  We determine the prime strongly positive amphicheiral knots up to 16
crossings and show that a large fraction of them admit knot diagrams with a
double symmetry (rotational symmetry for strongly positive amphicheirality and
an additional mirror symmetry for the ribbon property). The remaining knots are
presented as `almost doubly symmetric' diagrams, defined as diagrams with
double symmetry where exactly one symmetric pair of crossings is switched. We
also find that the rosette knot 14a19470, which has period 7, is the first
prime strongly positive amphicheiral knot in the knot tables which is not
slice.
