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Cube Nets Rotation

Cube Nets Rotation
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2019-05-24 02:25
Solid GeometryMatrixGeometric Construction
This example demonstrates the nets of a cube and their rotational transformations. It involves core math concepts like solid geometry, matrix transformations, and geometric constructions. GeoGebra commands used include Cube, Rotate, Midpoint, OrthogonalLine, Segment, and Translate. Suitable for high school mathematics teaching or beginners in geometry.

GeoGebra Commands & Parameters

  1. Cube(A, B, xOyPlane) → a, C, faceBCGF, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, D, edgeEF, edgeBF, edgeFG, edgeCG, edgeGH, E, F, G, H, faceABCD, faceADHE, faceABFE
  2. Rotate(faceABFE, (90° * t), edgeAB) → faceABFE'
  3. Midpoint(A, C) → I
  4. OrthogonalLine(I, xOyPlane) → b
  5. Rotate(faceABFE', 90*°, b) → faceABFE''
  6. Rotate(faceABFE', 180*°, b) → faceABFE''_1
  7. Rotate(faceABFE', 270*°, b) → faceABFE''_2
  8. Rotate(E, (90° * t), edgeAB) → E'
  9. Rotate(F, (90° * t), edgeAB) → F'
  10. Segment(E', F') → c
  11. Rotate(Rotate[faceEFGH, (90° * t), edgeAB], (90° * t), Segment[E', F']) → poly1
  12. Translate(J, Vector[A, B]) → K
  13. Translate(faceABFE''_1, Vector[A, J]) → poly2
  14. Translate(faceABCD, Vector[A, J]) → faceABCD'
  15. Translate(faceABFE', Vector[A, J]) → faceABFE''_3
  16. Translate(poly1, Vector[A, J]) → poly1'
  17. Translate(Rotate[Rotate[faceADHE, (90° * t), edgeAB], (((-90))° * t), Segment[Rotate[E, (90° * t), edgeAB], Rotate[A, (90° * t), edgeAB]]], Vector[A, J]) → poly4
  18. Translate(faceABFE'', Vector[A, J]) → faceABFE'''
  19. Translate(faceABCD, Vector[A, L]) → faceABCD'_1
  20. Translate(faceABFE''_1, Vector[A, L]) → poly3
  21. Translate(faceABFE', Vector[A, L]) → faceABFE''_4
  22. Translate(poly1, Vector[A, L]) → poly1'_1
  23. Translate(faceABFE'', Vector[A, L]) → faceABFE'''_1
  24. Midpoint(B, E') → M
  25. OrthogonalLine(M, faceABFE') → d
  26. Translate(Rotate[faceABFE'', 180*°, d], Vector[A, L]) → poly5
  27. Translate(faceABCD, Vector[A, O]) → faceABCD'_2
  28. Translate(faceABFE''_1, Vector[A, O]) → poly6
  29. Translate(faceABFE', Vector[A, O]) → faceABFE''_5
  30. Translate(poly1, Vector[A, O]) → poly1'_2
  31. Translate(faceABFE'', Vector[A, O]) → faceABFE'''_2
  32. Translate(Rotate[Rotate[faceADHE, (90° * t), edgeCD], (90° * t), Segment[Rotate[H, (90° * t), edgeCD], Rotate[D, (90° * t), edgeCD]]], Vector[A, O]) → poly8
  33. Translate(faceABCD, Vector[A, N]) → faceABCD'_3
  34. Translate(faceABFE''_1, Vector[A, N]) → poly7
  35. Translate(faceABFE', Vector[A, N]) → faceABFE''_6
  36. Translate(poly1, Vector[A, N]) → poly1'_3
  37. Translate(Rotate[faceABFE'', 180*°, d], Vector[A, N]) → poly9
  38. Rotate(Rotate[H, (90° * t), edgeAB], (90° * t), Segment[E', F']) → P
  39. Midpoint(P, F') → Q
  40. OrthogonalLine(Q, poly1) → e
  41. Translate(Rotate[Rotate[faceABFE'', 180*°, d], 180*°, e], Vector[A, N]) → poly10
  42. Translate(faceABCD, Vector[A, R]) → faceABCD'_4
  43. Translate(faceABFE''_1, Vector[A, R]) → poly11
  44. Translate(faceABFE', Vector[A, R]) → faceABFE''_7
  45. Translate(poly1, Vector[A, R]) → poly1'_4
  46. Translate(Rotate[faceABFE'', 180*°, d], Vector[A, R]) → poly12
  47. Rotate(F', 180*°, b) → F''
  48. Midpoint(C, F'') → S
  49. OrthogonalLine(S, faceABFE''_1) → g
  50. Translate(Rotate[Rotate[Rotate[faceADHE, (90° * t), edgeCD], (90° * t), Segment[Rotate[H, (90° * t), edgeCD], Rotate[D, (90° * t), edgeCD]]], 180*°, g], Vector[A, R]) → poly15
  51. Translate(faceABCD, Vector[A, T]) → faceABCD'_5
  52. Translate(faceABFE''_1, Vector[A, T]) → poly13
