  We study the partition function of the six-vertex model in the rational limit
on arbitrary Baxter lattices with reflecting boundary. Every such lattice is
interpreted as an invariant of the twisted Yangian. This identification allows
us to relate the partition function of the vertex model to the Bethe wave
function of an open spin chain. We obtain the partition function in terms of
creation operators on a reference state from the algebraic Bethe ansatz and as
a sum of permutations and reflections from the coordinate Bethe ansatz.
