3D Shape Rotation and Construction

3D Shape Rotation and Construction
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2014-04-06 11:05
This example demonstrates the rotation construction and dynamic changes of 3D shapes like polygons; involves core math concepts including solid geometry, rotation transformation, polygon construction, and optimization problems; constructed using GeoGebra commands/objects such as Polygon, Segment, Rotate; suitable for high school and above learning solid geometry, geometric construction, and transformation applications.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3) → poly1, a, b, c, C
  2. Segment(B, D) → d
  3. Segment(D, E) → e
  4. Segment(E, F) → f
  5. Segment(F, G) → g
  6. Segment(G, H) → h
  7. Segment(H, I) → i
  8. Segment(I, J) → j
  9. Segment(J, K) → k
  10. Segment(K, L) → l
  11. Segment(L, M) → m
  12. Segment(M, N) → n
  13. Segment(N, O) → p
  14. Segment(O, P) → q
  15. Segment(P, Q) → r
  16. Segment(Q, R) → s
  17. Segment(R, S) → t
  18. Segment(S, T) → a_1
  19. Segment(T, U) → b_1
  20. Segment(U, V) → c_1
  21. Segment(V, W) → d_1
  22. Segment(W, Z) → e_1
  23. Segment(Z, A_1) → f_1
  24. Segment(A_1, B_1) → g_1
  25. Segment(B_1, C) → h_1
  26. Rotate(B, 60*°, B) → B'
  27. Rotate(D, 60*°, B) → D'
  28. Segment(B', D') → d'
  29. Rotate(D, 60*°, B) → D'_1
  30. Rotate(E, 60*°, B) → E'
  31. Segment(D'_1, E') → e'
  32. Rotate(E, 60*°, B) → E'_1
  33. Rotate(F, 60*°, B) → F'
  34. Segment(E'_1, F') → f'
  35. Rotate(F, 60*°, B) → F'_1
  36. Rotate(G, 60*°, B) → G'
  37. Segment(F'_1, G') → g'
  38. Rotate(G, 60*°, B) → G'_1
  39. Rotate(H, 60*°, B) → H'
  40. Segment(G'_1, H') → h'
  41. Rotate(H, 60*°, B) → H'_1
  42. Rotate(I, 60*°, B) → I'
  43. Segment(H'_1, I') → i'
  44. Rotate(I, 60*°, B) → I'_1
  45. Rotate(J, 60*°, B) → J'
  46. Segment(I'_1, J') → j'
  47. Rotate(J, 60*°, B) → J'_1
  48. Rotate(K, 60*°, B) → K'
  49. Segment(J'_1, K') → k'
  50. Rotate(K, 60*°, B) → K'_1
  51. Rotate(L, 60*°, B) → L'
  52. Segment(K'_1, L') → l'
  53. Rotate(L, 60*°, B) → L'_1
  54. Rotate(M, 60*°, B) → M'
  55. Segment(L'_1, M') → m'
  56. Rotate(M, 60*°, B) → M'_1
  57. Rotate(N, 60*°, B) → N'
  58. Segment(M'_1, N') → n'
  59. Rotate(N, 60*°, B) → N'_1
  60. Rotate(O, 60*°, B) → O'
  61. Segment(N'_1, O') → p'
  62. Rotate(O, 60*°, B) → O'_1
  63. Rotate(P, 60*°, B) → P'
  64. Segment(O'_1, P') → q'
  65. Rotate(P, 60*°, B) → P'_1
  66. Rotate(Q, 60*°, B) → Q'
  67. Segment(P'_1, Q') → r'
  68. Rotate(Q, 60*°, B) → Q'_1
  69. Rotate(R, 60*°, B) → R'
  70. Segment(Q'_1, R') → s'
  71. Rotate(R, 60*°, B) → R'_1
  72. Rotate(S, 60*°, B) → S'
  73. Segment(R'_1, S') → t'
  74. Rotate(S, 60*°, B) → S'_1
  75. Rotate(T, 60*°, B) → T'
  76. Segment(S'_1, T') → i_1
  77. Rotate(T, 60*°, B) → T'_1
  78. Rotate(U, 60*°, B) → U'
  79. Segment(T'_1, U') → j_1
  80. Rotate(U, 60*°, B) → U'_1
  81. Rotate(V, 60*°, B) → V'
  82. Segment(U'_1, V') → k_1
  83. Rotate(V, 60*°, B) → V'_1
  84. Rotate(W, 60*°, B) → W'
  85. Segment(V'_1, W') → l_1
  86. Rotate(W, 60*°, B) → W'_1
  87. Rotate(Z, 60*°, B) → Z'
  88. Segment(W'_1, Z') → m_1
  89. Rotate(Z, 60*°, B) → Z'_1
  90. Rotate(A_1, 60*°, B) → C_1
  91. Segment(Z'_1, C_1) → n_1
  92. Rotate(A_1, 60*°, B) → D_1
  93. Rotate(B_1, 60*°, B) → E_1
  94. Segment(D_1, E_1) → p_1
  95. Rotate(B_1, 60*°, B) → F_1
  96. Rotate(C, 60*°, B) → C'
  97. Segment(F_1, C') → q_1
  98. Rotate(B', 60*°, A) → B''
