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Building a Cuboid

Building a Cuboid
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2014-05-25 05:30
PolygonVectorSolid GeometryGeometric Construction
This example demonstrates how to construct a 3D cuboid using GeoGebra. The core math concepts involved include polygons, vectors, translation transformations, and solid geometry. Key construction steps utilize commands and objects such as Polygon, Line, Point, Segment, Vector, Translate, and Sequence to generate the faces of the cuboid through vector translation and sequence operations. It is suitable for high school students learning solid geometry and understanding spatial figure construction methods.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → مضلع1, a, b, c, d
  2. Line(E, F) → e
  3. Point(Circle[E, abs(n)]) → G
  4. Segment(E, G) → f
  5. Point(f) → H
  6. Vector(E, H) → u
  7. Translate(A, u) → A'
  8. Translate(B, u) → B'
  9. Translate(C, u) → C'
  10. Translate(D, u) → D'
  11. Polygon(A', B', C', D') → مضلع1', a', b', c', d'
  12. Polygon(B', B, A, A') → مضلع2, b'_1, b_1, a_1, a'_1
  13. Polygon(D', C', C, D) → مضلع3, d'_1, c'_1, c_1, d_1
  14. Sequence(Polygon[A + (i, 0), B + (i, 0), C + (i, 0), D + (i, 0)], i, 0, m) → list1
  15. Sequence(Polygon[A' + (i, 0), B' + (i, 0), C' + (i, 0), D' + (i, 0)], i, 0, m) → list2
  16. Sequence(Polygon[B' + (i, 0), B + (i, 0), A + (i, 0), A' + (i, 0)], i, 0, m) → list3
  17. Sequence(Polygon[C' + (i, 0), C + (i, 0), D + (i, 0), D' + (i, 0)], i, 0, m) → list4
  18. Sequence(Polygon[A - (0, i), B - (0, i), C - (0, i), D - (0, i)], i, 1, r) → list6
  19. Sequence(Polygon[A' - (0, i), B' - (0, i), C' - (0, i), D' - (0, i)], i, 1, r) → list5
  20. Sequence(Polygon[A' - (0, i), A - (0, i), D - (0, i), D' - (0, i)], i, 1, r) → list7
  21. Sequence(Polygon[B' - (0, i), B - (0, i), C - (0, i), C' - (0, i)], i, 1, r) → list8
  22. Sequence(Polygon[B' - (0, i) + (m, 0), B - (0, i) + (m, 0), C - (0, i) + (m, 0), C' - (0, i) + (m, 0)], i, 1, r) → list9
  23. Sequence(Sequence[Polygon[B' - (0, i) + (j, 0), B - (0, i) + (j, 0), C - (0, i) + (j, 0), C' - (0, i) + (j, 0)], i, 1, r], j, 1, m) → list10
  24. Sequence(Sequence[Polygon[A' - (0, i) + (j, 0), A - (0, i) + (j, 0), D - (0, i) + (j, 0), D' - (0, i) + (j, 0)], i, 1, r], j, 0, m) → list11
  25. Sequence(Sequence[Polygon[A - (0, i) + (j, 0), B - (0, i) + (j, 0), C - (0, i) + (j, 0), D - (0, i) + (j, 0)], i, 1, r], j, 0, m) → list12
  26. Sequence(Sequence[Polygon[A' - (0, i) + (j, 0), B' - (0, i) + (j, 0), C' - (0, i) + (j, 0), D' - (0, i) + (j, 0)], i, 1, r], j, 0, m) → list13
  27. Sequence(Translate[list1, Vector[-u - (0.34 * i, 0.35 * i)]], i, 0, t) → list14
  28. Sequence(Translate[list2, Vector[-u - (0.34 * i, 0.35 * i)]], i, 0, t) → list15
  29. Sequence(Translate[list3, Vector[-u - (0.34 * i, 0.35 * i)]], i, 0, t) → list16
  30. Sequence(Translate[list4, Vector[-u - (0.34 * i, 0.35 * i)]], i, 0, t) → list17
  31. Sequence(Translate[list5, Vector[-u - (0.34 * i, 0.35 * i)]], i, 0, t) → list18
  32. Sequence(Translate[list6, Vector[-u - (0.34 * i, 0.35 * i)]], i, 0, t) → list19
  33. Sequence(Translate[list7, Vector[-u - (0.34 * i, 0.35 * i)]], i, 0, t) → list20
  34. Sequence(Translate[list8, Vector[-u - (0.34 * i, 0.35 * i)]], i, 0, t) → list21
  35. Sequence(Translate[list9, Vector[-u - (0.34 * i, 0.35 * i)]], i, 0, t) → list22
  36. Sequence(Translate[list10, Vector[-u - (0.34 * i, 0.35 * i)]], i, 0, t) → list23
  37. Sequence(Translate[list12, Vector[-u - (0.34 * i, 0.35 * i)]], i, 0, t) → list24
  38. Sequence(Translate[list13, Vector[-u - (0.34 * i, 0.35 * i)]], i, 0, t) → list25
  39. Sequence(Translate[list11, Vector[-u - (0.34 * i, 0.35 * i)]], i, 0, t) → list26

AI Drawing Prompt Reference

Draw a 3D cuboid by first creating a base quadrilateral, then defining a height direction with a segment, translating the base along that direction to form the top face, and connecting corresponding vertices for side faces. Replicate this cuboid horizontally in a row, then stack multiple rows vertically to form a grid of cuboids. Finally, translate the entire grid diagonally multiple times to create a staggered, layered 3D arrangement.
The prompt above was compiled from the original drawing commands and is for reference only.