  In Bachmann's Aufbau der Geometrie aus dem Spiegelungsbegriff (1959), it was
shown that a finite metric plane is a Desarguesian affine plane of odd order
equipped with a perpendicularity relation on lines, and conversely. Sherk
(1967) generalised this result to characterise the finite affine planes of odd
order by removing the 'three reflections axioms' from a metric plane. We show
that one can obtain a larger class of natural finite geometries, the so-called
Bruck nets of even degree, by weakening Sherk's axioms to allow non-collinear
points.
