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Cube colored with Varignon motifs

Cube colored with Varignon motifs
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2020-01-09 00:08
PolygonSolid Geometry
In collections Color 3D surfaces
This example demonstrates a cube colored with Varignon motifs, involving core mathematical concepts like solid geometry, polygons, integral calculus, and geometric construction. It utilizes GeoGebra commands such as Point, Cube, Line, Intersect, Polygon, Midpoint, and Centroid. Suitable for high school and above students to explore complex geometric constructions.

GeoGebra Commands & Parameters

  1. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  2. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, arêteAD, arêteAB, arêteBC, arêteCD, arêteAE, arêteDH, arêteEH, arêteEF, E, arêteBF, arêteFG, arêteCG, arêteGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  3. PointIn(faceABFE) → I
  4. Line(I, arêteEF) → f
  5. Line(I, arêteAE) → g
  6. Intersect(g, arêteEF) → J
  7. Intersect(arêteAB, g) → K
  8. Intersect(f, arêteAE) → L
  9. Intersect(arêteBF, f) → M
  10. Polygon(E, J, I, L) → q1, e, j, i, l
  11. Midpoint(E, J) → N
  12. Midpoint(I, L) → O
  13. Midpoint(J, I) → P
  14. Midpoint(L, E) → Q
  15. Polygon(N, Q, O, P) → q2, n, q, o, p
  16. Midpoint(n) → R
  17. Midpoint(p) → S
  18. Midpoint(o) → T
  19. Midpoint(q) → U
  20. Polygon(R, S, T, U) → q3, r, s, t, u
  21. Midpoint(r) → V
  22. Midpoint(u) → W
  23. Midpoint(s) → Z
  24. Midpoint(t) → A_1
  25. Polygon(V, W, A_1, Z) → q4, v, w, a_1, z_1
  26. Midpoint(N, E) → B_1
  27. Midpoint(N, J) → C_1
  28. Midpoint(J, P) → D_1
  29. Midpoint(P, I) → E_1
  30. Midpoint(I, O) → F_1
  31. Midpoint(O, L) → G_1
  32. Midpoint(L, Q) → H_1
  33. Midpoint(Q, E) → I_1
  34. Polygon(B_1, I_1, H_1, G_1, F_1, E_1, D_1, C_1) → poly1, b_1, i_1, h_1, g_1, f_1, e_1, d_1, c_1
  35. Polygon(J, F, M, I) → q5, j_1, f_2, m, i_2
  36. Midpoint(J, F) → J_1
  37. Midpoint(F, M) → K_1
  38. Midpoint(M, I) → L_1
  39. Midpoint(J_1, J) → M_1
  40. Midpoint(J_1, F) → N_1
  41. Midpoint(F, K_1) → O_1
  42. Midpoint(K_1, M) → P_1
  43. Midpoint(L_1, M) → Q_1
  44. Midpoint(L_1, I) → R_1
  45. Polygon(N_1, O_1, P_1, Q_1, R_1, E_1, D_1, M_1) → poly2, n_1, o_1, p_1, q_1, r_1, h, k, m_1
  46. Polygon(J_1, P, L_1, K_1) → q6, b, p_2, l_1, k_1
  47. Centroid(q6) → S_1
  48. Midpoint(b) → T_1
  49. Midpoint(k_1) → U_1
