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# Serie VII, Nr 11

## Surface of order three with an *A*_{2} double point, whose tangent
planes at that point are imaginary conjugated.

**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 *A*_{2} double point and 15 lines. Its tangent planes at that
point are imaginary conjugated.

**Title model and translation**

Fläche dritter Ordnung mit *B*_{3}, dessen Ebenen conjugiert imaginär sind.

Surface of order three with an *A*_{2} double point, whose tangent planes at that point
are imaginary conjugated.

**Text on Sticker and translation**

Fl. 3. Ord. mit bipl. Knotenpunkt *B*_{3}.

Surface of order three with an *A*_{2} double point.

**Designer**

Dr. Carl Rodenberg

Darmstadt in 1881

**Company**

L. Brill in Darmstadt

**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