Steiner surface

From Free net encyclopedia

In geometry, the Steiner surfaces, discovered by Jakob Steiner, are certain self-intersecting embeddings (that is to say, immersions) of the real projective plane into three-dimensional space. More particularly, they are linear projections of a six-dimensional embedding called the Veronese surface, which is the image of an ordinary 2-sphere centered at the origin under the map

f(x, y, z) = (x², y², z², yz, xz, xy).

There are ten different types, including the Roman surface and cross-cap.

References

• Adam Coffman, Steiner Surfaces, (undated, 2005 or earlier)