  In this note we construct a flag simplicial $3$-sphere $\Delta$ with the
following properties: - $\Delta$ is not a suspension; - $\Delta$ has no edge
that can be contracted to obtain another flag sphere; - The only equators
(induced subcomplexes which are spheres of codimension $1$) of $\Delta$ are
vertex links. Our construction has $12$ vertices, the minimum number of
vertices such a simplicial complex can have. This answers a question posed by
Chudnovsky and Nevo.
