We construct Alexandrov-embedded complete minimal surfaces in R3 which have genus zero and finitely many horizontal ends with prescribed geometry at infinity: the ends of the surface must be asymptotic to some prefixed Catenoids. This family of Catenoids can be viewed as an immersed planar polygon. To do that  identify each Catenoid with the vector whose direction and length  are  given by  the axis and the neck of the Catenoid respectively.  As minimal surfaces are balanced systems,  the sum of these vectors must be zero or, equivalently, when we draw these vectors consecutively  we must have a closed polygon. 
We show that the surface wanted exists if and only if the prescribed polygon is the boundary of an immersed disk. Moreover, each one of these disks produce a minimal surface. In particular, if the polygon is embedded, then the above Plateau problem at infinity has exactly one solution.