  In the present paper we revisit the geometry of smooth plane quartics and
their bitangents from various viewpoints. First of all, we study in detail the
weak combinatorics of arrangements of bitangents associated with highly
symmetric quartic curves. We look at these quartic curves automorphism-wise and
we establish a lower bound on the number of quadruple intersection points for
arrangements of bitangents associated to smooth plane quartics being smooth and
reduced members of Ciani's pencil. Then we construct new examples of $3$-syzygy
reduced plane curves using smooth plane quartics and their bitangents.
