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.

Click here to return to

- the main picture of the Steiner surface

Go back to the JGV homepage.

Back to my homepage

*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

USA

Office: 351 Vincent Hall

Phone: (612) 625-1076

Dept. FAX: (612) 626-2017

e-mail: `roberts@math.umn.edu
http://www.math.umn.edu/~roberts
`