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Serie VII, Nr 24b

Surface of third order. Star shaped part of the preceding for a pentaeder, which consists of the infinitely far plane and a regular tetrahedron.


Mathematical description
Let S be a surface in the projective space given by a homogeneous polynomial equation f(x1, x2, x3, x4) = 0. The Hessian surface is given by:
H = | δ2f |
δxiδxj
Let d be the degree of f, then the Hessian surface will have degree 4(d-2).
This model is a star-shaped part of the Hessian surface with 14 double real points.

Title model and translation
Fläche dritter Ordnung. Sternförmiger Teil der vorhergehenden für ein Pentaeder, das aus der unendlich fernen Ebene und einem regulären Tetraeder besteht.
Surface of third order. Star shaped part of the preceding for a pentaeder, which consists of the infinitely far plane and a regular tetrahedron.

Text on Sticker and translation
Hesse'sche Fl. einer Fl. 3. Ord.
Hessian surface of order three.

Designer
Dr. Carl Rodenberg
Darmstadt in 1881

Company
L. Brill in Darmstadt

Original price
Mark 11

Dimension
13-16 cm

Material
Plaster

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