Regarding numerous remarkable feats of paper-folding that were achieved by students in Josef Albers’s basic design studios, Albers wrote that “through the years of cooperative efforts, [he was] pursuing consecutive and/or conclusive improvements” in that exploratory exercise (Albers 1969: 36).

 This is precisely how I treated a handful of major design projects that I developed and assigned, recurringly (though not necessarily annually), throughout my years of teaching basic design from 1960 to 1998—always building on the results that came out of earlier classes’ work on each project. One, on my short list of major design projects, came late. First given in 1971, it had its origin in basic design work that I saw at the Krakow Academy of Fine Arts in Poland: The sectioning of any regular or semi-regular solid into congruent parts. The original version of this project was given a more focused brief as a consequence of one of Martin Gardner’s Scientific American monthly columns in which he had erred (Gardner 1980): The trisectioning of the cube into congruent parts.

 As the trisection of the cube was assigned again and again, more and more about this problem became evident. Implemented through sustained inquiry, keen observation and pure happenstance. a number of trisection types (or strategies) have been identified (even to this day with latter-day analyses of the body of the students’ achievements). I must make the point, however, that the list, presented here, needs a rigorous topological re-classification.