  We extend the calculations of holographic entanglement entropy in AdS(4) for
entangling curves with singular non-smooth points that generalize cusps. Our
calculations are based on minimal surfaces that correspond to elliptic
solutions of the corresponding Pohlmeyer reduced system. For these minimal
surfaces, the entangling curve contains singular points that are not cusps, but
the joint point of two logarithmic spirals one being the rotation of the other
by a given angle. It turns out that, similarly to the case of cusps, the
entanglement entropy contains a logarithmic term, which is absent when the
entangling curve is smooth. The latter depends solely on the geometry of the
singular points and not on the global characteristics of the entangling curve.
The results suggest that a careful definition of the geometric characteristic
of such a singular point that determines the logarithmic term is required,
which does not always coincide with the definition of the angle. Furthermore,
it is shown that the smoothness of the dependence of the logarithmic terms on
this characteristic is not in general guaranteed, depending on the uniqueness
of the minimal surface for the given entangling curve.
