Abstract
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.
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Leanos, J., Lomeli, M., Merino, C. et al. Simple Euclidean Arrangements with No (≥ 5)-Gons. Discrete Comput Geom 38, 595–603 (2007). https://doi.org/10.1007/s00454-007-1351-6
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DOI: https://doi.org/10.1007/s00454-007-1351-6