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Cayley Graph

Cayley Graph
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2013-04-12 21:20
FunctionCalculusGraphing
A Cayley graph is a graph that illustrates the generators and their relations in a group. This example uses GeoGebra commands like Sequence, Polygon, Mirror to construct a Cayley graph. Suitable for high school and above math enthusiasts and learners.

GeoGebra Commands & Parameters

  1. Sequence(Rotate[O1 + (Zoom; α), 2 * π / 5 * i, O1], i, 0, 5) → l01
  2. Sequence(Rotate[Element[l01, 1], 2 * π / 3 * i, O2], i, 0, 2) → l02
  3. Polygon(l01) → V01, , , , , ,
  4. Polygon(l02) → V02, , ,
  5. Sequence(Rotate[Element[l02, 3], 2 * π / 5 * i, O3], i, 0, 5) → l03
  6. Polygon(l03) → V03, , , , , ,
  7. Sequence(Rotate[Element[l03, 2], 2 * π / 3 * i, O4], i, 0, 2) → l04
  8. Polygon(l04) → V04, , ,
  9. Sequence(Rotate[Element[l04, 2], 2 * π / 5 * i, O5], i, 0, 5) → l05
  10. Polygon(l05) → V05, , , , , ,
  11. Sequence(Rotate[Element[l05, 2], 2 * π / 3 * i, O6], i, 0, 2) → l06
  12. Polygon(l06) → V06, , ,
  13. Sequence(Rotate[V06, 2 * π / 5 * i, O5], i, 0, 3) → V16
  14. Mirror(V16, Line[O3, O4]) → V16'
  15. Mirror(V05, Line[O3, O4]) → V05'
  16. Sequence(Rotate[{V16, V16'}, 2 * π / 5 * i, O3], i, 0, 3) → V16''
  17. Sequence(Rotate[{V05, V05'}, 2 * π / 5 * i, O3], i, 0, 3) → V15''
  18. Sequence(Rotate[V04, 2 * π / 5 * i, O3], i, 0, 3) → V14''
  19. Mirror(V14'', Line[O1, O2]) → V14'''
  20. Sequence(Rotate[{V16'', Mirror[V16'', Line[O1, O2]]}, 2 * π / 5 * i, O1], i, 0, 4) → V160
  21. Sequence(Rotate[{V15'', Mirror[V15'', Line[O1, O2]]}, 2 * π / 5 * i, O1], i, 0, 4) → V150
  22. Sequence(Rotate[{V14'', Mirror[V14'', Line[O1, O2]]}, 2 * π / 5 * i, O1], i, 0, 4) → V140
  23. Sequence(Rotate[{V03, Mirror[V03, Line[O1, O2]]}, 2 * π / 5 * i, O1], i, 0, 4) → V130
  24. Sequence(Rotate[V02, 2 * π / 5 * i, O1], i, 0, 4) → V120

AI Drawing Prompt Reference

Draw a Cayley graph to illustrate the generators and their relations, using rotations and mirrors to construct multiple polygons, first rotating generators around a central point, then rotating around other points, and finally obtaining symmetric shapes through mirror operations, presenting a complex geometric structure overall.
The prompt above was compiled from the original drawing commands and is for reference only.