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# Serie VII, Nr 16

## Surface of order three with a *D*_{4} double point, whose tangent plane
intersects the surface in three real lines.

**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 *A*_{1}, *A*_{2}, *A*_{3}, *A*_{4},
*A*_{5}, *D*_{4}, *D*_{5} and *E*_{6}. There are
only 20 possible combinations.

This cubic surface has one *D*_{4} double point whose tangent plane intersects the surface
in three real lines. It has 6 lines.

**Title model and translation**

Fläche dritter Ordnung mit *U*_{6}, dessen Ebene in drei reellen Strahlen
schneidet.

Surface of order three with a *D*_{4} double point, whose tangent plane intersects the
surface in three real lines.

**Text on Sticker and translation**

Fl. 3. Ord. mit unipl. Knotenpunkt *U*_{6}.

Surface of order three with an *D*_{4} double point.

**Designer**

Dr. Carl Rodenberg

Darmstadt in 1881

**Company**

Martin Schilling in Halle a.S.

**Original price**

Mark 11,-

**Dimension**

12-15 cm

**Material**

Plaster

**Literature**

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