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An analytic expression for the electromagnetic wave scattered in singular directions on the vertex of a perfectly conducting cone is obtained. The approach used in the paper is a generalization to the electromagnetic case of the approach previously developed by the authors. In singular directions, the spherical front set of a wave scattered by the vertex is tangent to the front set of a wave reflected by the cone surface. The wave field is expressed in terms of parabolic-cylinder functions. Bibliography: 8 titles.