  We generalize the link between fluctuation theorems and thermodynamic
uncertainty relations by deriving a bound on the variance of fluxes that
satisfy an isometric fluctuation theorem. The resulting bound, which depends on
the system's dimension $d$, naturally interpolates between two known bounds.
The bound derived from the entropy production fluctuation theorem is recovered
for $d=1$, and the original entropy production thermodynamic uncertainty
relation is obtained in the $d \to \infty$ limit. We show that our result can
be generalized to order parameters in equilibrium systems, and we illustrate
the results on a Heisenberg spin chain.
