Clebsch Diagonal Surface with Double Six

The model of the Clebsch Diagonal Surface is probably the best known mathematical model. We show a modern version of this 140-year-old classic which exists in math departments all over the world together with its famous 27 straight lines on it. These 27 lines are colored so that it is easy to see the famous double-six-configuration: each pink line does not meet any other pink line, but meets all but exactly one of the cyan lines. Actually, it is even possible to number the 6 pink lines p_1, ..., p_6, and the 6 cyan lines c_1, ..., c_6, such that the lines p_i and c_j meet if and only if the values of the indices i and j not the same.