Non Placet Net of a Dodecahedron
It seems that (in 1537 in an unpublished paper) Maurolico was the first to give a chain of 12 regular pentagons that is not a net of a dodecahedron [1, pp. 70–71]. He denoted it "non placet". In principle, you can determine whether a chain is or is not a net by trying all possible foldings.
 M. Friedman, A History of Folding in Mathematics: Mathematizing the Margins, New York: Springer Berlin Heidelberg, 2018.