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# Serie VII, Nr 7

## Surface of order three with 3 real ordinary double points.

**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 is the outer part of a cubic surface that has 3 *A*_{1} double points and 12 lines.

**Title model and translation**

Fläche dritter Ordnung mit 3 reellen *C*_{2}.

Surface of order three with 3 real ordinary double points.

**Text on Sticker and translation**

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

Surface of order three with 3 real double points.

**Designer**

Dr. Carl Rodenberg

Darmstadt in 1881

**Company**

L. Brill in Darmstadt

**Original price**

Mark 11,-

**Dimension**

11-15 cm

**Material**

Plaster

**Literature**

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