  Let $C$ be a closed convex subset of a real Hilbert space containing the
origin, and assume that $K$ is the homogenization cone of $C$, i.e., the
smallest closed convex cone containing $C \times \{1\}$. Homogenization cones
play an important role in optimization as they include, for instance, the
second-order/Lorentz/"ice cream" cone.
  In this note, we discuss the polar cone of $K$ as well as an algorithm for
finding the projection onto $K$ provided that the projection onto $C$ is
available. Various examples illustrate our results.
