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:

• 28.04 € : The Clebsch Diagonal Surface, no lines shown, height: 119mm (4.7in).
• 29.07 € : The Clebsch Diagonal Surface, all 27 lines shown, height: 119mm (4.7in).
• 111.60 € : The Clebsch Diagonal Surface, no lines shown, height: 199mm (7.8in).
• 114.82 € : The Clebsch Diagonal Surface, all 27 lines shown, height: 199mm (7.8in).

Attention: These prices include German VAT (19%). Depending on your country, there might be lower or higher costs. 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