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Transform Cube to Octahedron

Transform Cube to Octahedron
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2017-08-15 23:54
Solid GeometryTransformationGeometric Construction
This example demonstrates how to transform a cube into an octahedron using geometric transformations. Key mathematical concepts include solid geometry. Commands used include Sphere, Segment, Intersect, Polygon, Midpoint, Line, Distance. Suitable for high school geometry lessons.

GeoGebra Commands & Parameters

  1. Sphere(A, B) → a
  2. Segment(G, E) → b
  3. Segment(E, D) → c
  4. Segment(D, F) → d
  5. Segment(F, G) → e
  6. Segment(G, K) → f
  7. Segment(E, I) → g
  8. Segment(D, H) → h
  9. Segment(J, F) → i
  10. Segment(J, H) → j
  11. Segment(H, I) → k
  12. Segment(I, K) → l
  13. Segment(K, J) → m
  14. Intersect(c, a) → C, L
  15. Intersect(h, a) → M, N
  16. Intersect(g, a) → O, P
  17. Intersect(k, a) → Q, R
  18. Intersect(d, a) → S, T
  19. Intersect(i, a) → U, V
  20. Intersect(j, a) → W, Z
  21. Intersect(e, a) → A_1, B_1
  22. Intersect(m, a) → C_1, D_1
  23. Intersect(f, a) → E_1, F_1
  24. Intersect(b, a) → G_1, H_1
  25. Intersect(l, a) → I_1, J_1
  26. Polygon(T, V, A_1) → poly1, a_1, t, v
  27. Polygon(B_1, E_1, G_1) → poly2, g_1, b_1, e_1
  28. Polygon(O, H_1, C) → poly3, c_1, o, h_1
  29. Polygon(M, L, S) → poly4, s, m_1, l_1
  30. Polygon(Z, Q, N) → poly5, n, z_1, q
  31. Polygon(D_1, U, W) → poly6, w, d_1, u
  32. Polygon(C_1, J_1, F_1) → poly7, f_1, c_2, j_1
  33. Polygon(I_1, R, P) → poly8, p, i_1, r
  34. Polygon(J_1, I_1, P, O, H_1, G_1, E_1, F_1) → poly9, j_2, i_2, p_1, o_1, h_2, g_2, e_2, f_2
  35. Polygon(C, L, M, N, Q, R, P, O) → poly10, c_3, l_2, m_2, n_1, q_1, r_1, p_2, o_2
  36. Polygon(Z, N, M, S, T, V, U, W) → poly11, z_2, n_2, m_3, s_1, t_1, v_1, u_1, w_1
  37. Polygon(D_1, U, V, A_1, B_1, E_1, F_1, C_1) → poly12, d_2, u_2, v_2, a_2, b_2, e_3, f_3, c_4
  38. Polygon(B_1, A_1, T, S, L, C, H_1, G_1) → poly13, b_3, a_3, t_2, s_2, l_3, c_5, h_3, g_3
  39. Polygon(Q, Z, W, D_1, C_1, J_1, I_1, R) → poly14, q_2, z_3, w_2, d_3, c_6, j_3, i_3, r_2
  40. Midpoint(F, G) → K_1
  41. Midpoint(G, E) → L_1
  42. Midpoint(E, D) → M_1
  43. Midpoint(D, F) → N_1
  44. Midpoint(F, J) → O_1
  45. Midpoint(G, K) → P_1
  46. Midpoint(I, E) → Q_1
  47. Midpoint(D, H) → R_1
  48. Midpoint(H, J) → S_1
  49. Midpoint(J, K) → T_1
  50. Midpoint(K, I) → U_1
  51. Midpoint(I, H) → V_1
  52. Segment(Q_1, M_1) → k_2
  53. Segment(L_1, Q_1) → q_3
  54. Segment(L_1, M_1) → a_4
  55. Line(L_1, k_2) → k_1
  56. Segment(K_1, O_1) → k_3
  57. Line(N_1, k_3) → n_3
  58. Intersect(n_3, k_1) → W_1
  59. Line(M_1, W_1) → p_3
