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WOLFRAM NOTEBOOK
{{1,2,3,4,5,6,7,8},{2,3,4,5,6,7,8,1},{3,4,5,6,7,8,1,2},{4,5,6,7,8,1,2,3},{5,6,7,8,1,2,3,4},{6,7,8,1,2,3,4,5},{7,8,1,2,3,4,5,6},{8,1,2,3,4,5,6,7}}
Permute
{{1,2,3,4,5,6,7,8},{2,3,4,5,6,7,8,1},{3,4,5,6,7,8,1,2},{4,5,6,7,8,1,2,3},{5,6,7,8,1,2,3,4},{6,7,8,1,2,3,4,5},{7,8,1,2,3,4,5,6},{8,1,2,3,4,5,6,7}}
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GroupMultiplicationTable[CyclicGroup[10]]
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ListPointPlot3D[%]
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ListPointPlot3D[GroupMultiplicationTable[AlternatingGroup[5]],BoxRatiosAutomatic,TicksNone]
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PermutationList[#,4]&/@GroupElements[CyclicGroup[4]]
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{{1,2,3,4},{2,3,4,1},{3,4,1,2},{4,1,2,3}}
In[]:=
Catenate[MapIndexed[Append[#2,#1]&,GroupMultiplicationTable[AlternatingGroup[5]],{2}]]
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Graphics3D[Point[%]]
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In[]:=
Graph3D[NearestNeighborGraph[%392,2]]
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In[]:=
DimensionReduce[%392,3]
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In[]:=
Graphics3D[Point[%]]
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