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Find the Faces of the Cube

Find the Faces of the Cube
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2020-12-16 17:18
PolygonSolid GeometryGeometric Construction
This example demonstrates how to dynamically visualize the faces of a cube using GeoGebra. Key math concepts include solid geometry, polygon construction, random selection, and geometric transformations. Construction highlights involve commands like Polygon, Random, If, Element, Centroid, and Text. Suitable for high school students and above for learning solid geometry and geometric constructions, or for educational demonstrations.

GeoGebra Commands & Parameters

  1. Polygon(A_1, A_1 + (1, 0), A_1 + (1, -1), A_1 + (0, -1)) → poly1, a, b, c, d
  2. Polygon(A_2, A_2 + (1, 0), A_2 + (1, -1), A_2 + (0, -1)) → poly2, e, f, g, h
  3. Polygon(A_3, A_3 + (1, 0), A_3 + (1, -1), A_3 + (0, -1)) → poly3, i, j, k, l
  4. Polygon(A_4, A_4 + (1, 0), A_4 + (1, -1), A_4 + (0, -1)) → poly4, m, n, p, a_1
  5. Polygon(A_5, A_5 + (1, 0), A_5 + (1, -1), A_5 + (0, -1)) → poly5, q, r, s, t
  6. Polygon(A_6, A_6 + (1, 0), A_6 + (1, -1), A_6 + (0, -1)) → poly6, b_1, c_1, d_1, e_1
  7. Random(1, 6) → decalage
  8. If(Random[0, 1] ≟ 1, true, false) → voir3
  9. If(Random[0, 1] ≟ 1, true, false) → voir2
  10. If(Random[0, 1] ≟ 1, true, false) → voir1
  11. If(choisir, np, Random[1, 11]) → npp
  12. Element(patrons, npp) → patron
  13. Centroid(poly3) → A
  14. Centroid(poly2) → B
  15. Centroid(poly1) → C
  16. Centroid(poly6) → D
  17. Text(de6, D - (0.15, 0.15)) → txt6
  18. Centroid(poly5) → E
  19. Text(de5, E + (-0.15, -0.15)) → txt5
  20. Centroid(poly4) → F
  21. Text(de4, F - (0.15, 0.15)) → txt4
  22. Text(de2, B - (0.15, 0.15)) → txt2
  23. Centroid(poly3) → G
  24. Text(de3, G - (0.15, 0.15)) → txt3
  25. Text(de1, C - (0.15, 0.15)) → txt1

AI Drawing Prompt Reference

Draw a cube net consisting of six square faces, each formed by translating a unit square. Place a random number or symbol at the center of each face. Some faces may be shown or hidden based on random conditions. The overall figure is a dynamic, interactive solid geometry visualization showing the six faces of a cube and their spatial relationships. Each face is a polygon with four vertices, a centroid marker, and a text label.
The prompt above was compiled from the original drawing commands and is for reference only.