= Solution
<boron> is sufficiently small for effective oxygen-$2p$/boron-$2p$ overlap, and three-coordinate planar <boron> benefits from the pi donation just described. A six-membered <boroxine> ring provides this overlap without severe angle strain. The larger <aluminium> centre has poorer oxygen-$2p$/aluminium-$3p$ matching and remains strongly Lewis acidic. It can lower its <electron> deficiency by accepting additional <oxygen> coordination, making a three-dimensional <aluminoxane> cage favourable. Four-coordinate <aluminium> does not require a boroxine-like planar pi system.
An appropriate \b[hexamer model is an alternating Al/O <hexagonal prism>], with six <aluminium> and six <oxygen> vertices. Colour the twelve-vertex prism alternately Al and O: each <aluminium> then has three <oxygen> neighbours and an outward organic <substituent>, making it four-coordinate, while each <oxygen> bridges three <aluminium> centres. The graph has 18 Al–O edges, hence six Al centres with three Al–O bonds each. Different polyhedral connectivities and sizes can meet similar local coordination requirements, so the hexamer is a proposal rather than a claim that the empirical repeat unit fixes a unique cage.
\Image[/past-exam-of-the-chemistry-b-course-of-the-university-of-cambridge/2021/paper-2-aluminoxane.png]
{title=An alternating aluminium–oxygen prism satisfying the hexamer composition}
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