Examining the achiral building blocks of [2] catenanes confirms the set of stereogenic units is complete. We first recognize that the highest symmetry ring point group, D∞h, contains the achiral Dnd, Cnh, Cnv and S2n subgroups and that therefore rings of these symmetries are the complete set of building blocks of catenane mechanical stereochemistry (see ESI section 1 for further discussion). Second, we recognize that any ring that has a C2 axis in the macrocycle plane (C2(x)) 11 cannot give rise to a conditional mechanical stereogenic unit because this symmetry operation of the separated rings corresponds to the notional process of switching their relative orientations in the corresponding [2]catenane (Figure ). Although this observation appears obvious, to our knowledge, this is the first time it has been stated explicitly. 12 Thus, we can discard rings of Dnd, and C2v(x) and C2h(x) symmetry. 11,13,14 The visually tractable D4h point group contains the C4v, C4h and S4 subgroups, representative of Cnv, Cnh and S2n, and so we modified a D4h ring to generate these structures by adding 4 equally spaced, equivalent vectors perpendicular and/or tangential to the ring plane in different relative orientations to highlight the key features of these achiral macrocycles (Figure ). Taking this approach, we find that to ensure that C2(x) is not a symmetry operation of the ring it must either be oriented (Cnh or S2n; characterised by vectors tangential to the ring circumference that define its direction), or facially dissymmetric (Cnv; characterised vectors perpendicular to the ring plane that differentiate its faces).