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Serie VII, Nr 8

Surface of order three, the same kind, considered from the inside, for the formation of the 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 is the inner part of a cubic surface that has 3 A1 double points and 12 lines.

Title model and translation
Fläche dritter Ordnung, dieselbe Art, von der anderen Flächenseite betrachtet, zur Bildung des U6.
Surface of order three, the same kind, considered from the inside, for the formation of the D4 double point.

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