The photo shows a smoothed Kummer surface in steel (inflated with bronze). This post also features links to plastic versions of this shape. The Kummer surface is a classic from the 19th century; our model is a smoothed version of it.
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.
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.