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# Serie VII, Nr 2

## Surface of order three with four real double points (*A*_{1}).

**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 model is representing a singular cubic surface with 4 *A*_{1} double points. It has 9
lines on it (complex and real).

**Title model and translation**

Fläche dritter Ordnung mit 4 reellen *C*_{2}.

Surface of order three with three real double points (*A*_{1}).

**Text on Sticker and translation**

Fl. 3. Ord. mit 4 reellen con. Knpktn.

Surface of order three with 4 real double points.

**Designer**

Dr. Carl Rodenberg

Darmstadt in 1881

**Company**

L. Brill in Darmstadt

**Original price**

Mark 12,-

**Dimension**

13-15 cm

**Material**

Plaster

**Literature**

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