  We investigate the electronic structure of a triatomic Rydberg molecule
formed by a Rydberg atom and two neutral ground-state atoms. Taking into
account the $s$-wave and $p$-wave interactions we perform electronic structure
calculations and analyze the adiabatic electronic potentials evolving from the
Rb$(n=35, l\ge 3)$ Rydberg degenerate manifold. We hereby focus on three
different classes of geometries of the Rydberg molecules, including symmetric,
asymmetric and planar configurations. The metamorphosis of these potential
energy surfaces in the presence of an external electric field is explored.
