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This paper deals with a special class of 6th order surfaces with a quadruple straight line in a three-dimensional Euclidean space. These surfaces, denoted by P6 4 , are the pedal surfaces of one special 1st order 4th class congruence C1 4 . The parametric and implicit equations of P6 4 are derived, some of their properties are proved and their visualizations are given. The singularities of P6 4 are classi ed according to the shapes of their tangent cones. The methods applied are analytic, synthetic and algebraic, supported by the program Mathematica 6.
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