A selection of symmetric knots; groups of order greater than 10

The symmetry groups of these knots were computed by Jeff Weeks's program SnapPea, using the canonical triangulation of the knot complement. The pictures were produced with the help of Geomview, and the minimal energy configurations were obtained with Ken Brakke's Evolver, using in particular energy methods created by Greg Buck . All these programs are obtainable from the Geometry Center . Rendering was accomplished using Larry Gritz's Blue Moon Rendering Tools .

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Two views of a 12-crossing knot whose symmetry group is the dihedral group D6 of order 12.


This knot has D7 symmetry and is the closure of the 3-string braid (s1s2-1)7.t , where s1, s2 are standard braid generators and t is a full twist. .



Two 16-crossing hyperbolic knots with symmetry group D8.