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五角梯形准周期拼嵌图“Pentatrap”

五角梯形准周期拼嵌图“Pentatrap”
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2021-01-16 10:13
多边形角三角函数变换几何作图
本范例展示如何用一组“梯形/三角形规则”构造出具有准周期美感的瓷砖拼嵌图案（quasiperiodic tile）。核心数学概念包括：几何变换下的拼嵌结构、等腰三角形与平行线/分割关系、利用几何比值与几何均值思想（对应原站标签中的几何均值与整数/比值）、以及通过正弦等三角函数参数化角度或方向，使重复结构呈现非严格周期但仍有有序性的效果。作图要点可从构造摘要提炼：使用 GeoGebra 命令 Point 生成多组关键点（A、B、C…等及其衍生点 A′、B′、A″）；用 Rotate 实现旋转以形成拼嵌的定向复制；用 Segment 与 Polygon 连接点并绘制边界多边形瓷砖；用 Midpoint 获得中点以控制比例与对称/等腰结构。对象列表中包含大量命名点与多段参数化量（如 q1、q2、q3、q4 与 a/c/d 等），体现了以三角/比值参数驱动的几何构造。适合高中到大学初级阶段的几何作图与数学可视化教学，用于讲解变换、拼嵌与三角函数参数化如何生成准周期结构。

GeoGebra 命令及参数

  1. Point(Circle[A, 1]) → B
  2. Rotate(A, 108°, B) → A'
  3. Rotate(B, (-(72°)), A) → B'
  4. Rotate(A', 72°, B') → A''
  5. Segment(A, B) → f
  6. Midpoint(A'', B) → C
  7. Polygon(A, C, D, B') → q1, a, c, d, b'
  8. Point(Circle[E, Segment[A, C]]) → F
  9. Rotate(F + (Segment[C, D], 0), Angle[D - C] + Angle[F - E] - Angle[C - A], F) → G
  10. Rotate(G + (Segment[D, B'], 0), Angle[B' - D] + Angle[G - F] - Angle[D - C], G) → H
  11. Polygon(E, F, G, H) → q2, e, f_1, g, h
  12. Point(Circle[I, Segment[A, C]]) → J
  13. Rotate(J + (Segment[C, D], 0), Angle[D - C] + Angle[J - I] - Angle[C - A], J) → K
  14. Rotate(K + (Segment[D, B'], 0), Angle[B' - D] + Angle[K - J] - Angle[D - C], K) → L
  15. Polygon(I, J, K, L) → q3, i, j, k, l
  16. Point(Circle[M, Segment[A, C]]) → N
  17. Rotate(N + (Segment[C, D], 0), Angle[D - C] + Angle[N - M] - Angle[C - A], N) → O
  18. Rotate(O + (Segment[D, B'], 0), Angle[B' - D] + Angle[O - N] - Angle[D - C], O) → P
  19. Polygon(M, N, O, P) → q4, m, n, o, p
  20. Point(Circle[Q, Segment[A, C]]) → R
  21. Rotate(R + (Segment[C, D], 0), Angle[D - C] + Angle[R - Q] - Angle[C - A], R) → S
  22. Rotate(S + (Segment[D, B'], 0), Angle[B' - D] + Angle[S - R] - Angle[D - C], S) → T
  23. Polygon(Q, R, S, T) → q5, q, r, s, t
  24. Point(Circle[U, Segment[A, C]]) → V
  25. Rotate(V + (Segment[C, D], 0), Angle[D - C] + Angle[V - U] - Angle[C - A], V) → W
  26. Rotate(W + (Segment[D, B'], 0), Angle[B' - D] + Angle[W - V] - Angle[D - C], W) → Z
  27. Polygon(U, V, W, Z) → q6, u, v, w, z_1
  28. Point(Circle[A_1, Segment[A, C]]) → B_1
  29. Rotate(B_1 + (Segment[C, D], 0), Angle[D - C] + Angle[B_1 - A_1] - Angle[C - A], B_1) → C_1
