The structural space of nucleic acids is commonly explored through local conformational variants of duplex DNA. However, if a tetra-stranded hereditary polymer such as Q-DNA is considered as a canonical genome-scale state, topology becomes a primary organizing principle rather than a secondary constraint. In this work, I develop a topological classification framework for tetra-stranded helices, introducing a catalogue of admissiblearchitectures defined by strand number, chirality, winding modes, and inter-strand entanglement. I define generalized topological invariants—including multi-strand linking numbers and generalized supercoiling—and analyze their conservation and transformation across structural transitions. I then formalize Q↔D transitions, describing how a tetra-stranded canonical state may interconvert with duplex-dominant states under controlled topological operations. The result is an atlas of tetra-strandedarchitectures and a conceptual phase diagram of topological regimes, providing a foundation for subsequent energetic, kinetic, and evolutionary analyses of Q-DNA. Keywords: tetra-stranded helices, DNA topology, linking number, supercoiling, genome architecture, Q-DNA, non-canonical nucleic acids.