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In this paper the elementary moves of the BFACF-algorithm for latticepolygons are generalised to elementary moves of BFACF-style algorithms forlattice polygons in the body-centred (BCC) and face-centred (FCC) cubiclattices. We prove that the ergodicity classes of these new elementary movescoincide with the knot types of unrooted polygons in the BCC and FCC latticesand so expand a similar result for the cubic lattice. Implementations of thesealgorithms for knotted polygons using the GAS algorithm produce estimates ofthe minimal length of knotted polygons in the BCC and FCC lattices.

BFACF-style algorithms for polygons in the body-centered and face-centered cubic lattices