I have been working through the standard list of small prime knots, with the aim of creating elegant and, where possible, symmetric three-dimensional realizations. Here you will find my versions of the knots described in terms of 2D diagrams, lists of coordinates of points along the curve, Fourier series, .scad files and .stl files. I follow the nomenclature used in Knotinfo and Knotserver.

Knot 3_{1} Trefoil |
Knot 4_{1} Figure-eight |
Knot 5_{1} Cinquefoil |
Knot 5_{2} Three-twist |
Knot 6_{1} Stevedore |
Knot 6_{2} |
Knot 6_{3} |
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Knot 7_{1} |
Knot 7_{2} |
Knot 7_{3} |
Knot 7_{4} Eternal |
Knot 7_{5} |
Knot 7_{6} |
Knot 7_{7} |
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Knot 8_{1} |
Knot 8_{2} |
Knot 8_{3} |
Knot 8_{4} |
Knot 8_{5} |
Knot 8_{6} |
Knot 8_{7} |
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Knot 8_{8} |
Knot 8_{9} |
Knot 8_{10} |
Knot 8_{11} |
Knot 8_{12} |
Knot 8_{13} |
Knot 8_{14} |
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Knot 8_{15} |
Knot 8_{16} |
Knot 8_{17} |
Knot 8_{18} |
Knot 8_{19} |
Knot 8_{20} |
Knot 8_{21} |
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Knot 12a_{1202} |
Knot 15331 |

Many small knots have symmetric three-dimensional realizations.
I have therefore sought to offer these when possible. On the pages devoted to individual knots, I name symmetries (D_{2}, D_{4} etc) when I have found them. Note that a knot may have various symmetries witnessed by different realizations, as described in the pages devoted to individual knots.
By "symmetry" here what I really mean is a conjugacy class of finite subgroups of the isometry group of S^{3, but I think most of us would prefer to have a list of descriptions relating to the rather arbitrary names I have used:
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Note that a knot has a D_{2}(p) version iff 2 is a period. Knots with D_{2}(r) symmetry are strongly invertible. Of the knots here, 4_{1}, 6_{3}, 8_{3}, 8_{9}, 8_{12}, 8_{18} and 12a_{1202} are
fully amphichiral; 8_{17} and 15331 are negatively amphichiral. I believe that 15331 is prime.

Table of symmetries, questions,

*6.7.15*