  Nearest-neighbor coupled-mode theory is a powerful framework to describe
electromagnetic-wave propagation in multicore fibers but it lacks precision as
the separation between cores decreases. We use abstract symmetries to study a
ring of evenly distributed identical cores around a central core, a common
configuration used in telecommunications and sensing. We find its normal modes
and their effective propagation constants while including the effect of all
high-order inter-core couplings. Finite-element simulations support our results
to good agreement. Only two of these effective modes involve fields in all the
cores. These two modes display opposite-sign phase configurations between the
fields in the external cores and the central core. These two modes still appear
in the limit where the external cores become a continuous ring. Our results
might help improve predictions for crosstalk in telecommunications or precision
in sensing applications.
