Complex chromosome aberrations (any exchange involving three or more breaks in two or more chromosomes) are effectively induced in peripheral blood lymphocytes (PBL) after exposure to low doses (mostly single particles) of densely ionising high-linear energy transfer (LET) α-particle radiation. The complexity, when observed by multiplex fluorescence in situ hybridisation (m-FISH), shows that commonly four but up to eight different chromosomes can be involved in each rearrangement. Given the territorial organisation of chromosomes in interphase and that only a very small fraction of the nucleus is irradiated by each α-particle traversal, the aim of this study is to address how aberrations of such complexity can be formed. To do this, we applied theoretical “cycle” analyses using m-FISH paint detail of PBL in their first cell division after exposure to high-LET α-particles. In brief, “cycle” analysis deconstructs the aberration “observed” by m-FISH to make predictions as to how it could have been formed in interphase. We propose from this that individual high-LET α-particle-induced complex aberrations may be formed by the misrepair of damaged chromatin in single physical “sites” within the nucleus, where each “site” is consistent with an “area” corresponding to the interface of two to three different chromosome territories. Limited migration of damaged chromatin is “allowed” within this “area”. Complex aberrations of increased size, reflecting the path of α-particle nuclear intersection, are formed through the sequential linking of these individual sites by the involvement of common chromosomes.