In the 19^th century, cubic surfaces - defined by an implicit equation of degree three in three variables - were among the first interesting examples in the development of modern algebraic geometry. A well-known result by Arthur Cayley and George Salmon is that any smooth cubic contains exactly 27 straight lines. Other prominent facts are the classification of all cubic surfaces w.r.t. their singularities by Ludwig Schläfli, and Alfred Clebsch's birational map between the plane and such surfaces where six points play an essential role.

The talk will present both the historical and the mathematical background of classical hand-crafted and also recent 3d-printed cubic surface models. Some of their fascinating features such as the movement of the straight lines as the surfaces vary may very well be visualized using interactive software. In 2011 and 2014, the speaker created two versions of a complete series of more than 45 types of 3d-printed cubic surface models. Copies of these are now part of several university collections such as those at Lisbon, Strasbourg, Dresden, and Mainz, as well as at the IHP at Paris. He will bring some examples of these sculptures with him in order to illustrate facts which may better be appreciated when seeing and touching a real object.