This paper studies the uniqueness and the asymptotic stability of a pyramidal traveling front in the three-dimensional whole space. For a given admissible pyramid we prove that a pyramidal traveling front is uniquely determined and that it is asymptotically stable under the condition that given perturbations decay at infinity.For this purpose we characterize the pyramidal traveling front asa combination of planar fronts on the lateral surfaces.Moreover we characterize the pyramidal traveling front in another way, that is, we write it as a combination of two-dimensional V-form waveson the edges. This characterization also uniquely determines a pyramidal traveling front.
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