  50. Midpoint(l_1) → V_1
  51. Midpoint(p_2) → W_1
  52. Polygon(T_1, U_1, V_1, W_1) → q7, t_1, u_1, v_1, w_1
  53. Midpoint(t_1) → Z_1
  54. Midpoint(u_1) → A_2
  55. Midpoint(v_1) → B_2
  56. Midpoint(w_1) → C_2
  57. Polygon(Z_1, C_2, B_2, A_2) → q8, c, c_2, b_2, a_2
  58. Polygon(L, I, K, A) → q9, l_2, i_3, k_2, a_3
  59. Midpoint(L, A) → D_2
  60. Midpoint(I, K) → E_2
  61. Midpoint(A, K) → F_2
  62. Midpoint(L, D_2) → G_2
  63. Midpoint(D_2, A) → H_2
  64. Midpoint(A, F_2) → I_2
  65. Midpoint(F_2, K) → J_2
  66. Midpoint(E_2, I) → K_2
  67. Midpoint(E_2, K) → L_2
  68. Polygon(G_2, H_2, I_2, J_2, L_2, K_2, F_1, G_1) → poly3, g_2, h_2, d, j_2, s_1, m_2, n_2, q_2
  69. Polygon(O, D_2, F_2, E_2) → q10, o_2, d_2, r_2, e_2
  70. Midpoint(e_2) → M_2
  71. Midpoint(o_2) → N_2
  72. Midpoint(d_2) → O_2
  73. Midpoint(r_2) → P_2
  74. Polygon(N_2, M_2, P_2, O_2) → q11, s_2, t_2, f_3, g_3
  75. Midpoint(s_2) → Q_2
  76. Midpoint(g_3) → R_2
  77. Midpoint(f_3) → S_2
  78. Midpoint(t_2) → T_2
  79. Polygon(Q_2, R_2, S_2, T_2) → q12, h_3, j_3, k_3, l_3
  80. Polygon(I, M, B, K) → q13, i_4, m_3, b_3, k_4
  81. Midpoint(M, B) → U_2
  82. Midpoint(K, B) → V_2
  83. Midpoint(M, U_2) → W_2
  84. Midpoint(B, U_2) → Z_2
  85. Midpoint(V_2, B) → A_3
  86. Midpoint(V_2, K) → B_3
  87. Polygon(R_1, K_2, L_2, B_3, A_3, Z_2, W_2, Q_1) → poly4, n_3, p_3, q_3, r_3, s_3, z_2, w_2, t_3
  88. Polygon(L_1, E_2, V_2, U_2) → q14, c_3, d_3, v_2, u_2
  89. Midpoint(u_2) → C_3
  90. Midpoint(c_3) → D_3
  91. Midpoint(d_3) → E_3
  92. Midpoint(v_2) → F_3
  93. Polygon(C_3, F_3, E_3, D_3) → q15, e_3, f_4, g_4, h_4
  94. Midpoint(h_4) → G_3
  95. Midpoint(e_3) → H_3
  96. Midpoint(f_4) → I_3
  97. Midpoint(g_4) → J_3
  98. Polygon(G_3, J_3, I_3, H_3) → q16, j_4, l_4, m_4, n_4
  99. Midpoint(C, A) → K_3
  100. Line(K_3, zAxis) → p_4
  101. Sequence(Rotate[q1, i, p_4], i, 0, (2 * π), (2 * π / 4)) → l1
  102. Sequence(Rotate[q5, i, p_4], i, 0, (2 * π), (2 * π / 4)) → l2
  103. Sequence(Rotate[q9, i, p_4], i, 0, (2 * π), (2 * π / 4)) → l3
  104. Midpoint(E, C) → L_3
  105. Midpoint(E, D) → M_3
  106. Line(M_3, L_3) → q_4
  107. Sequence(Rotate[q13, i, p_4], i, 0, (2 * π), (2 * π / 4)) → l4
  108. Sequence(Rotate[poly1, i, p_4], i, 0, (2 * π), (2 * π / 4)) → l5
  109. Sequence(Rotate[poly2, i, p_4], i, 0, (2 * π), (2 * π / 4)) → l6
  110. Sequence(Rotate[poly3, i, p_4], i, 0, (2 * π), (2 * π / 4)) → l7
