General expressions for the components of magnetic field and magnetic field gradient are given for polygonal gradient coils of the point-group symmetry Dn. It is shown that triangular coils (n = 3) are particularly suitable for NMR applications and supply the high and uniform value of the gradient over relatively great volume. Moreover, for n > 3, it is found that at the magic angle between symmetry axis Cn and axis Z, of external magnetic field B0, the gradient of Bz is perpendicular to B0. This new feature may be very useful in NMR spin-echo measurements of anisotropic translational diffusion. © 1982.