  Minimizing the bending energy within knot classes leads to the concept of
elastic knots which has been initiated in [von der Mosel, Asymptot. Anal.
1998]. Motivated by numerical experiments in arxiv:1804.02206
(doi:10.1090/mcom/3633) we prescribe dihedral symmetry and establish existence
of dihedrally symmetric elastic knots for knot classes admitting this type of
symmetry. Among other results we prove that the dihedral elastic trefoil is the
union of two circles that form a (planar) figure-eight. We also discuss some
generalizations and limitations regarding other symmetries and knot classes.
