DNA is a compact right-handed duplex form, and a G-quadruplex is built from stacked guanine-rich tetrads rather than three interwoven strands.