Schläfli double six
Schläfli double six. The 6 white fibers form a family, the 6 red the other; each line of the one family intersects with 5 of the other and is out of square to the rest. All the lines lay on the planes of a cube.
Showcase of this model is Case number 29
Schläfli(1858). An attempt to determine the twenty-seven lines upon a surface of the third order, and to derive such surfaces in species, in reference to the reality of the lines upon the surface. The Quarterly Journal of Pure and Applied Mathematics II, p. 55-65; 110-120. Online version
Stenfors, E.(1921). Die Schläflische Konfiguration von 12 Geraden einer Fläche 3.Ordnung (Dissertation), Helsingfors, B 349 . Online version