The tri-plane crossing number of the spun trefoil

Let the tri-plane crossing number of a $2$-knot be the minimum total number of crossings among its tri-plane diagrams. The spun trefoil is the $2$-knot obtained by spinning the trefoil knot in $S^3$ around an axis in $S^4$. The spun trefoil crossing-number conjecture. The tri-plane crossing number of the spun trefoil is six. This conjecture asserts the sharpness of the six-crossing diagram exhibited in the paper; its status is not resolved in the supplied text.