Enumeration of self-intersecting and simple concave quadrilaterals via paired partitions

摘要

Grünbaum's side-angle reciprocity property for convex quadrilaterals (Grünbaum [7]) has led to further mathematical research and generalizations (Alonso [1], [2] and [3], for a full discussion of developments related to this property, see Grünbaum [8]). This work reports on the classification of self-intersecting and simple concave quadrilaterals via paired partitions. It shows that for such quadrangles there is no side-angle reciprocity; this is established by the lack of symmetry of the classification results in the organizational tables.