An UnorientedKnot is represented by its Orientations, a Set<OrientedKnot>: the distinct normal forms of a knot and its reverse. Unoriented knots form the quotient of oriented knots under reversal.
The table has three columns: Name, Orientations, and Reversible. For example, u3_1 has orientations {3_1}, while u8_17 has orientations {8_17, r8_17}.
Each set appears once. Its name uses the smallest member in numeric knot order: crossing number, then index (for example, 0_1 < 3_1 < 10_1 < 10_2 < 10_124). Display order does not give the set an intrinsic ordering. Mirrors remain separate unless normalization identifies them with a member of the set.
Within a crossing number, alternating names precede nonalternating names; variants follow K, rK, mK, mrK. Connected sums use the sum of factor crossing numbers, then compare their factors in this order.
Reversible is true exactly when the Orientations set has cardinality one. False means the normalizer has not identified them; incomplete symmetry information may leave reversible knots unrecognized.