  Reflective light collectors with hexagonal entrance and exit apertures are
frequently used in front of the focal-plane camera of a very-high-energy
gamma-ray telescope to increase the collection efficiency of atmospheric
Cherenkov photons and reduce the night-sky background entering at large
incident angles. The shape of a hexagonal light collector is usually based on
Winston's design, which is optimized for only two-dimensional optical systems.
However, it is not known whether a hexagonal Winston cone is optimal for the
real three-dimensional optical systems of gamma-ray telescopes. For the first
time we optimize the shape of a hexagonal light collector using quadratic and
cubic B\'ezier curves. We demonstrate that our optimized designs simultaneously
achieve a higher collection efficiency and background reduction rate than
traditional designs.
