  The intersection of the conifold $z_1^2+z_2^2+z_3^2 =0$ and $S^5$ is a
compact 3--dimensional manifold $X^3$. We review the description of $X^3$ as a
principal U(1) bundle over $S^2$ and construct the associated monopole line
bundles. These monopoles can have only even integers as their charge. We also
show the Kaluza--Klein reduction of $X^3$ to $S^2$ provides an easy
construction of these monopoles. Using the analogue of the Jordon-Schwinger
map, our techniques are readily adapted to give the fuzzy version of the
fibration $X^3 \rightarrow S^2$ and the associated line bundles. This is an
alternative new realization of the fuzzy sphere $S^2_F$ and monopoles on it.
