  The Szekeres metric is an inhomogeneous cosmological model without any
symmetries. The standard Riemann-type coordinates can be transformed into
spherical-type coordinates, but the metric is no longer diagonal, and the
constant "radius" 2-spheres, 2-hyperboloids or 2-planes are known to be
"non-concentric". Since the transformation into spherical-type coordinates is
"radius" dependent, we question whether these coordinates have the same
orientation on each 2-surface. To answer this question, we set up an
orthonormal tetrad (ONT), and investigate its variation. We find that a
relative rotation of the tetrad is generic, and it can increase systematically
under conditions that are not very restrictive. We search for paths along which
the tetrad is constant, and find they only exist under very restrictive
conditions. In the process, we create a systematic method for defining an ONT
with chosen properties from a given metric.
