  Catenanes as interlocked molecules with a nonplanar graph have gained
increasing attention for their unique features such as topological chirality.
To date, the majority of research in this field has been focusing on catenanes
comprising monocyclic rings. Due to the lack of rational synthetic strategy,
catenanes of cage-like monomers are hardly accessible. Here we report on the
construction of an interwoven trimeric catenane that is composed of achiral
organic cages, which exhibits topological chirality. Our rational design begins
with a pure mathematical analysis, revealing that the formation probability of
the interwoven trimeric catenane surpasses that of its chain-like analogue by
20%; while driven by efficient template effect provided by strong {\pi}-{\pi}
stacking of aromatic panels, the interwoven structure emerges as the dominant
species, almost ruling out the formation of the chain-like isomer. Its
topological chirality is unambiguously unravelled by chiral-HPLC, CD
spectroscopy and X-ray diffraction. Our probability analysis-aided rational
design strategy would pave a new venue for the efficient synthesis of
topologically sophisticated structures in one pot.
