Quadrangles of order (s − 1, s + 1)

AbstractA generalized quadrangle P∗ of order (s − 1, s + 1) may be constructed from a quadrangle P of order s by expanding about a regular point or line. Likewise, P is obtained from P∗ by constricting about a suitable family of lines or points. These expansion and constriction processes are studied, with certain examples worked out in detail. In the process a new class of quadrangles of order (s − 1, s + 1) is discussed