  Compass states deliver sub-Planck phase-space structure in the sense that
sensitivity to phase-space displacement is superior to the sensitivity of
displacing the vacuum state in any direction, but this sensitivity is
anisotropic: better sensitivity for some directions of phase-space displacement
vs others. Here we introduce generalised compass states as superpositions of
$n$ compass states, with each oriented by $\frac\pi{2n}$ with respect to its
predecessor. Specifically, we derive Wigner functions for these generalised
compass states and approximate closed-form expressions for overlaps between
generalised compass states and their displaced counterparts. Furthermore, we
show that generalised compass states, in the limit $n\to\infty$, display
isotropic sensitivity to phase-space displacement in any direction.
