  In [1], the author considered the problem of the optimal approximation of
symmetric surfaces by biquadratic B\'ezier patches. Unfortunately, the results
therein are incorrect, which is shown in this paper by considering the optimal
approximation of spherical squares. A detailed analysis and a numerical
algorithm are given, providing the best approximant according to the
(simplified) radial error, which differs from the one obtained in [1]. The
sphere is then approximated by the continuous spline of two and six tensor
product quadratic B\'ezier patches. It is further shown that the $G^1$ smooth
spline of six patches approximating the sphere exists, but it is not a good
approximation. The problem of an approximation of spherical rectangles is also
addressed and numerical examples indicate that several optimal approximants
might exist in some cases, making the problem extremely difficult to handle.
Finally, numerical examples are provided that confirm theoretical results.
