Osculating behavior of the Kummer surface in P5

In an article of 1967 Edge gave a description of some beautiful geometric properties of the Kummer surface complete intersection of three quadrics in P^5. Working on it, Dye proved in 1982 and 1992 that all its osculating spaces have dimension less than the expected 5. Here we discuss these results, also in the light of some recent result about varieties with hypo-osculating behaviour.