The generation of a uniform field in a cubic cavity enclosed by a permanent magnet composed of uniformly magnetized polyhedrons of magnetic material is discussed. In the three-dimensional yokeless magnet considered, the ratio of the volume of the layers to the volume of the cavity is equal to 85% of the same ratio of volumes per unit length of the two-dimensional yokeless magnet. In spite of this, the figure of merit is lower, because of the addition of an external layer. The external layer, required to confine the field, does not contribute to the field in the cavity, and therefore its function is similar to that of the external layer of the spherical magnet.
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