This is a collection of models of mathematical knots, which are tied in closed loops of rope. The knots have all been classified, and these are all the knots with a projection which has 8 or fewer crossings and cannot be written as two simpler knots spliced together (such knots are called "prime"). The shapes for the knots are generated by an optimization algorithm which virtually ties the knots in a loop of tube (with a constant diameter) and then pulls them tight.