Altanisation originated in the chemical literature as a formal device for constructing generalised coronenes from smaller structures. The altan graph of $G$, $\mathfrak{a}(G, H)$, is constructed from graph $G$ by choosing an attachment set $H$ from the vertices of $G$ and attaching vertices of $H$ to alternate vertices of a new perimeter cycle of length $2|H|$. We prove sharp bounds for the nullity of altan and iterated altan graphs based on a general parent graph: the nullity of the altan exceeds the nullity of the parent graph by at most $2$. The case of excess nullity $2$ had not been noticed before; for benzenoids it occurs first for a parent structure with merely $5$ hexagons. We also exhibit an infinite family of convex benzenoids with $3$-fold dihedral symmetry (point group $D_{3h}$), where nullity increases from $2$ to $3$ under altanisation. This family accounts for all known examples with the excess nullity of $1$ where the parent graph is a singular convex benzenoid.

This is joint work with Patrick W. Fowler.

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