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It is shown that if a simple Euclidean arrangement of n pseudolines has no (>= 5)-gons, then it has exactly n - 2 triangles and (n - 2)(n - 3)/2 quadrilaterals. We also describe how to construct all such arrangements, and as a consequence we show that they are all stretchable

Simple Euclidean Arrangements with No (≥ 5)-Gons