# Clebsch Diagonal Surface

The Clebsch Diagonal Surface is certainly one of the most famous surfaces in mathematics. It was described by Alfred Clebsch in 1871. It is a very special example of the so-called cubic surfaces which is highly symmetric and on which there are 27 lines in a very special position.

Every smooth cubic surface contains exactly 27 lines as was shown already in 1849 in a letter-exchange by Arthur Cayley and George Salmon, but here these lines can actually all be seen and have a high symmetry and interesting intersection properties, e.g. on the Clebsch Diagonal Cubic it happens 10 times that three of the 27 lines meet in a point (called Eckhardt Point, see the lower central part of the picture).

The related Math Objects in our sculpture shop:

- The Clebsch Diagonal Surface, no lines shown, height: 119mm (4.7in).
- The Clebsch Diagonal Surface, all 27 lines shown, height: 119mm (4.7in).
- The Clebsch Diagonal Surface, no lines shown, height: 199mm (7.8in).
- The Clebsch Diagonal Surface, all 27 lines shown, height: 199mm (7.8in).

Just click on the links above to see the exact prices in your case on our Sculpture-Shop-Site. Some related links to external sites:

- Illustrating the Classification of Real Cubic Surfaces (PDF), by Stephan Holzer and Oliver Labs.
- Kubische Flächen und die Coblesche Hexaederform (in German, PDF), Diploma Thesis of Oliver Labs.
- The Wikipedia Site on the Clebsch Diagonal Surface.
- Alfred Clebsch on the MacTutor History of Mathematics Archive