  We present a detailed exploration of certain outstanding features of the
transversely-projected three-gluon vertex, using the corresponding
Schwinger-Dyson equation in conjunction with key results obtained from quenched
lattice simulations. The main goal of this study is the scrutiny of the
approximate property denominated ``planar degeneracy'', unveiled when the Bose
symmetry of the vertex is properly exploited. The planar degeneracy leads to a
particularly simple parametrization of the vertex, reducing its kinematic
dependence to essentially a single variable. Our analysis, carried out in the
absence of dynamical quarks, reveals that the planar degeneracy is particularly
accurate for the description of the form factor associated with the classical
tensor, for a wide array of arbitrary kinematic configurations. Instead, the
remaining three form factors display considerable violations of this property.
In addition, and in close connection with the previous point, we demonstrate
the numerical dominance of the classical form factor over all others, except in
the vicinity of the soft-gluon kinematics. The final upshot of these
considerations is the emergence of a very compact description for the
three-gluon vertex in general kinematics, which may simplify significantly
nonperturbative applications involving this vertex.
