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Rotating Cube

Rotating Cube
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2016-12-18 02:15
Solid GeometryProbability & StatisticsGeometric Construction
In collections surface 3D /3D-Oberflächen 1 surface 3D /3D-Oberflächen 1
This example demonstrates a rotatable cube and its geometric properties, involving core math concepts like solid geometry, rotation, polygons, piecewise-defined functions, and probability & statistics. It is constructed using GeoGebra commands: Cube, Segment, Line; objects include angles α, β, γ, sliders w_1, w_2, w_3 for rotation control, vertices A, B, C..., faces FlächeABCD..., edges KanteAD...; suitable for high school and above students to explore spatial geometry, probability distributions, and dynamic geometry visualization.

GeoGebra Commands & Parameters

  1. Cube(A, B, C) → a, D, FlächeCDHG, FlächeEFGH, KanteAD, KanteAB, KanteBC, KanteCD, KanteAE, KanteDH, KanteEH, KanteEF, E, KanteBF, KanteFG, KanteCG, KanteGH, F, G, H, FlächeABCD, FlächeADHE, FlächeABFE, FlächeBCGF
  2. Segment(A', B') → f
  3. Segment(B', C') → g
  4. Segment(C', D') → h
  5. Segment(D', A') → i
  6. Segment(A', E') → j
  7. Segment(B', F') → k
  8. Segment(C', G') → l
  9. Segment(D', H') → m
  10. Segment(E', F') → n
  11. Segment(F', G') → p
  12. Segment(G', H') → q
  13. Segment(H', E') → r
  14. Segment(A''', B''') → s
  15. Segment(B''', C''') → t
  16. Segment(C''', D''') → b
  17. Segment(D''', A''') → c
  18. Segment(A''', E''') → d
  19. Segment(B''', F''') → e
  20. Segment(C''', G''') → f_1
  21. Segment(D''', H''') → h_1
  22. Segment(E''', F''') → i_1
  23. Segment(F''', G''') → j_1
  24. Segment(G''', H''') → k_1
  25. Segment(H''', E''') → l_1
  26. Segment(A'', B'') → m_1
  27. Segment(B'', C'') → n_1
  28. Segment(C'', D'') → p_1
  29. Segment(D'', A'') → q_1
  30. Segment(B'', F'') → r_1
  31. Segment(A'', E'') → s_1
  32. Segment(C'', G'') → t_1
  33. Segment(D'', H'') → a_1
  34. Segment(H'', G'') → b_1
  35. Segment(E'', F'') → c_1
  36. Segment(G'', F'') → d_1
  37. Segment(H'', E'') → e_1
  38. Segment(A, A') → f_2
  39. Segment(B, B') → h_2
  40. Segment(C, C') → i_2
  41. Segment(D, D') → j_2
  42. Segment(E, E') → k_2
  43. Segment(F, F') → l_2
  44. Segment(H, H') → m_2
  45. Segment(G, G') → n_2
  46. Segment(A, A''') → p_2
  47. Segment(D, D''') → s_2
  48. Segment(F, F''') → t_2
  49. Segment(E, E''') → a_2
  50. Segment(G, G''') → b_2
  51. Segment(A, A'') → c_2
  52. Segment(D, D'') → f_3
  53. Segment(E, E'') → h_3
  54. Segment(H, H'') → i_3
  55. Segment(F, F'') → j_3
  56. Segment(G, G'') → k_3
  57. Segment(H, H''') → q_2
  58. Segment(C, C'') → r_2
  59. Segment(C, C''') → d_2
  60. Segment(B, B''') → e_2
  61. Segment(B, B'') → l_3
  62. Line(M, xAxis) → g_1
  63. Line(M, yAxis) → g_2
  64. Line(M, zAxis) → g_3

AI Drawing Prompt Reference

Draw a rotatable cube demonstrating its 3D geometric properties. Start with a base cube having eight vertices, six faces, and twelve edges. Then, create three rotated copies of the cube positioned around the original, connecting corresponding vertices with line segments to show rotation paths. Add three sliders to control rotation angles around the x, y, and z axes, allowing real-time rotation. Highlight the edges of each copy with distinct colors while keeping the original cube's outline visible, to observe spatial changes during rotation.
The prompt above was compiled from the original drawing commands and is for reference only.