  Edmonds famously proved that every periodic knot of genus g possesses an
equivariant Seifert surface of genus g. We show that this is not true if one
instead considers nonorientable spanning surfaces of a periodic knot. We
demonstrate by example that the difference between the first Betti number of an
equivariant and a nonequivariant nonorientable spanning surface of a periodic
knot, can be arbitrarily large.