  53. Translate(faceABFE', Vector[A, T]) → faceABFE''_8
  54. Translate(Rotate[faceABFE', 270*°, b], Vector[A, T]) → poly14
  55. Translate(Rotate[poly1, -90*°, b], Vector[A, T]) → poly16
  56. Translate(Rotate[Rotate[Rotate[faceADHE, (90° * t), edgeAB], (((-90))° * t), Segment[Rotate[E, (90° * t), edgeAB], Rotate[A, (90° * t), edgeAB]]], 180*°, d], Vector[A, T]) → poly17
  57. Translate(faceABCD, Vector[A, U]) → faceABCD'_6
  58. Translate(faceABFE''_1, Vector[A, U]) → poly18
  59. Translate(faceABFE', Vector[A, U]) → faceABFE''_9
  60. Translate(Rotate[faceABFE', 270*°, b], Vector[A, U]) → poly19
  61. Translate(Rotate[Rotate[Rotate[faceADHE, (90° * t), edgeAB], (((-90))° * t), Segment[Rotate[E, (90° * t), edgeAB], Rotate[A, (90° * t), edgeAB]]], 180*°, d], Vector[A, U]) → poly20
  62. Translate(Rotate[faceABFE'', 270*°, d], Vector[A, U]) → poly22
  63. Translate(faceABCD, Vector[A, V]) → faceABCD'_7
  64. Translate(faceABFE''_1, Vector[A, V]) → poly21
  65. Translate(Rotate[faceABFE, (90° * t), edgeAB], Vector[A, V]) → poly23
  66. Translate(Rotate[Rotate[faceADHE, (90° * t), edgeCD], (90° * t), Segment[Rotate[H, (90° * t), edgeCD], Rotate[D, (90° * t), edgeCD]]], Vector[A, V]) → poly24
  67. Rotate(Rotate[faceADHE, (90° * t), edgeCD], (90° * t), Segment[Rotate[H, (90° * t), edgeCD], Rotate[D, (90° * t), edgeCD]]) → poly25
  68. Rotate(Rotate[E, (90° * t), edgeCD], (90° * t), Segment[Rotate[H, (90° * t), edgeCD], Rotate[D, (90° * t), edgeCD]]) → W
  69. Midpoint(D, W) → Z
  70. OrthogonalLine(Z, poly25) → h
  71. Rotate(faceABFE''_1, 90*°, h) → poly26
  72. Translate(Rotate[faceABFE''_1, 90*°, h], Vector[A, V]) → poly27
  73. Rotate(C, 90*°, h) → C'
  74. Midpoint(W, C') → A_1
  75. OrthogonalLine(A_1, poly26) → i
  76. Rotate(poly25, 180*°, i) → poly25'
  77. Translate(Rotate[poly25, 180*°, i], Vector[A, V]) → poly28
  78. Translate(faceABCD, Vector[A, B_1]) → faceABCD'_8
  79. Translate(faceABFE''_1, Vector[A, B_1]) → poly29
  80. Translate(faceABFE', Vector[A, B_1]) → faceABFE''_{10}
  81. Translate(Rotate[Rotate[Rotate[faceADHE, (90° * t), edgeAB], (((-90))° * t), Segment[Rotate[E, (90° * t), edgeAB], Rotate[A, (90° * t), edgeAB]]], 180*°, d], Vector[A, B_1]) → poly30
  82. Translate(Rotate[Rotate[faceADHE, (90° * t), edgeCD], (90° * t), Segment[Rotate[H, (90° * t), edgeCD], Rotate[D, (90° * t), edgeCD]]], Vector[A, B_1]) → poly31
  83. Translate(Rotate[faceABFE''_1, 90*°, h], Vector[A, B_1]) → poly32
  84. Translate(faceABCD, Vector[A, C_1]) → faceABCD'_9
  85. Translate(faceABFE''_1, Vector[A, C_1]) → poly33
  86. Translate(Rotate[Rotate[faceADHE, (90° * t), edgeCD], (90° * t), Segment[Rotate[H, (90° * t), edgeCD], Rotate[D, (90° * t), edgeCD]]], Vector[A, C_1]) → poly34
  87. Translate(Rotate[faceABFE''_1, 90*°, h], Vector[A, C_1]) → poly35
  88. Translate(faceABFE'', Vector[A, C_1]) → faceABFE'''_3
  89. Rotate(G, 90*°, b) → G'
  90. Rotate(F', 90*°, b) → F''_1
  91. Midpoint(B, F''_1) → D_1
  92. OrthogonalLine(D_1, faceABFE'') → j
  93. Rotate(faceABCD, 90*°, j) → faceABCD'_{10}
  94. Translate(Rotate[faceABCD, 90*°, j], Vector[A, C_1]) → poly36

AI Drawing Prompt Reference

Draw a cube net and its rotational transformations around an edge by 90°, 180°, and 270°. Start by creating the net of a cube, then rotate the net around one of its edges to generate three new nets. Next, translate these rotated nets based on the center point of the original net to form multiple layers. Finally, add guide lines and points to illustrate the geometric relationships between rotations and translations.
The prompt above was compiled from the original drawing commands and is for reference only.