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Serie VII, Nr 12

Surface of order three with an A3 double point and two real ordinary (A1) double points. The tangent planes at the A3 double point are real.


  

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 A3 double point and 2 A1. It has 5 lines and real tangent planes at A3.

Title model and translation
Fläche dritter Ordnung mit B4 + 2 reellen C2. Die Ebenen des B4 sind reell.
Surface of order three with an A3 double point and two real ordinary (A1) double points. The tangent planes at the A3 double point are real.

Text on Sticker and translation
Fl. 3. Ord. mit bipl. knotenpunkt B4.
Surface of order three with an A3 double point.

Designer
Dr. Carl Rodenberg
Darmstadt in 1881

Company
Martin Schilling in Halle a.S.

Original price
Mark 11,-

Dimension
13-15 cm

Material
Plaster

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