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Compound of Five Cubes

Compound of Five Cubes
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2019-03-30 18:21
Solid GeometryTransformationGeometric Construction
This example demonstrates the geometric construction of a compound of five cubes. It involves core concepts of cubes and solid geometry. Using GeoGebra commands such as Intersect, Point, Circle, Rotate, etc., it dynamically shows the rotation and combination of cubes. Suitable for high school and above students or teachers for teaching and research in solid geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Circle(A, B) → c
  4. Point(c, 1 - v) → C
  5. Rotate(C, 72°, A) → C'
  6. Angle(C, A, C') → α
  7. Rotate(C, 144°, A) → D
  8. Dodecahedron(C, C', D) → a, E, N, O, P, Q, R, S, T, U, faceCC'DEF, faceCFJPK, F, faceCC'GLK, faceC'DHMG, faceDEINH, faceEFJOI, faceJOTUP, faceKLQUP, faceGLQRM, faceHMRSN, faceINSTO, faceQRSTU, G, edgeCF, edgeCC', edgeC'D, edgeDE, edgeEF, edgeCK, edgeFJ, edgeJP, edgeKP, edgeKL, H, edgeGL, edgeC'G, edgeGM, edgeHM, edgeDH, edgeHN, edgeIN, edgeEI, edgeIO, edgeJO, I, edgeOT, edgeTU, edgePU, edgeQU, edgeLQ, edgeQR, edgeMR, edgeRS, edgeNS, edgeST, J, K, L, M
  9. Polygon(L, U, S, M) → q1, l, u, s, m
  10. Polygon(S, U, J, I) → q2, s_1, u_1, j, i
  11. Polygon(M, S, I, D) → q3, m_1, s_2, i_1, d
  12. Polygon(L, M, D, C) → q4, l_1, m_2, d_1, c_1
  13. Polygon(J, U, L, C) → q5, j_1, u_2, l_2, c_2
  14. Polygon(I, J, C, D) → q6, i_2, j_2, c_3, d_2
  15. Polygon(Q, M, N, T) → q7, q, m_3, n, t
  16. Polygon(T, J, E, N) → q8, t_1, j_3, e, n_1
  17. Polygon(J, T, Q, K) → q9, j_4, t_2, q_1, k
  18. Polygon(K, Q, M, C') → q10, k_1, q_2, m_4, c'
  19. Polygon(C', M, N, E) → q11, f, m_5, n_2, e_1
  20. Polygon(J, K, C', E) → q12, j_5, k_2, g, e_2
  21. Polygon(R, T, I, H) → q13, r, t_3, i_3, h
  22. Polygon(R, L, P, T) → q14, r_1, l_3, p, t_4
  23. Polygon(T, P, F, I) → q15, t_5, p_1, f_1, i_4
  24. Polygon(P, L, C', F) → q16, p_2, l_4, b, f_2
  25. Polygon(L, R, H, C') → q17, l_5, r_2, h_1, g_1
  26. Polygon(H, I, F, C') → q18, h_2, i_5, f_3, a_1
  27. Polygon(U, R, N, O) → q19, u_3, r_3, n_3, o
  28. Polygon(R, N, D, G) → q20, r_4, n_4, d_3, g_2
  29. Polygon(O, U, K, F) → q22, o_1, u_5, k_4, f_4
  30. Polygon(D, N, O, F) → q23, d_4, n_5, o_2, f_5
  31. Polygon(D, F, K, G) → q24, d_5, f_6, k_5, g_4
  32. Polygon(Q, S, H, G) → q25, q_3, s_3, h_3, g_5
  33. Polygon(S, O, E, H) → q26, s_4, o_3, e_3, h_4
  34. Polygon(O, S, Q, P) → q27, o_4, s_5, q_4, p_3
  35. Polygon(P, Q, G, C) → q28, p_4, q_5, g_6, c_4
  36. Polygon(E, O, P, C) → q29, e_4, o_5, p_5, c_5
  37. Polygon(C, G, H, E) → q30, c_6, g_7, h_5, e_5
  38. Intersect(q1, q10) → V, W, Z, A_1, B_1
  39. Intersect(q_2, l_5) → C_1
  40. Intersect(l_5, q_5) → D_1
  41. Intersect(l_1, q_5) → E_1
  42. Intersect(k_5, g_1) → I_1
  43. Intersect(k_5, l_2) → J_1
  44. Intersect(l_2, k_2) → K_1
  45. Intersect(c_6, k_2) → L_1
  46. Intersect(c_6, g_1) → M_1
  47. Intersect(j_5, f_2) → H_1
  48. Intersect(j_5, p_5) → N_1
  49. Intersect(f_6, p_5) → O_1
  50. Intersect(j_2, f_6) → P_1
  51. Intersect(f_2, j_2) → Q_1
  52. Intersect(o_1, j_4) → R_1
  53. Intersect(t_5, o_1) → S_1
  54. Intersect(j_1, t_5) → T_1
  55. Intersect(o_5, j_4) → U_1
  56. Intersect(j_1, o_5) → V_1
  57. Intersect(s_5, t_2) → W_1
  58. Intersect(s_1, t_2) → Z_1
  59. Intersect(s_1, t_4) → A_2
  60. Intersect(t_4, s_5) → B_2
  61. Intersect(n_5, i_4) → E_2
  62. Intersect(o_4, i_4) → F_2
  63. Intersect(o_4, n_1) → G_2
  64. Intersect(s_2, n_1) → H_2
  65. Intersect(s_2, n_5) → I_2
  66. Intersect(r_2, m_1) → J_2
  67. Intersect(r_4, m_1) → K_2
  68. Intersect(h_4, r_4) → L_2
  69. Intersect(h_4, m_5) → M_2
  70. Intersect(m_5, r_2) → N_2
  71. Intersect(u_2, p_4) → O_2
  72. Intersect(p_4, u_5) → P_2
  73. Intersect(u_5, p_2) → Q_2
  74. Intersect(p_2, k_1) → R_2
  75. Intersect(g_7, m_2) → S_2
  76. Intersect(a_1, g_4) → T_2
  77. Intersect(n_2, h_2) → U_2
  78. Intersect(h_2, d_4) → V_2
  79. Intersect(h_5, d_4) → W_2
  80. Intersect(d_2, h_5) → Z_2
  81. Intersect(d_2, n_2) → A_3
  82. Intersect(f_3, e_5) → B_3
  83. Intersect(d_5, e_5) → C_3
  84. Intersect(d_5, c_3) → D_3
  85. Intersect(g, c_3) → E_3
  86. Intersect(f_3, c_3) → F_3
  87. Intersect(d_5, g) → G_3
  88. Intersect(f, g_7) → H_3
  89. Intersect(g_4, f) → I_3
  90. Intersect(a_1, m_2) → J_3
  91. Intersect(i_2, e_4) → K_3
  92. Intersect(o_2, i_2) → L_3
  93. Intersect(o_2, e_2) → M_3
  94. Intersect(e_2, i_5) → N_3
  95. Intersect(e_4, i_5) → O_3
  96. PointIn(q6) → Q_3
  97. Polygon(U, R, G, K) → q21, u_4, r_5, g_3, k_3
  98. Rotate(C, 144°, A) → C'_1