A receiver for electromagnetic measurements includes a polyhedron structure having m faces, where m.gtoreq.4 and m.noteq.6: n electrodes each disposed on one face of the polyhedron structure, wherein 3.ltoreq.n.ltoreq.m; and at least one circuitry connected to the n electrodes for signal measurement. A method for electromagnetic measurements includes obtaining a plurality of electric current measurements using a plurality of electrodes each disposed on a surface of a polyhedron receiver, wherein the plurality of electric current measurements comprise at least three different measurements; and determining electric field components in a three dimensional space from the plurality of electric current measurements by using a number of matrices that correlate orientations of surfaces of the polyhedron receiver to a coordinate system in the three dimensional space.