This is a simple example using interactive 3-dimensional graphics:

Instructions: put cursor into graphics window, and with left button pressed, drag the cursor. The knot shown will rotate. There are three other things one can do: translate, scale, and reset. To do these use pop-up menu at top of frame. The translating and scaling are done by dragging the cursor in the window as with rotation.

NOTE: the software used here is the JGV viewer was originally available from the Geometry Center.

Shown is a trefoil knot with edges of different colors to aid in seeing the over and under relations at the crossings. In the default position the knot has three crossings. As you rotate the knot, notice that the number of crossings will change. For example is some positions one can see eight crossings.