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Cube Nets by milanofff

Cube Nets by milanofff
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2013-09-11 22:13
Solid GeometryTransformationGeometric Construction
In collections Cuboids & their Nets
This example demonstrates the 11 nets of a cube. It involves basic concepts of solid geometry, and uses GeoGebra commands such as Line, If, Polygon, Translate, and PolyLine to visually show the process of unfolding a cube. Suitable for middle school and above students learning solid geometry.

GeoGebra Commands & Parameters

  1. Line(O, u) → Ox
  2. Line(O, v) → Oy
  3. Line(O, w) → Oz
  4. If(t < 1, 1, If[(t ≥ 1) ∧ (t < 2), 2 - t, 0]) → t2
  5. If(t < 2, 1, If[(t ≥ 2) ∧ (t < 3), 3 - t, 0]) → t3
  6. If(t < 3, 1, If[(t ≥ 3) ∧ (t < 4), 4 - t, 0]) → t4
  7. If(t < 4, 1, If[(t ≥ 4) ∧ (t < 5), 5 - t, 0]) → t5
  8. If(t < 0, 1, If[t < 1, 1 - t, 0]) → t1
  9. If(t < 0, 0, If[t < 1, t, 1]) → t11
  10. If(t < 2, 0, If[(t ≥ 2) ∧ (t < 3), t - 2, 1]) → t31
  11. If(t < 3, 0, If[(t ≥ 3) ∧ (t < 4), t - 3, 1]) → t41
  12. If(t < 1, 0, If[(t ≥ 1) ∧ (t < 2), t - 1, 1]) → t21
  13. If(t < 4, 0, If[(t ≥ 4) ∧ (t < 6), t - 4, 1]) → t51
  14. If(t < 5, 1, If[(t ≥ 5) ∧ (t < 6), 6 - t, 0]) → t6
  15. If(t < 5, 0, If[(t ≥ 5) ∧ (t < 6), t - 5, 1]) → t61
  16. Polygon({A, B, C, D}) → ABCD, , , ,
  17. Translate(E, Vector[A, B]) → F
  18. Polygon({A, E, F, B}) → AEFB, , , ,
  19. If(t < 1, E + a * (-cos(t11 * π / 2) * u + sin(t11 * π / 2) * w), E + a * (cos(t2 * π / 2) * u + sin(t2 * π / 2) * w)) → G
  20. Polygon({E, G, H, F}) → EGHF, , , ,
  21. If(t < 1, G + Vector[E, A], If[t < 2, G + a * (-cos(t21 * π / 2) * u + sin(t21 * π / 2) * w), G + a * (cos(t3 * π / 2) * u + sin(t3 * π / 2) * w)]) → I
  22. Polygon({G, I, J, H}) → GIJH, , , ,
  23. Polygon({D, L, K, A}) → DLKA, , , ,
  24. Polygon({B, M, N, C}) → BMNC, , , ,
  25. If(t < 1, F + a * (-cos(t11 * π / 2) * u + sin(t11 * π / 2) * w), F + a * (-cos(t2 * π / 2) * v + sin(t2 * π / 2) * w)) → M2
  26. Polygon({F, M2, N2, B}) → FMNB2, , , ,
  27. If(t < 2, J, H + a * (-cos(t3 * π / 2) * v + sin(t3 * π / 2) * w)) → M3
  28. Polygon({H, M3, N3, F}) → HMNF3, , , ,
  29. If(t < 2, N3, If[t < 3, J + a * (-cos(t31 * π / 2) * u + sin(t31 * π / 2) * w), J + a * (-cos(t4 * π / 2) * v + sin(t4 * π / 2) * w)]) → M4
  30. Polygon({J, M4, N4, H}) → JMNH4, , , ,
  31. If(t < 1, E + a * (-cos(t11 * π / 2) * u + sin(t11 * π / 2) * w), E + a * (cos(t2 * π / 2) * v + sin(t2 * π / 2) * w)) → K5
  32. Polygon({A, L5, K5, E}) → ALKE5, , , ,