  111. Sequence(Rotate[poly4, i, p_4], i, 0, (2 * π), (2 * π / 4)) → l8
  112. Sequence(Rotate[q2, i, p_4], i, 0, (2 * π), (2 * π / 4)) → l9
  113. Sequence(Rotate[q3, i, p_4], i, 0, (2 * π), (2 * π / 4)) → l10
  114. Sequence(Rotate[q4, i, p_4], i, 0, (2 * π), (2 * π / 4)) → l11
  115. Sequence(Rotate[q6, i, p_4], i, 0, (2 * π), (2 * π / 4)) → l12
  116. Sequence(Rotate[q7, i, p_4], i, 0, (2 * π), (2 * π / 4)) → l13
  117. Sequence(Rotate[q8, i, p_4], i, 0, (2 * π), (2 * π / 4)) → l14
  118. Sequence(Rotate[q10, i, p_4], i, 0, (2 * π), (2 * π / 4)) → l15
  119. Sequence(Rotate[q11, i, p_4], i, 0, (2 * π), (2 * π / 4)) → l16
  120. Sequence(Rotate[q12, i, p_4], i, 0, (2 * π), (2 * π / 4)) → l17
  121. Sequence(Rotate[q14, i, p_4], i, 0, (2 * π), (2 * π / 4)) → l18
  122. Sequence(Rotate[q15, i, p_4], i, 0, (2 * π), (2 * π / 4)) → l19
  123. Sequence(Rotate[q16, i, p_4], i, 0, (2 * π), (2 * π / 4)) → l20
  124. Midpoint(H, C) → N_3
  125. Sequence(Rotate[q1, i, q_4], i, π / 2, (3 * π / 2), (4 * π / 4)) → l21
  126. Sequence(Rotate[q5, i, q_4], i, π / 2, (3 * π / 2), (4 * π / 4)) → l22
  127. Sequence(Rotate[q9, i, q_4], i, π / 2, (3 * π / 2), (4 * π / 4)) → l23
  128. Sequence(Rotate[q13, i, q_4], i, π / 2, (3 * π / 2), (4 * π / 4)) → l24
  129. Sequence(Rotate[poly1, i, q_4], i, π / 2, (3 * π / 2), (4 * π / 4)) → l25
  130. Sequence(Rotate[poly2, i, q_4], i, π / 2, (3 * π / 2), (4 * π / 4)) → l26
  131. Sequence(Rotate[poly3, i, q_4], i, π / 2, (3 * π / 2), (4 * π / 4)) → l27
  132. Sequence(Rotate[poly4, i, q_4], i, π / 2, (3 * π / 2), (4 * π / 4)) → l28
  133. Sequence(Rotate[q2, i, q_4], i, π / 2, (3 * π / 2), π) → l29
  134. Sequence(Rotate[q3, i, q_4], i, π / 2, (3 * π / 2), π) → l30
  135. Sequence(Rotate[q4, i, q_4], i, π / 2, (3 * π / 2), π) → l31
  136. Sequence(Rotate[q6, i, q_4], i, π / 2, (3 * π / 2), π) → l32
  137. Sequence(Rotate[q7, i, q_4], i, π / 2, (3 * π / 2), π) → l33
  138. Sequence(Rotate[q8, i, q_4], i, π / 2, (3 * π / 2), π) → l34
  139. Sequence(Rotate[q10, i, q_4], i, π / 2, (3 * π / 2), π) → l35
  140. Sequence(Rotate[q11, i, q_4], i, π / 2, (3 * π / 2), π) → l36
  141. Sequence(Rotate[q12, i, q_4], i, π / 2, (3 * π / 2), π) → l37
  142. Sequence(Rotate[q14, i, q_4], i, π / 2, (3 * π / 2), π) → l38
  143. Sequence(Rotate[q15, i, q_4], i, π / 2, (3 * π / 2), π) → l39
  144. Sequence(Rotate[q16, i, q_4], i, π / 2, (3 * π / 2), π) → l40
  145. Polygon(D, C, B, A) → q17, d_4, c_4, b_4, a_4