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This paper introduces universal matrices for the computation of edge-element matrices on triangles and tetrahedra. Universal matrices are useful because they allow a simple and efficient implementation of edge-element codes for computational electromagnetics. These matrices are partially derived from nodal universal matrices, permitting some reuse of nodal finite-element codes. Although universal matrices are limited to noncurvilinear elements, some intermediate matrices instrumental to their construction can be used for the efficient computation of edge-element matrices on curvilinear elements.