I'm not sure I follow.
Every knot is defined as if you close the ends it cannot be unravelled without cutting the ends again.
So the trifoil knot is included in this... but so is almost if not every other knot aren't they? Do we have "knots" that aren't mathematical? I feel like if you tie any "knot" then fix the ends together most or all of them would not be possible to untangle.