  The energy, area and excess energy of a decorated vertex in a 2D foam are
calculated. The general shape of the vertex and its decoration are described
analytically by a reference pattern mapped by a parametric Moebius
transformation. A single parameter of control allows to describe, in a common
framework, different types of decorations, by liquid triangles or 3-sided
bubbles, and other non-conventional cells. A solution is proposed to explain
the stability threshold in the flower problem.