  30. Rotate(C_1 + (Segment[D, B'], 0), Angle[B' - D] + Angle[C_1 - B_1] - Angle[D - C], C_1) → D_1
  31. Polygon(A_1, B_1, C_1, D_1) → q7, a_1, b_1, c_1, d_1
  32. Point(Circle[E_1, Segment[A, C]]) → F_1
  33. Rotate(F_1 + (Segment[C, D], 0), Angle[D - C] + Angle[F_1 - E_1] - Angle[C - A], F_1) → G_1
  34. Rotate(G_1 + (Segment[D, B'], 0), Angle[B' - D] + Angle[G_1 - F_1] - Angle[D - C], G_1) → H_1
  35. Polygon(E_1, F_1, G_1, H_1) → q8, e_1, b, g_1, h_1
  36. Point(Circle[I_1, Segment[A, C]]) → J_1
  37. Rotate(J_1 + (Segment[C, D], 0), Angle[D - C] + Angle[J_1 - I_1] - Angle[C - A], J_1) → K_1
  38. Rotate(K_1 + (Segment[D, B'], 0), Angle[B' - D] + Angle[K_1 - J_1] - Angle[D - C], K_1) → L_1
  39. Polygon(I_1, J_1, K_1, L_1) → q9, i_1, j_1, k_1, l_1
  40. Point(Circle[M_1, Segment[A, C]]) → N_1
  41. Rotate(N_1 + (Segment[C, D], 0), Angle[D - C] + Angle[N_1 - M_1] - Angle[C - A], N_1) → O_1
  42. Rotate(O_1 + (Segment[D, B'], 0), Angle[B' - D] + Angle[O_1 - N_1] - Angle[D - C], O_1) → P_1
  43. Polygon(M_1, N_1, O_1, P_1) → q10, m_1, n_1, o_1, p_1
  44. Point(Circle[Q_1, Segment[A, C]]) → R_1
  45. Rotate(R_1 + (Segment[C, D], 0), Angle[D - C] + Angle[R_1 - Q_1] - Angle[C - A], R_1) → S_1
  46. Rotate(S_1 + (Segment[D, B'], 0), Angle[B' - D] + Angle[S_1 - R_1] - Angle[D - C], S_1) → T_1
  47. Polygon(Q_1, R_1, S_1, T_1) → q11, q_1, r_1, s_1, t_1
  48. Point(Circle[U_1, Segment[A, C]]) → V_1
  49. Rotate(V_1 + (Segment[C, D], 0), Angle[D - C] + Angle[V_1 - U_1] - Angle[C - A], V_1) → W_1
  50. Rotate(W_1 + (Segment[D, B'], 0), Angle[B' - D] + Angle[W_1 - V_1] - Angle[D - C], W_1) → Z_1
  51. Polygon(U_1, V_1, W_1, Z_1) → q12, u_1, v_1, w_1, f_2
  52. Point(Circle[A_2, Segment[A, C]]) → B_2
  53. Rotate(B_2 + (Segment[C, D], 0), Angle[D - C] + Angle[B_2 - A_2] - Angle[C - A], B_2) → C_2
  54. Rotate(C_2 + (Segment[D, B'], 0), Angle[B' - D] + Angle[C_2 - B_2] - Angle[D - C], C_2) → D_2
  55. Polygon(A_2, B_2, C_2, D_2) → q13, a_2, b_2, c_2, d_2
  56. Point(Circle[E_2, Segment[A, C]]) → F_2
  57. Rotate(F_2 + (Segment[C, D], 0), Angle[D - C] + Angle[F_2 - E_2] - Angle[C - A], F_2) → G_2
  58. Rotate(G_2 + (Segment[D, B'], 0), Angle[B' - D] + Angle[G_2 - F_2] - Angle[D - C], G_2) → H_2
  59. Polygon(E_2, F_2, G_2, H_2) → q14, e_2, g_2, h_2, i_2
  60. Point(Circle[I_2, Segment[A, C]]) → J_2
  61. Rotate(J_2 + (Segment[C, D], 0), Angle[D - C] + Angle[J_2 - I_2] - Angle[C - A], J_2) → K_2
