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Net of a Rectangular Prism Exploration

Net of a Rectangular Prism Exploration
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2012-12-06 10:44
PolygonSolid GeometryTransformationGeometric Construction
In collections Cuboids & their Nets
This example demonstrates the net of a rectangular prism and its structural relationships. Core math concepts include polygons, solid geometry, and spatial visualization. Construction highlights involve commands like Sequence, Element, Polygon, Segment to draw the net's faces, and transformation commands (R_x, R_y, R_z) for 3D-to-2D unfolding. Suitable for middle school and above students to understand solid geometry and polygon relationships, enhancing spatial reasoning skills.

GeoGebra Commands & Parameters

  1. Sequence(Mat * Element[cube, k], k, 1, 8) → cube'
  2. Element(Element[AE, 3], 1) → droite
  3. Sequence(I + (Element[cube', k, 1, 1], Element[cube', k, 2, 1]), k, 1, 8) → listepoints
  4. Element(listepoints, 2) → A
  5. Element(listepoints, 1) → E
  6. Element(listepoints, 4) → C_1
  7. Element(listepoints, 3) → D
  8. Polygon(A, E, C_1, D) → poly1, a_1, b, c_1, d
  9. Element(listepoints, 6) → B
  10. Element(listepoints, 7) → F
  11. Element(listepoints, 8) → G
  12. Element(listepoints, 5) → H
  13. Polygon(B, F, G, H) → poly2, e, f, g, h
  14. Element(listepoints, 3) → C
  15. Polygon(F, C, A, B) → poly3, f_1, i, a_2, b_1
  16. Element(AB, 3, 1) → avant
  17. Polygon(C_1, G, H, E) → poly4, c_2, g_1, h_1, e_1
  18. Element(AC, 3, 1) → dessus
  19. Polygon(F, C, C_1, G) → poly5, f_2, c_3, c_4, g_2
  20. Polygon(A, B, H, E) → poly6, a_3, b_2, h_2, e_2
  21. Segment(E, A) → c
  22. Segment(A, C) → j
  23. Segment(A, B) → k
  24. Segment(C, C_1) → l
  25. Segment(C_1, E) → m
  26. Segment(A, B) → p
  27. Segment(B, H) → q
  28. Segment(H, E) → r
  29. Segment(H, G) → s
  30. Segment(B, F) → t
  31. Segment(G, C_1) → d_1
  32. Segment(F, G) → i_1
  33. Segment(F, C) → j_1
  34. Polygon(A, B, F', D') → poly7, a_4, b_3, f', d'
  35. Polygon(E, A, D'', C') → poly8, e_3, a_5, d'', c'
  36. Polygon(B, F'', G', H) → poly9, b_4, f'', g', h_3
  37. Polygon(H, G'', C''', E) → poly10, h_4, g'', c''', e_4
  38. Polygon(A_2, B_2, G'', C''') → poly11, a_6, b_5, g''_1, c'''_1

AI Drawing Prompt Reference

Draw the net of a rectangular prism with six rectangular faces, connected by lines to show the 3D structure. Start by sketching three rectangles, then add the remaining three to form a clear, unfoldable layout that highlights the spatial relationships of the prism.
The prompt above was compiled from the original drawing commands and is for reference only.