Related pagesSmall projective planes
Finite projective planes
Theorem. Up to isomorphism, there exists exactly one non-Desarguesian translation plane of order 9.
This translation plane is defined by a spreadset in a 2-dimensional vector space over the field GF(3), consisting of the following matrices.
As it turns out, the coordinatizing quasifield is a nearfield. Moreover the non-Desarguesian translation plane of order 9 has Lenz-Barlotti type IVa.3