  60. Line(W_1, K_1) → r_3
  61. Segment(M_1, N_1) → s_3
  62. Line(R_1, s_3) → t_3
  63. Intersect(t_3, n_3) → Z_1
  64. Line(Z_1, O_1) → b_4
  65. Line(S_1, Z_1) → d_4
  66. Intersect(t_3, p_3) → A_2
  67. Line(Q_1, A_2) → e_4
  68. Line(A_2, V_1) → f_4
  69. Intersect(b_4, r_3) → B_2
  70. Intersect(e_4, k_1) → C_2
  71. Intersect(d_4, f_4) → D_2
  72. Segment(Z_1, B_2) → g_4
  73. Segment(B_2, C_2) → h_4
  74. Segment(C_2, A_2) → i_4
  75. Segment(A_2, Z_1) → j_4
  76. Segment(A_2, W_1) → k_4
  77. Segment(A_2, D_2) → l_4
  78. Segment(Z_1, W_1) → m_4
  79. Segment(Z_1, D_2) → n_4
  80. Segment(D_2, B_2) → p_4
  81. Segment(B_2, W_1) → q_4
  82. Segment(D_2, C_2) → r_4
  83. Segment(C_2, W_1) → s_4
  84. Sphere(A, B1) → o_3
  85. Intersect(m_4, o_3) → E_2, G_2
  86. Intersect(q_4, o_3) → H_2, I_2
  87. Intersect(s_4, o_3) → J_2, K_2
  88. Intersect(k_4, o_3) → L_2, M_2
  89. Intersect(n_4, o_3) → N_2, O_2
  90. Intersect(i_4, o_3) → P_2, Q_2
  91. Intersect(j_4, o_3) → R_2, S_2
  92. Intersect(p_4, g_4) → T_2
  93. Intersect(g_4, o_3) → U_2, V_2
  94. Intersect(h_4, o_3) → W_2, Z_2
  95. Intersect(p_4, o_3) → A_3, B_3
  96. Intersect(p_4, r_4) → C_3
  97. Intersect(r_4, o_3) → D_3, E_3
  98. Intersect(r_4, l_4) → F_3
  99. Intersect(l_4, o_3) → G_3, H_3
  100. Polygon(M_2, G_2, I_2, K_2) → poly15, m_5, g_5, i_5, k_5
  101. Polygon(S_2, N_2, U_2, E_2) → poly16, s_5, n_5, u_3, e_5
  102. Polygon(V_2, H_2, W_2, B_3) → poly17, v_3, h_5, w_3, b_5
  103. Polygon(E_3, Z_2, J_2, P_2) → poly18, e_6, z_4, j_5, p_5
  104. Polygon(G_3, Q_2, L_2, R_2) → poly19, g_6, q_5, l_5, r_5
  105. Polygon(H_3, D_3, A_3, O_2) → poly20, h_6, d_5, a_5, o_4
  106. Polygon(W_2, Z_2, J_2, K_2, I_2, H_2) → poly21, w_4, z_5, j_6, k_6, i_6, h_7
  107. Polygon(P_2, J_2, K_2, M_2, L_2, Q_2) → poly22, p_6, j_7, k_7, m_6, l_6, q_6
  108. Polygon(R_2, L_2, M_2, G_2, E_2, S_2) → poly23, r_6, l_7, m_7, g_7, e_7, s_6
  109. Polygon(U_2, E_2, G_2, I_2, H_2, V_2) → poly24, u_4, e_8, g_8, i_7, h_8, v_4
  110. Polygon(O_2, N_2, U_2, V_2, B_3, A_3) → poly25, o_5, n_6, u_5, v_5, b_6, a_6
  111. Polygon(D_3, A_3, B_3, W_2, Z_2, E_3) → poly26, d_6, a_7, b_7, w_5, z_6, e_9
  112. Polygon(H_3, D_3, E_3, P_2, Q_2, G_3) → poly27, h_9, d_7, e_{10}, p_7, q_7, g_9
  113. Polygon(O_2, H_3, G_3, R_2, S_2, N_2) → poly28, o_6, h_{10}, g_{10}, r_7, s_7, n_7
  114. Intersect(m_5, k_5) → F_2
  115. Intersect(m_7, g_8) → I_3
  116. Intersect(e_5, u_3) → J_3
  117. Distance(F_2, I_3) → distanceF2I3
  118. Distance(I_3, J_3) → distanceI3J3
  119. Intersect(v, s_1) → K_3
  120. Intersect(v, e) → L_3
  121. Intersect(l_1, d) → M_3
  122. Distance(M_3, K_3) → distanceM3K3
  123. Distance(K_3, L_3) → distanceK3L3