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LMOrigami22 Belt Cube

LMOrigami22 Belt Cube
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2017-05-03 02:25
TrigonometrySolid GeometryGeometric Construction
This example demonstrates a belt cube constructed from points, polygons, and cubes. The core mathematical concepts involved include solid geometry, symmetry, and geometric construction. Key construction steps use GeoGebra commands such as Point, Intersect, Polygon, OrthogonalLine, Mirror, Cube, Line, and Dilate; objects include beltwidth, C, D, A, B, poly1, a, b, c, d, E, e, F, f, G, H, F', H', poly2, f', f_1, h, h', I, J, g, i, K, K', J', poly3, k, j, j', k', L, l, O, P, Q. Suitable for high school and above learning solid geometry and geometric construction.

GeoGebra Commands & Parameters

  1. Point(yAxis) → D
  2. Intersect(xAxis, yAxis) → A
  3. Point(xAxis) → B
  4. Polygon(A, B, C, D) → poly1, a, b, c, d
  5. Point(a) → E
  6. OrthogonalLine(E, a) → e
  7. OrthogonalLine(F, a) → f
  8. Intersect(e, c) → G
  9. Intersect(f, c) → H
  10. Mirror(F, e) → F'
  11. Mirror(H, e) → H'
  12. Polygon(F', F, H, H') → poly2, f', f_1, h, h'
  13. Point(b) → I
  14. OrthogonalLine(I, b) → g
  15. OrthogonalLine(J, b) → i
  16. Intersect(i, f_1) → K
  17. Mirror(K, g) → K'
  18. Mirror(J, g) → J'
  19. Polygon(K, J, J', K') → poly3, k, j, j', k'
  20. Intersect(d, yAxis) → L
  21. Cube(B, C, poly1) → l, O, faceCOSR, faceOPTS, faceQRST, edgeBP, edgeBC, edgeCO, edgeOP, edgeBQ, edgePT, edgeQT, P, edgeQR, edgeCR, edgeRS, edgeOS, edgeST, Q, R, S, T, faceBCOP, faceBPTQ, faceBCRQ
  22. Point(edgeBQ) → U
  23. Point(edgeQT) → W
  24. Point(edgeCR) → Z
  25. Point(edgeST) → B_1
  26. Point(edgePT) → C_1
  27. OrthogonalLine(U, edgeBQ, faceBPTQ) → p
  28. Mirror(U', p) → U''
  29. OrthogonalLine(U', edgeBQ, faceBPTQ) → q
  30. OrthogonalLine(U'', edgeBQ, faceBPTQ) → r
  31. Intersect(q, edgePT) → D_1
  32. Intersect(edgePT, r) → E_1
  33. Polygon(E_1, U'', U', D_1) → poly5, e_1, u'', u', d_1
  34. OrthogonalLine(J', b, faceBCRQ) → s
  35. OrthogonalLine(J, b, faceBCRQ) → t
  36. Intersect(t, edgeQR) → F_1
  37. Intersect(s, edgeQR) → G_1
  38. Polygon(G_1, F_1, J, J') → poly6, g_1, f_2, j_1, j'_1
  39. OrthogonalLine(U', edgeBQ, faceBCRQ) → m
  40. OrthogonalLine(U'', edgeBQ, faceBCRQ) → n
  41. Intersect(m, j'_1) → M
  42. Intersect(n, j'_1) → N
  43. Polygon(U'', N, M, U') → poly4, u''_1, n_1, m_1, u'_1
  44. OrthogonalLine(W, edgeQT, faceQRST) → a_1
  45. Mirror(W', a_1) → W''
  46. OrthogonalLine(W'', edgeQT, faceQRST) → b_1
  47. OrthogonalLine(W', edgeQT, faceQRST) → c_1
  48. Intersect(b_1, edgeRS) → V
  49. Intersect(c_1, edgeRS) → A_1
  50. Polygon(V, A_1, W', W'') → poly7, v, a_2, w', w''
  51. OrthogonalLine(W'', edgeQT, faceBPTQ) → h_1
  52. OrthogonalLine(W', edgeQT, faceBPTQ) → i_1
  53. OrthogonalLine(F, a, faceBPTQ) → k_1
  54. OrthogonalLine(F', a, faceBPTQ) → l_1
  55. Intersect(e_1, l_1) → H_1
  56. Intersect(k_1, e_1) → I_1
  57. Intersect(i_1, u') → J_1
  58. Intersect(h_1, u') → K_1
  59. Polygon(W'', K_1, J_1, W') → poly8, w''_1, k_2, j_2, w'_1
  60. Polygon(F', F, I_1, H_1) → poly9, f'_1, f_3, i_2, h_2
  61. OrthogonalLine(F_1, edgeQR, faceQRST) → p_1
  62. OrthogonalLine(G_1, edgeQR, faceQRST) → q_1
