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Serie VII, Nr 15

Surface of order three with an ordinary A1 double point and an A5 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 real A1 double point and one A5 double point with real tangent planes. It has 2 lines.

Title model and translation
Fläche dritter Ordnung mit B6 + C2.
Surface of order three with an ordinary A1 double point and an A5 double point.

Text on Sticker and translation
Fl. 3. Ord. mit bipl. Knotenpunkt B6.
Surface of order three with an A5 double point.

Designer
Dr. Carl Rodenberg
Darmstadt in 1881

Company
Martin Schilling in Halle a.S.

Original price
Mark 11,-

Dimension
12-15 cm

Material
Plaster

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