Bounds on the cardinalities of families of nearly neighborly quadrilaterals (Q810874)

A family of quadrilaterals in the Euclidean plane is called nearly neighborly if any two of them are separated by a line that contains a side of each. A line \(\ell\) is called base line for a neighborly family F of quadrilaterals if it contains a side of each member of F and all members of F lie in the same half-plane determined by \(\ell.\) The results: Examples of nearly neighborly families of nine quadrilaterals. A family of nearly neighborly quadrilaterals has at most 14 members. Four is the maximum number of members in a family of quadrilaterals on a base line.