  We revisit the static spherically symmetric solutions of Einstein's General
Relativity with a conformally coupled scalar field in arbitrary dimensions.
Using a four rank tensor introduced earlier we recast the field equations in a
manifestly symmetric form to elucidate a somewhat less-known feature of dual
mapping between solutions. We also show that there is a two-parameter subfamily
of solutions which enjoy a duality symmetry and in four dimensions both the
BBMB black hole and the Barcelo-Visser wormhole belong to this subfamily. Along
the way, we rederive the full three-parameter family of solutions by direct
integration of the field equations and a natural choice of ansatz which
arguably has several advantages over other previously known methods.
