  We consider the ideal of inner $2$-minors $I_{\mathcal{P}}$ of a finite set
of cells $\mathcal{P}$, which we call the cell ideal of $\mathcal{P}$. A nice
interpretation for the height of an unmixed ideal $I_{\mathcal{P}}$, in terms
of the number of cells of $\mathcal{P}$ is given. Moreover, the coordinate
rings of cell ideals with isolated singularities are determined.
