# Serie VII, Nr 10

## Surface of order three with an A2 double point, whose tangent planes at that point intersect the surface in three lines. The model is also valid for the transfer of the A2 into a D4 double point.

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 A2 double point and 15 lines. Its tangent planes at that point cut the surface along 3 real lines.

Title model and translation
Fläche dritter Ordnung mit B3, dessen Ebenen in je drei reellen Knotenstrahlen schneiden. Das model dient gleichzeitig zur überführung des B3 in einen U6.
Surface of order three with an A2 double point, whose tangent planes at that point intersect the surface in three lines. The model is also valid for the transfer of the A2 into a D4 double point.

Text on Sticker and translation
Wrong sticker.

Designer
Dr. Carl Rodenberg

Company