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This paper deals with the typical cell in a Poisson line tessellation in theplane whose directional distribution is concentrated on three equally spreadvalues with possibly different weights. Such a random polygon can only be atriangle, a quadrilateral, a pentagon or a hexagon. The probability for each ofthese cases is determined explicitly in terms of the weights. Extremal casesare discussed as well.

Vertex number of the typical cell in a tri-directional Poisson line tessellation