  62. Rotate(K_2 + (Segment[D, B'], 0), Angle[B' - D] + Angle[K_2 - J_2] - Angle[D - C], K_2) → L_2
  63. Polygon(I_2, J_2, K_2, L_2) → q15, j_2, k_2, l_2, m_2
  64. Point(Circle[M_2, Segment[A, C]]) → N_2
  65. Rotate(N_2 + (Segment[C, D], 0), Angle[D - C] + Angle[N_2 - M_2] - Angle[C - A], N_2) → O_2
  66. Rotate(O_2 + (Segment[D, B'], 0), Angle[B' - D] + Angle[O_2 - N_2] - Angle[D - C], O_2) → P_2
  67. Polygon(M_2, N_2, O_2, P_2) → q16, n_2, p_2, o_2, q_2
  68. Point(Circle[Q_2, Segment[A, C]]) → R_2
  69. Rotate(R_2 + (Segment[C, D], 0), Angle[D - C] + Angle[R_2 - Q_2] - Angle[C - A], R_2) → S_2
  70. Rotate(S_2 + (Segment[D, B'], 0), Angle[B' - D] + Angle[S_2 - R_2] - Angle[D - C], S_2) → T_2
  71. Polygon(Q_2, R_2, S_2, T_2) → q17, r_2, s_2, t_2, f_3
  72. Point(Circle[U_2, Segment[A, C]]) → V_2
  73. Rotate(V_2 + (Segment[C, D], 0), Angle[D - C] + Angle[V_2 - U_2] - Angle[C - A], V_2) → W_2
  74. Rotate(W_2 + (Segment[D, B'], 0), Angle[B' - D] + Angle[W_2 - V_2] - Angle[D - C], W_2) → Z_2
  75. Polygon(U_2, V_2, W_2, Z_2) → q18, u_2, v_2, w_2, z_2
  76. Point(Circle[A_3, Segment[A, C]]) → B_3
  77. Rotate(B_3 + (Segment[C, D], 0), Angle[D - C] + Angle[B_3 - A_3] - Angle[C - A], B_3) → C_3
  78. Rotate(C_3 + (Segment[D, B'], 0), Angle[B' - D] + Angle[C_3 - B_3] - Angle[D - C], C_3) → D_3
  79. Polygon(A_3, B_3, C_3, D_3) → q19, a_3, b_3, c_3, d_3
  80. Point(Circle[E_3, Segment[A, C]]) → F_3
  81. Rotate(F_3 + (Segment[C, D], 0), Angle[D - C] + Angle[F_3 - E_3] - Angle[C - A], F_3) → G_3
  82. Rotate(G_3 + (Segment[D, B'], 0), Angle[B' - D] + Angle[G_3 - F_3] - Angle[D - C], G_3) → H_3
  83. Polygon(E_3, F_3, G_3, H_3) → q20, e_3, g_3, h_3, i_3
  84. Point(Circle[I_3, Segment[A, C]]) → J_3
  85. Rotate(J_3 + (Segment[C, D], 0), Angle[D - C] + Angle[J_3 - I_3] - Angle[C - A], J_3) → K_3
  86. Rotate(K_3 + (Segment[D, B'], 0), Angle[B' - D] + Angle[K_3 - J_3] - Angle[D - C], K_3) → L_3
  87. Polygon(I_3, J_3, K_3, L_3) → q21, j_3, k_3, l_3, m_3
  88. Point(Circle[M_3, Segment[A, C]]) → N_3
  89. Rotate(N_3 + (Segment[C, D], 0), Angle[D - C] + Angle[N_3 - M_3] - Angle[C - A], N_3) → O_3
  90. Rotate(O_3 + (Segment[D, B'], 0), Angle[B' - D] + Angle[O_3 - N_3] - Angle[D - C], O_3) → P_3
  91. Polygon(M_3, N_3, O_3, P_3) → q22, n_3, p_3, o_3, q_3
  92. Point(Circle[Q_3, Segment[A, C]]) → R_3
