Introduction. A surface of order three, P, in the real projective threespace P 3 is met by every line, not in P, in at most three points. F is biplanar if it contains exactly one non-differentiable point v and the set of tangents of F at v is the union of two distinct planes, say n and 72. In the present paper, we classify and describe those biplanar F which contain the line n C\ r 2 . We describe a surface by determining the tangent plane sections of the surface at the differentiable points.

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... is approach was introduced in [1] and it is based upon A. Marchaud's definition of * 'surfaces of order three" in [4] . We denote the planes, lines and points of P 3 by the letters a, 0, .