The triple point of the Steiner surface

The figure above shows a portion of the Steiner surface, including the triple point. The triple point is at the origin,
and there are double points along the portions of the coordinate axes that are shown in the figure. Equivalently,
the sheets of different colors intersect along the various coordinate axes. The 6 pinch points of the surface are
at the ends of those portions of the coordinate axes.
One more interesting feature of the Steiner surface can be seen in this figure: there are 4 plane conics on the surface.
(Actually, they are circles in this model.) They appear at the edges of the portion shown here, and they are lightly
sketched in black.
Under the projective duality that relates the Steiner surface to the Cayley surface, these 4 circles are collapsed to
the 4 nodes of the Cayley surface. Alternatively, Click here to see a page that shows the 9 lines on the Cayley surface
and also includes some discussion of this remarkable instance of projective duality.
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I made this page by substituting my own data in a Geometry Center webpage.

Prof. Joel Roberts
School of Mathematics
University of Minnesota
Minneapolis, MN 55455

Office: 351 Vincent Hall
Phone: (612) 625-1076
Dept. FAX: (612) 626-2017