Prime knots organized by their minimum crossing number. The crossing number is the fewest crossings in any diagram of the knot. Click any knot to view it in 3D.
The crossing number is the minimum over all possible diagrams. A trefoil has crossing number 3, but you can draw it with 5, 7, or more crossings if you choose a bad projection. The crossing number captures the intrinsic complexity of the knot.
Crossing number: