The crystal structures of the A(2)B(2)O(7-x) niobium based pyrochlores Y(2)(Nb(0.86)Y(0.14))(2)O(6.91), CaYNb(2)O(7), and Y(2)NbTiO(7) are reported, determined by means of powder neutron diffraction. These compounds represent the first observation of B-site displacements in the pyrochlore structure: the B-site ions are found to be displaced from the ideal pyrochlore positions, creating electric dipoles. The orientations of these dipoles are fully analogous to orientations of the magnetic moments in Ising spin based magnetically frustrated pyrochlores. Diffuse scattering in electron diffraction patterns shows that the displacements are only short range ordered, indicative of geometric frustration of the collective dielectric state of the materials. Comparison to the crystal structure of the Nb(5+) (d(0)) pyrochlore La(2)ScNbO(7) supports the prediction that charge singlets, driven by the tendency of Nb to form metal-metal bonds, are present in these pyrochlores. The observed lack of long range order to these singlets suggests that Nb(4+) based pyrochlores represent the dielectric analogy to the geometric frustration of magnetic moments observed in rare earth pyrochlores.