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Intersection of Three Cuboids

Intersection of Three Cuboids
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2020-06-08 19:35
PolygonSolid GeometryGeometric Construction
This example demonstrates the geometric intersection of three cuboids, showcasing complex spatial relationships. Key math concepts include solid geometry, polygons, prisms, intersections, and line segments. It is constructed using GeoGebra commands like Polygon, Prism, Intersect, and Segment. Suitable for high school geometry education or introductory geometric modeling.

GeoGebra Commands & Parameters

  1. Polygon(A_1, B_1, C_1, D_1) → v1, a_1, b_1, c_1, d_1
  2. Prism(v1, H_1) → a, A, Kante2, Kante3, Kante4, Kante5, KanteAB, KanteBC, Kante6, B, C, Fläche1, Fläche3, Fläche4, Fläche2, Fläche5, Kante1
  3. Polygon(A_2, B_2, C_2, D_2) → v2, a_2, b_2, c_2, d_2
  4. Prism(v2, H_2) → b, D, Kante8, Kante9, Kante10, Kante11, KanteDE, KanteEF, Kante12, E, F, Fläche6, Fläche8, Fläche9, Fläche7, Fläche10, Kante7
  5. Polygon(A_3, B_3, C_3, D_3) → v3, a_3, b_3, c_3, d_3
  6. Prism(v3, H_3) → c, G, Kante14, Kante15, Kante16, Kante17, KanteGH, KanteHI, Kante18, H, I, Fläche11, Fläche13, Fläche14, Fläche12, Fläche15, Kante13
  7. Intersect(Kante10, Kante14) → J
  8. Intersect(Kante13, Kante2) → K
  9. Intersect(Kante7, Fläche1) → L
  10. Intersect(Kante8, Kante14) → M
  11. Intersect(Kante13, Kante4) → N
  12. Intersect(Kante2, Kante15) → O
  13. Intersect(Kante1, Kante9) → P
  14. Intersect(Kante4, Kante15) → Q
  15. Intersect(Kante16, Kante10) → R
  16. Intersect(Kante3, Kante9) → S
  17. Intersect(Kante16, Kante8) → T
  18. Intersect(Kante3, Kante7) → U
  19. Intersect(Kante3, Kante16) → V
  20. Segment(K, V) → f
  21. Intersect(Kante2, Kante10) → W
  22. Segment(U, W) → g
  23. Intersect(xAxis, Kante13) → Z
  24. Segment(R, Z) → h
  25. Intersect(g, h) → E_1
  26. Segment(W, L) → i
  27. Segment(Z, J) → j
  28. Intersect(Kante1, Kante14) → F_1
  29. Segment(K, F_1) → k
  30. Intersect(i, j) → G_1
  31. Segment(O, F_1) → l
  32. Segment(W, P) → m
  33. Intersect(Kante15, Kante9) → I_1
  34. Segment(J, I_1) → n
  35. Intersect(m, n) → J_1
  36. Segment(R, I_1) → p
  37. Segment(V, O) → q
  38. Segment(W, S) → r
  39. Intersect(r, p) → K_1
  40. Intersect(Kante4, zAxis) → L_1
  41. Segment(U, L_1) → s
  42. Segment(V, N) → t
  43. Segment(Z, T) → e
  44. Intersect(t, s) → M_1
  45. Segment(L, L_1) → f_1
  46. Segment(N, F_1) → g_1
  47. Segment(Z, M) → h_1
  48. Intersect(g_1, f_1) → N_1
  49. Segment(P, L_1) → i_1
  50. Segment(M, I_1) → j_1
  51. Segment(F_1, Q) → k_1
  52. Intersect(j_1, k_1) → O_1
  53. Segment(S, L_1) → l_1
  54. Segment(Q, V) → m_1
  55. Segment(T, I_1) → n_1
  56. Intersect(l_1, m_1) → P_1
  57. Polygon(Z, G_1, W, E_1) → v4, z_1, p_1, w, e_1
  58. Polygon(G_1, F_1, J_1, W) → v5, q_1, r_1, s_1, w_1
  59. Polygon(J_1, I_1, K_1, W) → v6, t_1, f_2, g_2, w_2
  60. Polygon(W, K_1, V, E_1) → v7, w_3, h_2, v, i_2
  61. Polygon(V, M_1, Z, E_1) → v8, v_1, j_2, z_2, k_2
  62. Polygon(M_1, L_1, N_1, Z) → v9, l_2, m_2, n_2, z_3
  63. Polygon(Z, N_1, F_1, G_1) → v10, z_4, p_2, q_2, r_2
  64. Polygon(L_1, O_1, F_1, N_1) → v11, s_2, o_1, t_2, e_2
  65. Polygon(F_1, O_1, I_1, J_1) → v12, f_3, g_3, h_3, i_3
  66. Polygon(L_1, P_1, I_1, O_1) → v13, j_3, k_3, l_3, m_3
  67. Polygon(P_1, V, K_1, I_1) → v14, n_3, v_2, p_3, q_3
  68. Polygon(L_1, M_1, V, P_1) → v15, r_3, s_3, v_3, t_3