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At each vertex in a Cayley map, the darts emanating from that vertex are labeled by a generating set of a group. This generating set is closed under inverses. Two classes of Cayley maps are balanced and antibalanced maps. For these cases, the distributions of the inverses about the vertex are well understood. For a balanced Cayley map, either all the generators are involutions or each generator is directly opposite across the vertex from its inverse. For an antibalanced Cayley map, there is a line of reflection in the tangent plane of the vertex so that the inverse generator for each dart label is symmetric across that line. An \( e \)-balanced Cayley map is a recent generalization that has received much study, see for example [2, 6, 7, 13]. In this note, we examine the symmetries of the inverse distributions of \( e \)-balanced maps in a manner analogous to those of balanced and antibalanced maps.