  33. If(t < 2, I, G + a * (cos(t3 * π / 2) * v + sin(t3 * π / 2) * w)) → I7
  34. Polygon({E, J7, I7, G}) → EJIG7, , , ,
  35. If(t < 2, J, If[t < 3, I7 + a * (-cos(t31 * π / 2) * v + sin(t31 * π / 2) * w), I7 + a * (cos(t4 * π / 2) * u + sin(t4 * π / 2) * w)]) → K7
  36. Polygon({I7, K7, L7, G}) → IKLG7, , , ,
  37. If(t < 3, K7 + Vector[I7, J7], If[t < 4, K7 + a * (-cos(t41 * π / 2) * u + sin(t41 * π / 2) * w), K7 + a * (cos(t5 * π / 2) * u + sin(t5 * π / 2) * w)]) → M8
  38. Polygon({K7, M8, N8, L7}) → KMNL8, , , ,
  39. If(t < 1, K5 + Vector[E, F], If[t < 2, K5 + a * (-cos(t21 * π / 2) * v + sin(t21 * π / 2) * w), K5 + a * (cos(t3 * π / 2) * u + sin(t3 * π / 2) * w)]) → P
  40. Polygon({K5, P, Q, E}) → KPQE9, , , ,
  41. If(t < 2, P + Vector[K5, L5], If[t < 3, P + a * (-cos(t31 * π / 2) * u + sin(t31 * π / 2) * w), P + a * (cos(t4 * π / 2) * v + sin(t4 * π / 2) * w)]) → R
  42. Polygon({K5, S, R, P}) → KSRP9, , , ,
  43. If(t < 3, R + Vector[P, Q], If[t < 4, R + a * (-cos(t41 * π / 2) * v + sin(t41 * π / 2) * w), R + a * (cos(t5 * π / 2) * u + sin(t5 * π / 2) * w)]) → T
  44. Polygon({R, T, U, P}) → RTUP9, , , ,
  45. If(t < 3, R, P + a * (cos(t4 * π / 2) * u + sin(t4 * π / 2) * w)) → T10
  46. Polygon({P, T10, U10, Q}) → PTUQ10, , , ,
  47. If(t < 3, T10 + Vector[P, K5], If[t < 4, T10 + a * (-cos(t41 * π / 2) * u + sin(t41 * π / 2) * w), T10 + a * (cos(t5 * π / 2) * v + sin(t5 * π / 2) * w)]) → R11
  48. Polygon({P, S11, R11, T10}) → PSRT11, , , ,
  49. PolyLine({A, I, J, B, M, N, L, K, A}) → line1
  50. PolyLine({A, I, J, F, M2, N2, B, C, L, K, A}) → line2
  51. PolyLine({A, I, J, H, M3, N3, F, C, L, K, A}) → line3
  52. PolyLine({A, I, M4, N4, H, C, L, K, A}) → line4
  53. PolyLine({A, L5, K5, E, I, J, F, M2, N2, B, C, D, A}) → line5
  54. PolyLine({A, L5, K5, E, I, J, H, M3, N3, F, C, D, A}) → line6
  55. PolyLine({A, E, J7, K7, L7, G, M3, N3, F, C, D, A}) → line7
  56. PolyLine({A, E, J7, M8, N8, G, H, C, D, A}) → line8
  57. PolyLine({A, L5, K5, S, T, U, P, Q, E, F, C, D, A}) → line9
  58. PolyLine({A, L5, K5, S, R, P, T10, U10, E, F, C, D, A}) → line10
  59. PolyLine({A, L5, P, S11, R11, U10, E, F, C, D, A}) → line11

AI Drawing Prompt Reference

Draw an unfolded net of a cube, which includes 11 different configurations. Start by drawing the three coordinate axes Ox, Oy, and Oz. Then, based on the value of t, sequentially draw each face, such as ABCD, AEFB, EFGH, and GIJH. Each face is obtained through translation and rotation, ultimately forming the complete net.
The prompt above was compiled from the original drawing commands and is for reference only.