The Kurdjumov-Sachs relationship involves a "rotation" about an invariant <112> axis during transformation. The specific axes that act in this way lie in the {111} slip planes of deformed fcc materials, such as austenite, and are perpendicular to the active slip burgers vectors (or to burgers vectors produced by reaction). However, the "minimum angle" rotation axes can also be used as invariant axes. These angles are equal to 42.85degrees and their locations are best specified in the Rodrigues-Frank notation. Similar approaches to the Nishiyama-Wassermann and Bain correspondence relations lead to angles of 45.98degrees and 45degrees, respectively. The locations of these three sets of rotation axes are described together with the effects of dislocation reaction and cross-slip on the final variants that are expected to appear.