Amphichiral Knot

Author

Eric W. Weisstein
May 27, 2007

This notebook downloaded from http://mathworld.wolfram.com/notebooks/KnotTheory/AmphichiralKnot.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/AmphichiralKnot.html.

©2007 Wolfram Research, Inc. except for portions noted otherwise

Additional Authors

Amphichiral nonalternating knot picture courtesy of
Ed Pegg, Jr.
August 8, 2003

Enumeration

Knots

KnotData["Amphichiral","Missing"]

KnotData[#,"AlexanderBriggsNotation"]&/@(amph=KnotData["Amphichiral"])//TraditionalForm

Length[amph]

GraphicsGrid[Partition[Show[KnotData[#],PlotLabel->TraditionalForm[KnotData[#,"AlexanderBriggsNotation"]]]&/@Select[amph,First[#]<9&],4,4,{1,1},{}],ImageSize->500]

Show[GraphicsArray[
Partition[Graphics3D[{EdgeForm[],ClosedBraid[BraidWord[#],Style->TubeStyle][[1]]},Boxed->False,ViewPoint->{0,0,1}]&/@amph,5,5,{1,1},{}]
],ImageSize->500]

Nonalternating Amphichiral

KnotData[{"Nonalternating","Amphichiral"}]

Data initialization

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