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3-Mirror Kaleidoscope Pattern Exploration

3-Mirror Kaleidoscope Pattern Exploration
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2014-08-03 10:59
PolygonTransformationGeometric Construction
In collections Symmetry, Transformation and Tessellation
This example demonstrates symmetric patterns formed by multiple reflections using three mirrors. It involves core math concepts like symmetry, reflection transformations, and polygon construction. Key GeoGebra commands used include Polygon and Mirror for creating shapes and reflecting points respectively. Suitable for high school students or geometry enthusiasts to understand spatial symmetry and transformation applications.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3) → poly1, a, b, c, C
  2. Mirror(P, a) → Pa
  3. Mirror(P, b) → Pb
  4. Mirror(P, c) → Pc
  5. Mirror(Pa, b) → Pab
  6. Mirror(Pa, c) → Pac
  7. Mirror(Pb, a) → Pba
  8. Mirror(Pb, c) → Pbc
  9. Mirror(Pc, a) → Pca
  10. Mirror(Pc, b) → Pcb
  11. Mirror(Pab, a) → Paba
  12. Mirror(Pab, c) → Pabc
  13. Mirror(Pac, a) → Paca
  14. Mirror(Pac, b) → Pacb
  15. Mirror(Pba, b) → Pbab
  16. Mirror(Pba, c) → Pbac
  17. Mirror(Pbc, a) → Pbca
  18. Mirror(Pbc, b) → Pbcb
  19. Mirror(Pca, b) → Pcab
  20. Mirror(Pca, c) → Pcac
  21. Mirror(Pcb, a) → Pcba
  22. Mirror(Pcb, c) → Pcbc
  23. Mirror(Paba, c) → Pabac
  24. Mirror(Paba, b) → Pabab
  25. Mirror(Pabc, a) → Pabca
  26. Mirror(Pabc, b) → Pabcb
  27. Mirror(Paca, b) → Pacab
  28. Mirror(Paca, c) → Pacac
  29. Mirror(Pacb, a) → Pacba
  30. Mirror(Pacb, c) → Pacbc
  31. Mirror(Pbab, a) → Pbaba
  32. Mirror(Pbab, c) → Pbabc
  33. Mirror(Pbac, a) → Pbaca
  34. Mirror(Pbac, b) → Pbacb
  35. Mirror(Pbca, b) → Pbcab
  36. Mirror(Pbca, c) → Pbcac
  37. Mirror(Pbcb, a) → Pbcba
  38. Mirror(Pbcb, c) → Pbcbc
  39. Mirror(Pcab, a) → Pcaba
  40. Mirror(Pcab, c) → Pcabc
  41. Mirror(Pcac, a) → Pcaca
  42. Mirror(Pcac, b) → Pcacb
  43. Mirror(Pcba, b) → Pcbab
  44. Mirror(Pcba, c) → Pcbac
  45. Mirror(Pcbc, a) → Pcbca
  46. Mirror(Pcbc, b) → Pcbcb

AI Drawing Prompt Reference

Draw a symmetric pattern formed by multiple reflections using three mirrors, starting with constructing a triangle, then reflecting each vertex of the triangle over the three sides successively, and further reflecting each new point over the other two sides to create a complex, multi-level symmetric design that illustrates the geometric transformation of reflections.
The prompt above was compiled from the original drawing commands and is for reference only.