  Letting $C$ be a compact $C^\omega$-curve embedded in $\boldsymbol R^3$
($C^\omega$ means real analyticity), we consider a $C^\omega$-cuspidal edge $f$
along $C$. When $C$ is non-closed, in the authors' previous works, the local
existence of three distinct cuspidal edges along $C$ whose first fundamental
forms coincide with that of $f$ was shown, under a certain reasonable
assumption on $f$. In this paper, if $C$ is closed, that is, $C$ is a knot, we
show that there exist infinitely many cuspidal edges along $C$ having the same
first fundamental form as that of $f$ such that their images are non-congruent
to each other, in general.
