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Cube with Six Holes

Cube with Six Holes
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2022-11-06 19:24
Solid GeometryTransformationGeometric Construction
This example demonstrates the geometric construction of a cube with six holes, involving concepts like geometric transformations, vectors, and coordinate geometry. The construction uses GeoGebra commands such as CurveCartesian, Surface, Midpoint, and operations like rotation and mirroring. It is suitable for middle or high school mathematics education to understand solid geometry and spatial transformations.

GeoGebra Commands & Parameters

  1. CurveCartesian(cos(t), 2, sin(t), t, 0, (2 * pi)) → a
  2. CurveCartesian((2 * cos(t)), 2, (2 * sin(t)), t, 0, (2 * pi)) → b
  3. Surface(((1 - u) * a(t)) + (u * b(t)), u, 0, 1, t, 0, (4 * pi)) → c
  4. CurveCartesian(cos(t), -2, sin(t), t, 0, (2 * pi)) → d
  5. CurveCartesian((2 * cos(t)), -2, (2 * sin(t)), t, 0, (2 * pi)) → e
  6. Surface(((1 - u) * d(t)) + (u * e(t)), u, 0, 1, t, 0, (4 * pi)) → f
  7. CurveCartesian(cos(t), sin(t), 2, t, 0, (2 * pi)) → g
  8. CurveCartesian((2 * cos(t)), (2 * sin(t)), 2, t, 0, (2 * pi)) → h
  9. Surface(((1 - u) * g(t)) + (u * h(t)), u, 0, 1, t, 0, (4 * pi)) → i
  10. CurveCartesian(cos(t), sin(t), -2, t, 0, (2 * pi)) → j
  11. CurveCartesian((2 * cos(t)), (2 * sin(t)), -2, t, 0, (2 * pi)) → k
  12. Surface(((1 - u) * j(t)) + (u * k(t)), u, 0, 1, t, 0, (4 * pi)) → l
  13. CurveCartesian(2, cos(t), sin(t), t, 0, (2 * pi)) → m
  14. CurveCartesian(2, (2 * cos(t)), (2 * sin(t)), t, 0, (2 * pi)) → n
  15. Surface(((1 - u) * m(t)) + (u * n(t)), u, 0, 1, t, 0, (4 * pi)) → o
  16. CurveCartesian(-2, cos(t), sin(t), t, 0, (2 * pi)) → p
  17. CurveCartesian(-2, (2 * cos(t)), (2 * sin(t)), t, 0, (2 * pi)) → q
  18. Surface(((1 - u) * p(t)) + (u * q(t)), u, 0, 1, t, 0, (4 * pi)) → r
  19. Midpoint(A, C) → I
  20. Midpoint(A, B) → J
  21. Polygon(A, I, J) → t1, j_1, a_1, i_1
  22. Rotate(t1, 90°, zAxis) → t1'
  23. Rotate(t1, 180°, zAxis) → t1'_{1}
  24. Rotate(t1, 270°, zAxis) → t1'_{2}
  25. Rotate(t1, -90°, xAxis) → t1'_{3}
  26. Rotate(t1'_{3}, 90°, yAxis) → t2
  27. Rotate(t2, 90°, yAxis) → t2'
  28. Rotate(t2, 180°, yAxis) → t2'_{1}
  29. Rotate(t2, 90°, zAxis) → t2'_{2}
  30. Rotate(t2'_{2}, -90°, xAxis) → t3
  31. Rotate(t2'_{2}, -180°, xAxis) → t4
  32. Rotate(t2'_{2}, -270°, xAxis) → t5
  33. Mirror(t4, eq1) → t4'
  34. Mirror(t3, eq1) → t3'
  35. Mirror(t2'_{2}, eq1) → t6
  36. Mirror(t5, eq1) → t5'
  37. Mirror(t2'_{1}, s) → t7
  38. Mirror(t2', s) → t2''
  39. Mirror(t2, s) → t2'_{3}
  40. Mirror(t1'_{3}, s) → t8
  41. Mirror(t1'_{1}, t) → t9
  42. Mirror(t1'_{2}, t) → t10
  43. Mirror(t1, t) → t1'_{4}
  44. Mirror(t1', t) → t1''
  45. Segment(D, B) → f_1
  46. Segment(B, A) → g_1
  47. Segment(A, C) → h_1
  48. Segment(C, D) → k_1
  49. Segment(B, F) → l_1
  50. Segment(D, H) → m_1
  51. Segment(H, F) → n_1
  52. Segment(F, E) → p_1
  53. Segment(E, A) → q_1
  54. Segment(E, G) → r_1
  55. Segment(G, C) → s_1
  56. Segment(G, H) → t_1
  57. CurveCartesian(cos(t), 2, sin(t), t, 0, (2 * pi)) → u

AI Drawing Prompt Reference

Draw a cube with six holes. Start by drawing a cube, then create a hole on each of its six faces. Each hole consists of a circle and a cylindrical surface, with the circle centered on the face and the cylinder perpendicular to the face. Finally, use rotation and mirroring to duplicate the hole on all six faces.
The prompt above was compiled from the original drawing commands and is for reference only.