  In this paper, we prove an isoperimetric inequality for the domain of
dependence of a finite lightcone in the Minkowski spacetime of dimension
greater than or equal to $3$. The inequality involves two quantities: the
volume of the domain of dependence, and the perimeter of the finite lightcone.
It states that among all finite lightcones with the same perimeter, the maximal
volume of the domain of dependence is achieved by the spacelike hyperplane
truncated finite lightcone. A novelty of this isoperimetric inequality is the
codimension $2$ comparison feature.
  We introduce the Lorentz polarisation to prove the isoperimetric inequality
by studying the corresponding variational problem. A key observation is the
monotonicity of the domain of dependence of a finite lightcone under the
Lorentz polarisation. We show that any finite lightcone can be transformed by a
sequence of Lorentz polarisations to approximate a spacelike hyperplane
truncated finite lightcone with an equal or less perimeter.
