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A systematic conformal finite-difference time-domain (FDTD) algorithm for the direct modeling of dielectric interfaces in three dimensions is presented in this paper. The straightforward procedure is based on the proper reformation of the grid cells in the vicinity of the dielectric surface, leading thus to the creation of five-faced prisms on the primary grid, apart from the standard hexagonal ones. The new scheme overcomes any topological deficiency that forbids the contour path FDTD and conformal FDTD technique to directly simulate dielectric boundaries, since it maintains the lattice duality. Therefore, no instabilities, even late-time ones, are observed. On the other hand, the accuracy obtained, even with very coarse meshes, is very good as is proved by the numerical analysis of various resonance problems.