  The characterisation of small low conducting inclusions in an otherwise
uniform background from low-frequency electrical field measurements has
important applications in medical imaging using electrical impedance tomography
as well as in geological imaging using electrical resistivity tomography. It is
known that such objects can be characterised by a P\'oyla-Szeg\"o
(polarizability) tensor. Such characterisations have attracted interest as they
can provide object features in a machine learning classification algorithm and
provide an alternative imaging solution. However, to be able train machine
learning algorithms, large dictionaries are required and it is essential that
the characterisations are accurate. In this work, we obtain accurate numerical
approximations to the tensor coefficients, by applying an adaptive boundary
element method. The goal being to provide a sequence of benchmark
{computations} for the tensor coefficients to allow other software developers
check the accuracy of their codes.
