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Nets of the Cube (11 Different Nets)

Nets of the Cube (11 Different Nets)
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2020-05-09 00:58
Solid GeometryTransformationGeometric Construction
In collections Geometry - Areas and Volumes
This example demonstrates 11 different nets of a cube, helping to understand the spatial geometry of how a 3D shape can be unfolded into a 2D plane. Using GeoGebra commands such as Cube, Rotate, Midpoint, etc., it visually shows the relative positions and connections of each face. Suitable for students at the junior high school level and above studying solid 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 11 different nets of a cube, showing how a 3D cube can be unfolded into a 2D plane. Start by creating a cube, then use rotation and reflection to generate multiple nets, each consisting of 6 connected square faces. Use distinct colors or line styles to differentiate the faces and edges, making it easy to observe the structure and folding patterns of each net.
The prompt above was compiled from the original drawing commands and is for reference only.