  99. Rotate(D', 60*°, A) → D''
  100. Segment(B'', D'') → d''
  101. Rotate(D'_1, 60*°, A) → G_1
  102. Rotate(E', 60*°, A) → E''
  103. Segment(G_1, E'') → e''
  104. Rotate(E'_1, 60*°, A) → H_1
  105. Rotate(F', 60*°, A) → F''
  106. Segment(H_1, F'') → f''
  107. Rotate(F'_1, 60*°, A) → I_1
  108. Rotate(G', 60*°, A) → G''
  109. Segment(I_1, G'') → g''
  110. Rotate(G'_1, 60*°, A) → J_1
  111. Rotate(H', 60*°, A) → H''
  112. Segment(J_1, H'') → h''
  113. Rotate(H'_1, 60*°, A) → K_1
  114. Rotate(I', 60*°, A) → I''
  115. Segment(K_1, I'') → i''
  116. Rotate(I'_1, 60*°, A) → L_1
  117. Rotate(J', 60*°, A) → J''
  118. Segment(L_1, J'') → j''
  119. Rotate(J'_1, 60*°, A) → M_1
  120. Rotate(K', 60*°, A) → K''
  121. Segment(M_1, K'') → k''
  122. Rotate(K'_1, 60*°, A) → N_1
  123. Rotate(L', 60*°, A) → L''
  124. Segment(N_1, L'') → l''
  125. Rotate(L'_1, 60*°, A) → O_1
  126. Rotate(M', 60*°, A) → M''
  127. Segment(O_1, M'') → m''
  128. Rotate(M'_1, 60*°, A) → P_1
  129. Rotate(N', 60*°, A) → N''
  130. Segment(P_1, N'') → n''
  131. Rotate(N'_1, 60*°, A) → Q_1
  132. Rotate(O', 60*°, A) → O''
  133. Segment(Q_1, O'') → p''
  134. Rotate(O'_1, 60*°, A) → R_1
  135. Rotate(P', 60*°, A) → P''
  136. Segment(R_1, P'') → q''
  137. Rotate(P'_1, 60*°, A) → S_1
  138. Rotate(Q', 60*°, A) → Q''
  139. Segment(S_1, Q'') → r''
  140. Rotate(Q'_1, 60*°, A) → T_1
  141. Rotate(R', 60*°, A) → R''
  142. Segment(T_1, R'') → s''
  143. Rotate(R'_1, 60*°, A) → U_1
  144. Rotate(S', 60*°, A) → S''
  145. Segment(U_1, S'') → t''
  146. Rotate(S'_1, 60*°, A) → V_1
  147. Rotate(T', 60*°, A) → T''
  148. Segment(V_1, T'') → r_1
  149. Rotate(T'_1, 60*°, A) → W_1
  150. Rotate(U', 60*°, A) → U''
  151. Segment(W_1, U'') → s_1
  152. Rotate(U'_1, 60*°, A) → Z_1
  153. Rotate(V', 60*°, A) → V''
  154. Segment(Z_1, V'') → t_1
  155. Rotate(V'_1, 60*°, A) → A_2
  156. Rotate(W', 60*°, A) → W''
  157. Segment(A_2, W'') → a_2
  158. Rotate(W'_1, 60*°, A) → B_2
  159. Rotate(Z', 60*°, A) → Z''
  160. Segment(B_2, Z'') → b_2
  161. Rotate(Z'_1, 60*°, A) → C_2
  162. Rotate(C_1, 60*°, A) → D_2
  163. Segment(C_2, D_2) → c_2
  164. Rotate(D_1, 60*°, A) → E_2
  165. Rotate(E_1, 60*°, A) → F_2
  166. Segment(E_2, F_2) → d_2
  167. Rotate(F_1, 60*°, A) → G_2
  168. Rotate(C', 60*°, A) → C''
  169. Segment(G_2, C'') → e_2
  170. Rotate(B, 60*°, A) → B'_1
  171. Polygon(B, D', M', M'_1, O', P', Q', R', S', T', U', V', E', W', Z', C_1, E_1, A, F_2, D_2, Z'', W'', V'', F', U'', T'', S'', R'', Q'', P'', O'', N'', M'', L'', G', K'', J'', I'', H'', G'', E'', H_1, D'', C, B_1, H', A_1, Z, W, V, U, T, S, R, Q, P, I', O, N, M, L, K, J, I, H, G, F, J', E, D, K', L') → poly2, b_3, l'_1, m'_1, m'_2, o', p'_1, q'_1, r'_1, s'_1, t'_1, u', d'_1, v', w', z', c_3, e_3, a_3, f_2, d_3, z'', w'', e'_1, v'', u'', t''_1, s''_1, r''_1, q''_1, p''_1, o'', n''_1, m''_1, f'_1, l''_1, k''_1, j''_1, i''_1, h''_1, g''_1, e''_1, h_2, d''_1, c_4, g'_1, b_4, a_4, z, w, v, u, t_2, s_2, r_2, q_2, h'_1, p_2, o, n_2, m_2, l_2, k_2, j_2, i_2, h_3, g_2, i'_1, f_3, e_4, d_4, j'_1, k'_1

AI Drawing Prompt Reference

Draw a closed polygon made of multiple line segments, then rotate the entire polygon by 60 degrees around one of its vertices, marking the positions of each rotated vertex and connecting them to form a new polygon, demonstrating the rotation construction process.
The prompt above was compiled from the original drawing commands and is for reference only.