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Cube Nets by ümran

Cube Nets by ümran
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2018-08-11 20:17
Solid GeometryTransformationGeometric Construction
This example demonstrates the nets of a cube. Key mathematical concepts include solid geometry and geometric construction. Using GeoGebra commands such as Cube, Rotate, Midpoint, etc., the various faces of the cube and their nets can be constructed. Suitable for middle school and above students to learn solid geometry and geometric construction.

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