The lines on the Cayley surface
This page is dedicated in memory of my friend Sevín Recillas,
who got me interested in this surface.
of the main features of the Cayley surface.
This is a large figure and it simply may load slowly. So, the first
thing to try is just to be patient for a little while.
If nothing loads except the light blue background, it may help to
(i) click on your browser's "back" button, and then
(ii) click on the "forward" button to get back to this page.
If the picture absolutely won't load, please click on the
Static figure link.
|Cayley surface links:
Steiner surface links:
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 the lines join pairs of nodes. These lines are traced in black
on the figure. Thus, the nodes are the vertices of a tetrahedron,
and these six lines are the edges of the tetrahedron.
- The other three lines lie in the tritangent plane,
which is discussed on the duality page. These lines are traced in white
on the surface.
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.
The Java files used in this page were downloaded from the
Geometry Center webpage.
I generated the geometric data for this figure in March 2009.
Latest updates on May 10, 2018.
Prof. Joel Roberts
School of Mathematics
University of Minnesota
Minneapolis, MN 55455
Office: 109B Vincent Hall