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Hexagonal Kaleidoscope Pattern

Hexagonal Kaleidoscope Pattern
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2014-08-07 21:49
PolygonTransformationGeometric Construction
In collections Symmetry, Transformation and Tessellation
This example demonstrates the creation of a kaleidoscope pattern from hexagons through reflection and rotation; core math concepts include symmetry, rotation, and polygon construction; construction highlights involve commands like Segment, Midpoint, Mirror, Rotate, Vector, Sequence, and Line to build basic shapes and iterate for complexity; suitable for high school mathematics teaching to understand transformation geometry and symmetry principles.

GeoGebra Commands & Parameters

  1. Segment(M, Q) → f
  2. Segment(M, P) → e
  3. Segment(M, N) → d
  4. Segment(L, M) → c
  5. Segment(C, B) → h
  6. Midpoint(A, B) → H
  7. Segment(E, H) → b
  8. Mirror(cell1, b) → cell2
  9. Rotate(cell12, 240*°, E) → cell56
  10. Rotate(cell12, 120*°, E) → cell34
  11. Mirror(cell123456, h) → cell789012
  12. Midpoint(C, A) → G
  13. Midpoint(B, D) → I
  14. Midpoint(D, C) → J
  15. Midpoint(C, B) → K
  16. Vector(A, B) → u
  17. Vector(A, C) → v
  18. Segment(E, G) → a
  19. Sequence(Translate[Sequence[Translate[tile, Vector[(n * u)]], n, -3, 3], Vector[(m * v)]], m, -3, 3) → tiling
  20. Vector(B, D) → w
  21. Vector(C, D) → g
  22. Segment(F, J) → j
  23. Segment(F, I) → k
  24. Segment(E, F) → i
  25. Segment(A, E) → p
  26. Segment(E, C) → q
  27. Segment(E, B) → r
  28. Segment(F, C) → s
  29. Segment(F, B) → t
  30. Segment(F, D) → a_1
  31. Line(A, E) → b_1
  32. Line(C, E) → c_1
  33. Line(B, E) → d_1
  34. Line(B, F) → e_1
  35. Line(C, F) → f_1
  36. Line(C, B) → g_1
  37. Line(A, B) → h_1
  38. Line(C, D) → i_1
  39. Line(B, D) → j_1
  40. Line(A, C) → k_1
  41. Line(G, q) → l_1
  42. Line(K, q) → m_1
  43. Line(I, t) → n_1
  44. Line(H, r) → p_1
  45. Line(K, r) → q_1
  46. Line(J, k) → r_1
  47. Line(H, i) → s_1
  48. Line(G, i) → t_1
  49. Line(G, H) → a_2
  50. Line(H, K) → b_2
  51. Line(K, G) → c_2
  52. Line(I, J) → d_2

AI Drawing Prompt Reference

Create a kaleidoscope pattern using hexagons to demonstrate symmetry through reflection and rotation. Start by drawing a central point and then create three segments radiating from it to form the basic hexagon structure. Next, rotate the hexagon 120° and 240° around the center point, and reflect each rotated shape to generate symmetrical patterns. Finally, combine all the basic shapes to form a complex and intricate kaleidoscope design.
The prompt above was compiled from the original drawing commands and is for reference only.