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Nets of Pyramids

Nets of Pyramids
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2013-01-29 09:30
PolygonSolid GeometryGeometric Construction
In collections Geometry-Volume and Surface Area
This example demonstrates the construction of four different nets of pyramids. It involves core mathematical concepts such as polygon construction, rotation, and intersection. Key GeoGebra commands and objects used include Polygon, Rotate, Circle, Segment, and Intersect. Suitable for high school students learning solid geometry to understand the relationship between 3D shapes and their 2D nets.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3) → poly1, a, b, c, C
  2. Polygon(D, E, 4) → poly2, d, e, f, g, F, G
  3. Polygon(C, B, 3) → poly3, h, i, j, H
  4. Polygon(B, A, 3) → poly4, k, l, m, I
  5. Polygon(A, C, 3) → poly5, n, p, q, J
  6. Polygon(S, T, 5) → poly10, n_1, p_1, q_1, r_1, s_1, U, V, W
  7. Polygon(G, F, 3) → poly6, r, s, t, K
  8. Polygon(F, E, 3) → poly7, a_1, b_1, c_1, L
  9. Polygon(E, D, 3) → poly8, d_1, e_1, f_1, M
  10. Polygon(D, G, 3) → poly9, g_1, h_1, i_1, N
  11. Polygon(S, W, 3) → poly11, j_1, k_1, l_1, O
  12. Polygon(W, V, 3) → poly12, m_1, t_1, a_2, P
  13. Polygon(V, U, 3) → poly13, b_2, c_2, d_2, Q
  14. Polygon(U, T, 3) → poly14, e_2, f_2, g_2, R
  15. Polygon(T, S, 3) → poly15, h_2, i_2, j_2, Z
  16. Polygon(B_1, C_1, 4) → poly16, k_2, l_2, m_2, n_2, D_1, E_1
  17. Polygon(B_4, C_2, 4) → poly16_1, k_3, l_3, m_3, n_3, D_2, E_2
  18. Polygon(B_1, F_1, C_1) → poly17, c_3, b_3, f_3
  19. Rotate(B_1, 270*°, B_1) → G_1
  20. Rotate(C_1, 90*°, C_1) → J_1
  21. Circle(B_1, F_1) → p_2
  22. Circle(C_1, F_1) → q_2
  23. Segment(E_1, H_1) → r_2
  24. Segment(D_1, H_1) → s_2
  25. Circle(E_1, H_1) → t_2
  26. Circle(D_1, H_1) → d_3
  27. Intersect(p_2, t_2, 1) → I_1
  28. Intersect(q_2, d_3, 2) → K_1
  29. Segment(E_1, I_1) → a_3
  30. Segment(I_1, B_1) → e_3
  31. Segment(D_1, K_1) → g_3
  32. Segment(C_1, K_1) → h_3
  33. Polygon(E_1, D_1, H_1) → poly18, h_4, e_4, d_4
  34. Polygon(I_1, B_1, E_1) → poly19, e_5, i_3, b_4
  35. Polygon(C_1, K_1, D_1) → poly20, d_5, c_4, k_4

AI Drawing Prompt Reference

Draw four different nets of pyramids to demonstrate core mathematical concepts like polygon construction, rotation, and intersection. Start by creating multiple regular polygons for the bases and faces of the pyramids, then use rotation and intersection to construct the nets, and finally combine all parts into a complete pyramid net to understand the relationship between 3D shapes and their 2D unfoldings.
The prompt above was compiled from the original drawing commands and is for reference only.