Affordable Access

Special sextics with a quadruple line

Department of Mathematics, University of Osijek
Publication Date
  • Congruence Of Lines
  • Pedal Surface
  • Multiple Point
  • Pinch-Point
  • Tangent Cone
  • Mathematics


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 $mathcal P_4^6$, are the pedal surfaces of one special 1st order 4th class congruence $mathcal C_4^1$. The parametric and implicit equations of $mathcal P_4^6$ are derived, some of their properties are proved and their visualizations are given. The singularities of $mathcal P_4^6$ are classified according to the shapes of their tangent cones. The methods applied are analytic, synthetic and algebraic, supported by the program Mathematica 6.

There are no comments yet on this publication. Be the first to share your thoughts.