Osculating behavior of Kummer surface in ${\mathbb{P}}^5$

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