  93. Rotate(R_3 + (Segment[C, D], 0), Angle[D - C] + Angle[R_3 - Q_3] - Angle[C - A], R_3) → S_3
  94. Rotate(S_3 + (Segment[D, B'], 0), Angle[B' - D] + Angle[S_3 - R_3] - Angle[D - C], S_3) → T_3
  95. Polygon(Q_3, R_3, S_3, T_3) → q23, r_3, s_3, t_3, f_4
  96. Point(Circle[U_3, Segment[A, C]]) → V_3
  97. Rotate(V_3 + (Segment[C, D], 0), Angle[D - C] + Angle[V_3 - U_3] - Angle[C - A], V_3) → W_3
  98. Rotate(W_3 + (Segment[D, B'], 0), Angle[B' - D] + Angle[W_3 - V_3] - Angle[D - C], W_3) → Z_3
  99. Polygon(U_3, V_3, W_3, Z_3) → q24, u_3, v_3, w_3, z_3
  100. Point(Circle[A_4, Segment[A, C]]) → B_4
  101. Rotate(B_4 + (Segment[C, D], 0), Angle[D - C] + Angle[B_4 - A_4] - Angle[C - A], B_4) → C_4
  102. Rotate(C_4 + (Segment[D, B'], 0), Angle[B' - D] + Angle[C_4 - B_4] - Angle[D - C], C_4) → D_4
  103. Polygon(A_4, B_4, C_4, D_4) → q25, a_4, b_4, c_4, d_4
  104. Point(Circle[E_4, Segment[A, C]]) → F_4
  105. Rotate(F_4 + (Segment[C, D], 0), Angle[D - C] + Angle[F_4 - E_4] - Angle[C - A], F_4) → G_4
  106. Rotate(G_4 + (Segment[D, B'], 0), Angle[B' - D] + Angle[G_4 - F_4] - Angle[D - C], G_4) → H_4
  107. Polygon(E_4, F_4, G_4, H_4) → q26, e_4, g_4, h_4, i_4
  108. Point(Circle[I_4, Segment[A_4, B_4]]) → J_4
  109. Rotate(J_4 + (Segment[B_4, C_4], 0), Angle[C_4 - B_4] + Angle[J_4 - I_4] - Angle[B_4 - A_4], J_4) → K_4
  110. Rotate(K_4 + (Segment[C_4, D_4], 0), Angle[D_4 - C_4] + Angle[K_4 - J_4] - Angle[C_4 - B_4], K_4) → L_4
  111. Polygon(I_4, J_4, K_4, L_4) → q27, j_4, k_4, l_4, m_4
  112. Point(Circle[M_4, Segment[A_4, B_4]]) → N_4
  113. Rotate(N_4 + (Segment[B_4, C_4], 0), Angle[C_4 - B_4] + Angle[N_4 - M_4] - Angle[B_4 - A_4], N_4) → O_4
  114. Rotate(O_4 + (Segment[C_4, D_4], 0), Angle[D_4 - C_4] + Angle[O_4 - N_4] - Angle[C_4 - B_4], O_4) → P_4
  115. Polygon(M_4, N_4, O_4, P_4) → q28, n_4, p_4, o_4, q_4
  116. Point(Circle[Q_4, Segment[A_4, B_4]]) → R_4
  117. Rotate(R_4 + (Segment[B_4, C_4], 0), Angle[C_4 - B_4] + Angle[R_4 - Q_4] - Angle[B_4 - A_4], R_4) → S_4
  118. Rotate(S_4 + (Segment[C_4, D_4], 0), Angle[D_4 - C_4] + Angle[S_4 - R_4] - Angle[C_4 - B_4], S_4) → T_4
  119. Polygon(Q_4, R_4, S_4, T_4) → q29, r_4, s_4, t_4, f_5
  120. Point(Circle[U_4, Segment[A_4, B_4]]) → V_4
  121. Rotate(V_4 + (Segment[B_4, C_4], 0), Angle[C_4 - B_4] + Angle[V_4 - U_4] - Angle[B_4 - A_4], V_4) → W_4
