• Cayley surface:
     • With the lines
     • Without lines
     • Duality
     • Equation
• Steiner surface:
     • Introduction
  (Not yet available)
     • The triple point
  (Not yet available)
     •

• Cayley surface:
     • Introduction
     • Duality
     • Equation
     • View without    the lines
• Steiner surface:
     • Introduction
     • The triple point

• Surface thumbnails
• JGV homepage

Introduction:
 
    The figure shows part of the Cayley surface. It is a surface of degree 3, with 4 singular points. These singular points are often called nodes. Near each singular point, the surface is closely approximated by a quadric cone.

    There are 9 lines on the Cayley surface. All of these lines are shown in this figure. Six of them join pairs of nodes. Thus, we can view the nodes as vertices of a tetrahedron, and these six lines are the edges of the tetrahedron. The other three lines lie in the trigangent plane, which is discussed on the duality page.

    The Cayley surface is the dual variety of the Steiner surface.  This means that the points of the Cayley surface correspond bijectively to the tangent planes of the Steiner surface (except that the correspondence is not bijective along finitely many subvarieties).

    For a discussion of specific features of the duality correspondence, please click on the Duality link at the left.