  A subcomplex $X\leq \mathcal{C}$ of a simplicial complex is strongly rigid if
every locally injective, simplicial map $X\to\mathcal{C}$ is the restriction of
a unique automorphism of $\mathcal{C}$. Aramayona and the second author proved
that the curve complex of an orientable surface can be exhausted by finite
strongly rigid sets. The Hatcher sphere complex is an analog of the curve
complex for isotopy classes of essential spheres in a connect sum of $n$ copies
of $S^1\times S^2$. We show that there is an exhaustion of the sphere complex
by finite strongly rigid sets for all $n\ge 3$ and that when $n=2$ the sphere
complex does not have finite rigid sets.
