Together with the classical ones, Conway symbols are used for the first time as an alternative notation in the book Knots and Links by D. Rolfsen, and after that by some other authors (e.g., C.C. Adams, 1994). However, if you try to draw some KLs from their Conway symbols, you will sometimes be surprised: the projection obtained will not be isomorphic with that given by D. Rolfsen. For example, in the case of the knot 915, it is clear that from its Conway symbol 2 3 2 2 we obtain the projection with 5, and not with 4 digons.

It is interesting to notice that in Conway symbols of all non-alternating polyhedral KLs with n £ 10 crossings the symbol .-1, i.e., a single vertex with a changed sign never appears, except in the case of the 4-component link "103*-1.-1.-1.-1::.-1" (or 10-*** according to Conway's paper). The first polyhedral non-alternating knots that cannot be expressed by Conway symbols without .-1-s will be the 12-crossing knots

 8*2 0.-2.-1.-2 0.2 0,  8*2 0.-2 0.-1.-2 0.2 0,  1212*-1.-1.-1.-1.-1.-1
(12n801, 12n835, and 12n837 in the Knotscape notation, respectively).

In the program Knot 2000 (K2K), to get started by using the function GetPdatabyTracking (webMathematica GetPdatabyTracking), you need to draw a KL diagram on the mouse-tracking window, and then get its P-data. Thanks to the LinKnot function fCreatePData (webMathematica fCreatePData), instead of the graphical input, you can use the Conway notation of KLs represented as a Mathematica string. For example, the figure-eight knot 41 is denoted by "2 2", knot 95 by "5 1 3", link 512 is denoted by "2 1 2", link 9212 by "3 1,3,2" (for all of them a space between tangles denotes a product of tangles), etc. A sequence of k pluses at the end of the Conway symbol is denoted by +k, and a sequence of k minuses by +-k (e.g., knot 1076 given in Conway notation as 3,3,2++ is denoted by "3,3,2+2", and the link 9173 given in Conway notation as 3,2,2,2- by "3,2,2,2+-2"). The space denoting a product of tangles is used in the same way in all other symbols. For example, the knot 10133 is denoted by "2, 2 1,2+-1", and the knot 10154 by "(2 1,2) -(2 1,2)" (with spaces).