  122. Rotate(W_4 + (Segment[C_4, D_4], 0), Angle[D_4 - C_4] + Angle[W_4 - V_4] - Angle[C_4 - B_4], W_4) → Z_4
  123. Polygon(U_4, V_4, W_4, Z_4) → q30, u_4, v_4, w_4, z_4
  124. Point(Circle[A_5, Segment[A_4, B_4]]) → B_5
  125. Rotate(B_5 + (Segment[B_4, C_4], 0), Angle[C_4 - B_4] + Angle[B_5 - A_5] - Angle[B_4 - A_4], B_5) → C_5
  126. Rotate(C_5 + (Segment[C_4, D_4], 0), Angle[D_4 - C_4] + Angle[C_5 - B_5] - Angle[C_4 - B_4], C_5) → D_5
  127. Polygon(A_5, B_5, C_5, D_5) → q31, a_5, b_5, c_5, d_5
  128. Point(Circle[E_5, Segment[A_4, B_4]]) → F_5
  129. Rotate(F_5 + (Segment[B_4, C_4], 0), Angle[C_4 - B_4] + Angle[F_5 - E_5] - Angle[B_4 - A_4], F_5) → G_5
  130. Rotate(G_5 + (Segment[C_4, D_4], 0), Angle[D_4 - C_4] + Angle[G_5 - F_5] - Angle[C_4 - B_4], G_5) → H_5
  131. Polygon(E_5, F_5, G_5, H_5) → q32, e_5, g_5, h_5, i_5
  132. Point(Circle[I_5, Segment[A_4, B_4]]) → J_5
  133. Rotate(J_5 + (Segment[B_4, C_4], 0), Angle[C_4 - B_4] + Angle[J_5 - I_5] - Angle[B_4 - A_4], J_5) → K_5
  134. Rotate(K_5 + (Segment[C_4, D_4], 0), Angle[D_4 - C_4] + Angle[K_5 - J_5] - Angle[C_4 - B_4], K_5) → L_5
  135. Polygon(I_5, J_5, K_5, L_5) → q33, j_5, k_5, l_5, m_5
  136. Point(Circle[M_5, Segment[A_4, B_4]]) → N_5
  137. Rotate(N_5 + (Segment[B_4, C_4], 0), Angle[C_4 - B_4] + Angle[N_5 - M_5] - Angle[B_4 - A_4], N_5) → O_5
  138. Rotate(O_5 + (Segment[C_4, D_4], 0), Angle[D_4 - C_4] + Angle[O_5 - N_5] - Angle[C_4 - B_4], O_5) → P_5
  139. Polygon(M_5, N_5, O_5, P_5) → q34, n_5, p_5, o_5, q_5
  140. Point(Circle[Q_5, Segment[A_4, B_4]]) → R_5
  141. Rotate(R_5 + (Segment[B_4, C_4], 0), Angle[C_4 - B_4] + Angle[R_5 - Q_5] - Angle[B_4 - A_4], R_5) → S_5
  142. Rotate(S_5 + (Segment[C_4, D_4], 0), Angle[D_4 - C_4] + Angle[S_5 - R_5] - Angle[C_4 - B_4], S_5) → T_5
  143. Polygon(Q_5, R_5, S_5, T_5) → q35, r_5, s_5, t_5, f_6
  144. Point(Circle[U_5, Segment[A_4, B_4]]) → V_5
  145. Rotate(V_5 + (Segment[B_4, C_4], 0), Angle[C_4 - B_4] + Angle[V_5 - U_5] - Angle[B_4 - A_4], V_5) → W_5
  146. Rotate(W_5 + (Segment[C_4, D_4], 0), Angle[D_4 - C_4] + Angle[W_5 - V_5] - Angle[C_4 - B_4], W_5) → Z_5
  147. Polygon(U_5, V_5, W_5, Z_5) → q36, u_5, v_5, w_5, z_5
  148. Point(Circle[A_6, Segment[A_4, B_4]]) → B_6
  149. Rotate(B_6 + (Segment[B_4, C_4], 0), Angle[C_4 - B_4] + Angle[B_6 - A_6] - Angle[B_4 - A_4], B_6) → C_6