  63. Intersect(p_1, a_2) → L_1
  64. Intersect(q_1, a_2) → M_1
  65. Polygon(M_1, G_1, F_1, L_1) → poly10, m_2, g_2, f_4, l_2
  66. OrthogonalLine(Z, edgeCR, faceCOSR) → r_1
  67. Mirror(Z', r_1) → Z''
  68. OrthogonalLine(Z', edgeCR, faceCOSR) → s_1
  69. OrthogonalLine(Z'', edgeCR, faceCOSR) → t_1
  70. Intersect(s_1, edgeOS) → N_1
  71. Intersect(t_1, edgeOS) → O_1
  72. Polygon(Z'', O_1, N_1, Z') → poly11, z'', o_1, n_2, z'
  73. OrthogonalLine(A_1, edgeRS, faceCOSR) → b_2
  74. OrthogonalLine(V, edgeRS, faceCOSR) → c_2
  75. OrthogonalLine(H, c, faceCOSR) → d_2
  76. OrthogonalLine(H', c, faceCOSR) → e_2
  77. Intersect(t_1, d_2) → P_1
  78. Intersect(t_1, e_2) → Q_1
  79. Intersect(c_2, s_1) → R_1
  80. Intersect(s_1, b_2) → S_1
  81. Polygon(S_1, R_1, V, A_1) → poly12, s_2, r_2, v_1, a_3
  82. Polygon(H, H', Q_1, P_1) → poly13, h_3, h'_1, q_2, p_2
  83. OrthogonalLine(Z', edgeCR, faceBCRQ) → t_2
  84. OrthogonalLine(Z'', edgeCR, faceBCRQ) → b_3
  85. Intersect(t_2, f_2) → T_1
  86. Intersect(b_3, f_2) → U_1
  87. Polygon(U_1, Z'', Z', T_1) → poly14, u_1, z''_1, z'_1, t_3
  88. OrthogonalLine(B_1, edgeST, faceOPTS) → c_3
  89. OrthogonalLine(B_1', edgeST, faceOPTS) → d_3
  90. Mirror(B_1', c_3) → V_1
  91. OrthogonalLine(V_1, edgeST, faceOPTS) → e_3
  92. Intersect(d_3, d) → W_1
  93. Intersect(d, edgeOP) → Z_1
  94. Intersect(e_3, d) → A_2
  95. Polygon(W_1, A_2, V_1, B_1') → poly15, w_1, a_4, v_2, b_1'
  96. OrthogonalLine(O_1, edgeOS, faceOPTS) → g_3
  97. OrthogonalLine(N_1, edgeOS, faceOPTS) → i_3
  98. OrthogonalLine(E_1, edgePT, faceOPTS) → j_3
  99. OrthogonalLine(D_1, edgePT, faceOPTS) → k_3
  100. Intersect(d_3, g_3) → B_2
  101. Intersect(i_3, d_3) → C_2
  102. Intersect(e_3, k_3) → D_2
  103. Intersect(e_3, j_3) → E_2
  104. Polygon(O_1, B_2, C_2, N_1) → poly16, o_2, b_4, c_4, n_3
  105. Polygon(E_1, E_2, D_2, D_1) → poly17, e_4, e_5, d_4, d_5
  106. OrthogonalLine(B_1', edgeST, faceQRST) → l_3
  107. OrthogonalLine(V_1, edgeST, faceQRST) → m_3
  108. Intersect(l_3, w'') → F_2
  109. Intersect(m_3, w'') → G_2
  110. Polygon(B_1', V_1, G_2, F_2) → poly18, b_5, v_3, g_4, f_5
  111. OrthogonalLine(W_1, d, xOyPlane) → p_3
  112. OrthogonalLine(A_2, d, xOyPlane) → q_3
  113. Intersect(p_3, h') → H_2
  114. Intersect(q_3, h') → I_2
  115. Polygon(W_1, H_2, I_2, A_2) → poly19, w_2, h_4, i_4, a_5
  116. Line(A, R) → r_3
  117. Line(T, C) → s_3
  118. Intersect(s_3, r_3) → J_2
  119. Dilate(faceBCOP, cubescale, J_2) → faceBCOP'
  120. Dilate(faceBCRQ, cubescale, J_2) → faceBCRQ'
  121. Dilate(faceBPTQ, cubescale, J_2) → faceBPTQ'
  122. Dilate(faceCOSR, cubescale, J_2) → faceCOSR'
  123. Dilate(faceOPTS, cubescale, J_2) → faceOPTS'
  124. Dilate(faceQRST, cubescale, J_2) → faceQRST'

AI Drawing Prompt Reference

Draw a belt cube constructed from points and polygons, demonstrating solid geometry and symmetry. Start by creating a quadrilateral, then use orthogonal lines and mirror operations from its vertices to form multiple geometric shapes, including cubes and polygons. Combine these shapes to form a complex 3D structure, highlighting the process of geometric construction and symmetry.
The prompt above was compiled from the original drawing commands and is for reference only.