pennis part reminds me of pinnate

There is, indeed, a connection. While the normal definition of the term refers to a double-bladed ax, it's sort of payback for the use of gladiolus as a flower name. The roots are two (bi) and feather (penna) and it refers to something having two feather-like edges. The lovely ASp probably had the labrys (which its own self may beg some payback) in mind when she alluded to the Greek etymology.