# The Clebsch diagonal surface in the family room

A photo from our series “Math sculptures in context”. To purchase the model used in the photo and others, follow the links to our producer “shapeways” provided below.

Alfred Clebsch (1833-1872) presented his nowadays quite famous model of a diagonal surface in 1872 at Göttingen during a meeting – see our article on Clebsch and Klein in the family room for more information on that very special occasion.

Our photo shows a white 3D-printed modern version by MO-Labs, in front of Clebsch’s portrait. The setting was created in the MO-Labs office, inside a dollhouse built just for taking photos of math sculptures in historical environments. Alfred Clebsch’s portrait is taken from wikipedia. The wallpaper is not a historical design, but a 21st century piece of art which uses typography in a way similar to brush strokes with  ordinary paintings. It was created by www.artefont.com.

One of the main features of Clebsch’s diagonal surface model is the fact that it was the first model of a cubic surface which had all its 27 straight lines real and nicely situated on the object. It was known since 1849 that any smooth cubic surface contains exactly 27 straight lines – but possibly imaginary! Earlier attempts by others failed to produce such a beautiful model of a cubic with its 27 lines. Either not all lines were real or all were real, but some of the lines where either too close together or too far apart to be easily distinguishable. Or – in the case of Wiener’s model – the model was not symmetric and did thus not allow to easily understand the interesting intersection properties of the lines. In the early 1880s, a model of Clebsch’s diagonal surface became part of Rodenberg’s series of 26 cubic surface models.

Our modern version of the model shown in the photo is a version in a single color. The straight lines are almost invisible at first sight, allowing to appreciate the shape of Clebsch’s surface. If you are more interested in the lines than in the surface then you might prefer our model with colored lines which will be presented in another post.

#### MO-Labs sculptures used: Clebsch’s Diagonal Surface

To purchase our best selling version of Clebsch’s Diagonal Surface, just use the “buy now” button below. You will be sent to our MO-Labs shop on the “shapeways” website, so that you can choose the material and color there, and the let “shapeways” produce the object for you and send it to you in really short time.

We have designed a large variety of Clebsch Diagonal Surface sculptures, in one color, or with differently colored lines, or even together with two related planes.

In the MO-Labs shop on “shapeways”, you will also find versions in different sizes and at very different prices, from tiny and cheap to large and more valuable.

Here is a link to a tiny version of this (4.5 cm / 1.8 in tall) which is, of course, much cheaper:

We also have a museum size version, in sizes 25 cm, 28.6 cm, 31.3 cm.

#### Series: Math sculptures in context

This January 2017 photo is part of a series of photos of mathematical sculptures in exceptional settings. We use these and other posts on this site to show, describe, and make available for purchase our several hundred designs of mathematical sculptures.