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Stepwise Construction of a Cuboid with Reflection/Translation

Stepwise Construction of a Cuboid with Reflection/Translation
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2020-08-13 14:22
PolygonVectorSolid GeometryTransformationGeometric Construction
This GeoGebra example demonstrates how to build a cuboid step by step using planar polygon faces, then use geometric transformations to generate corresponding vertices/edges for the opposite sides. It highlights the 3D construction idea behind a cuboid: creating each face as a polygon, connecting edges via points, lines, and segments, and using vector-based transformations to replicate the structure. The core math concepts include solid geometry (cuboid face construction), transformation geometry with vectors and translation (Translate), and reflection/relocation to obtain matching geometry. Construction-wise, the model relies on Polygon to form face polygons (using vertices such as A, B, C, D, and their corresponding labeled points), Point/Line/Segment to define and connect key points and edges, Vector and Translate to move the base configuration to the needed positions, and Sequence to manage repeated or iterative elements (e.g., list1 and list2 and multiple prime-labeled point sets). Suitable for middle school through early university students for hands-on geometry construction, understanding transformations, and visual modeling.

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 cuboid by first defining a base face with points A, B, C, and D, then connecting these points with line segments to form a quadrilateral. Next, translate the base face to the opposite side using vector u to form another base face. Then, use the sequence command to generate a series of parallel planes to the base, dividing the cuboid into multiple parts. Finally, translate these planes to generate all the faces of the cuboid.
The prompt above was compiled from the original drawing commands and is for reference only.