Existing techniques for computing the gravitational field due to a homogene
ous polyhedron all transform the required volume integral, expressing the f
ield due to a volume distribution of mass, into a surface integral, express
ing the potential due to a surface mass distribution over the boundary of t
he source body. An alternative representation is also possible and results
in a surface integral expressing the potential due to a variable-strength d
ouble layer located on the polyhedral source boundary. Manipulation of this
integral ultimately allows the gravitational field component in an arbitra
ry direction to be expressed as a weighted sum of the potentials due to two
basic source distributions. These are a uniform-strength double layer loca
ted on all faces and a uniform-strength line source located along all edges
. The derivatives of the gravitational field components can also be express
ed in a similar form as can the magnetic field components due to a homogene
ous magnetic polyhedron. It follows that the present approach can be used t
o generate a universal program capable of modelling all the commonly used p
otential field responses due to 3D bodies of arbitrary shape.