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Jun 25, 2021 at 8:03 comment added Andrew Steane @roy ok; at a site there in cubic lattice of spacing $a$ there are 6 nearest neighbours giving zero net field at the centre, and next out there are 12 next-nearest neighbours at the corners of 3 squares of side $2a$, all giving non-zero total at the centre, in same direction. The next 8 (corners of cube of side $2a$) also give non-zero field. etc. Another way to set it up is to consider planes of charge of alternating sign.
Jun 25, 2021 at 0:03 comment added Roy Feynman is calculating at each site. Of course, I am not saying E-field is zero everywhere.
Jun 24, 2021 at 9:37 comment added Andrew Steane @Roy But it is not zero at the centre of a cube of dipoles, and the average over all locations is not zero.
Jun 24, 2021 at 8:11 comment added Roy Actually if you look at 2d plot provided by one answer, we can see it is 0. I did for much more dipoles and it is still 0 at each atom site.
Jun 21, 2021 at 10:07 history answered Andrew Steane CC BY-SA 4.0