Poncelet's Theorem in the four nonisomorphic finite projective planes of order 9

Abstract

We study Poncelet's Theorem in the four non-isomorphic finite projective planes of order 9. Among these planes, only the Desarguesian plane turns out to be a Poncelet plane, while the other three planes which are constructed over the miniquaternion near-field of order 9, are not. This gives a complete discussion of Poncelet's Theorem in finite projective planes of order 9.