DFT computations (ωB97X-D/6-31G(d)) of eight different cycloparaphenylenes that have three internal linking groups are shown to have two different conformations that express interesting Möbius topologies. The D3 conformers have linking numbers Lk of 3 (three half-twists as a trefoil), and the much more stable C2 conformers have a single half-twist, Lk = 1.