  The accurate computation of the electrostatic capacity of three dimensional
objects is a fascinating benchmark problem with a long and rich history. In
particular, the capacity of the unit cube has widely been studied, and recent
advances allow to compute its capacity to more than ten digits of accuracy.
However, the accurate computation of the capacity for general three dimensional
polyhedra is still an open problem. In this paper, we propose a new algorithm
based on a combination of ZZ-type a posteriori error estimation and effective
operator preconditioned boundary integral formulations to easily compute the
capacity of complex three dimensional polyhedra to 5 digits and more. While
this paper focuses on the capacity as a benchmark problem, it also discusses
implementational issues of adaptive boundary element solvers, and we provide
codes based on the boundary element package Bempp to make the underlying
techniques accessible to a wide range of practical problems.
