  A latin bitrade $(T^{\diamond}, T^{\otimes})$ is a pair of partial latin
squares which defines the difference between two arbitrary latin squares
$L^{\diamond} \supseteq T^{\diamond}$ and $L^{\diamond} \supseteq T^{\otimes}$
of the same order. A 3-homogeneous bitrade $(T^{\diamond}, T^{\otimes})$ has
three entries in each row, three entries in each column, and each symbol
appears three times in $T^{\diamond}$. Cavenagh (2006) showed that any
3-homogeneous bitrade may be partitioned into three transversals. In this paper
we provide an independent proof of Cavenagh's result using geometric methods.
In doing so we provide a framework for studying bitrades as tessellations of
spherical, euclidean or hyperbolic space.
