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Serie VII, Nr 17

Surface of order three with a D4 double point, whose tangent plane intersects the surface in one real line.


Mathematical description
The cubic surfaces are given by a homogeneous polynomial of degree 3. If the surface is smooth, it contains 27 lines. In case the surface has isolated singularities (or double points), some of the lines collapse. There is a Coxeter diagram associated with every double point. The singularities can be of type A1, A2, A3, A4, A5, D4, D5 and E6. There are only 20 possible combinations.
This cubic surface has one D4 double point whose tangent plane intersects the surface in one real line. It has 6 lines.

Title model and translation
Fläche dritter Ordnung mit U6, dessen Ebene in einem reellen Strahl schneide.
Surface of order three with a D4 double point, whose tangent plane intersects the surface in one real line.

Text on Sticker and translation
Fl. 3. Ord. mit unipl. Knotenpunkt U6.
Surface of order three with an D4 double point.

Designer
Dr. Carl Rodenberg
Darmstadt in 1881

Company
Martin Schilling in Halle a.S.

Original price
Mark 10,-

Dimension
12-15 cm

Material
Plaster

Literature
Schilling, M., Catalog mathematischer Modelle für den höheren mathematischen Unterricht, Leipzig: Verlag von Martin Schilling, 1911