Strongly positive amphicheiral knots with doubly symmetric diagrams

Abstract

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.