Cubic surfaces are classics from the 19th century. This particular cubic is smooth and has tetrahedral symmetry. All 27 lines are real, but only 24 are visible in the model because 3 are infinitly far away.
This so-called Boy surface represents a fascinating example of a non-orientable surface. The first such surface was constructed by Werner Boy in his dissertation in 1902.
In the 19th century, Olaus Henrici constructed a model of a quite symmetric cubic surface. This is a modern variant of it, allowing also to look "inside" of it from the bottom.
Our modern version of Klein's historical cubic surface model with four singularities is the main figure in our photo from the series "math sculptures in context". It is the pure white version with its 9 straight lines.
It was back in the 1872 Göttingen, Germany, at a meeting of the scientific society. Alfred Clebsch and Felix Klein each presented a model of a cubic surface. Our modern versions of these historical - nowadays quite famous - sculptures are the main figures in our photo.
Our modern version of Clebsch's historical - nowadays quite famous - diagonal surface model is the main figure in our photo from the series "math sculptures in context". It is the pure white version with the 27 straight lines.