  150. Rotate(C_6 + (Segment[C_4, D_4], 0), Angle[D_4 - C_4] + Angle[C_6 - B_6] - Angle[C_4 - B_4], C_6) → D_6
  151. Polygon(A_6, B_6, C_6, D_6) → q37, a_6, b_6, c_6, d_6
  152. Point(Circle[E_6, Segment[A_4, B_4]]) → F_6
  153. Rotate(F_6 + (Segment[B_4, C_4], 0), Angle[C_4 - B_4] + Angle[F_6 - E_6] - Angle[B_4 - A_4], F_6) → G_6
  154. Rotate(G_6 + (Segment[C_4, D_4], 0), Angle[D_4 - C_4] + Angle[G_6 - F_6] - Angle[C_4 - B_4], G_6) → H_6
  155. Polygon(E_6, F_6, G_6, H_6) → q38, e_6, g_6, h_6, i_6
  156. Point(Circle[I_6, Segment[A_4, B_4]]) → J_6
  157. Rotate(J_6 + (Segment[B_4, C_4], 0), Angle[C_4 - B_4] + Angle[J_6 - I_6] - Angle[B_4 - A_4], J_6) → K_6
  158. Rotate(K_6 + (Segment[C_4, D_4], 0), Angle[D_4 - C_4] + Angle[K_6 - J_6] - Angle[C_4 - B_4], K_6) → L_6
  159. Polygon(I_6, J_6, K_6, L_6) → q39, j_6, k_6, l_6, m_6
  160. Point(Circle[M_6, Segment[A_4, B_4]]) → N_6
  161. Rotate(N_6 + (Segment[B_4, C_4], 0), Angle[C_4 - B_4] + Angle[N_6 - M_6] - Angle[B_4 - A_4], N_6) → O_6
  162. Rotate(O_6 + (Segment[C_4, D_4], 0), Angle[D_4 - C_4] + Angle[O_6 - N_6] - Angle[C_4 - B_4], O_6) → P_6
  163. Polygon(M_6, N_6, O_6, P_6) → q40, n_6, p_6, o_6, q_6
  164. Point(Circle[Q_6, Segment[A_4, B_4]]) → R_6
  165. Rotate(R_6 + (Segment[B_4, C_4], 0), Angle[C_4 - B_4] + Angle[R_6 - Q_6] - Angle[B_4 - A_4], R_6) → S_6
  166. Rotate(S_6 + (Segment[C_4, D_4], 0), Angle[D_4 - C_4] + Angle[S_6 - R_6] - Angle[C_4 - B_4], S_6) → T_6
  167. Polygon(Q_6, R_6, S_6, T_6) → q41, r_6, s_6, t_6, f_7
  168. Point(Circle[U_6, Segment[E_4, F_4]]) → V_6
  169. Rotate(V_6 + (Segment[F_4, G_4], 0), Angle[G_4 - F_4] + Angle[V_6 - U_6] - Angle[F_4 - E_4], V_6) → W_6
  170. Rotate(W_6 + (Segment[G_4, H_4], 0), Angle[H_4 - G_4] + Angle[W_6 - V_6] - Angle[G_4 - F_4], W_6) → Z_6
  171. Polygon(U_6, V_6, W_6, Z_6) → q42, u_6, v_6, w_6, z_6
  172. Point(Circle[A_7, Segment[E_4, F_4]]) → B_7
  173. Rotate(B_7 + (Segment[F_4, G_4], 0), Angle[G_4 - F_4] + Angle[B_7 - A_7] - Angle[F_4 - E_4], B_7) → C_7
  174. Rotate(C_7 + (Segment[G_4, H_4], 0), Angle[H_4 - G_4] + Angle[C_7 - B_7] - Angle[G_4 - F_4], C_7) → D_7
  175. Polygon(A_7, B_7, C_7, D_7) → q43, a_7, b_7, c_7, d_7
  176. Point(Circle[E_7, Segment[E_4, F_4]]) → F_7
  177. Rotate(F_7 + (Segment[F_4, G_4], 0), Angle[G_4 - F_4] + Angle[F_7 - E_7] - Angle[F_4 - E_4], F_7) → G_7
  178. Rotate(G_7 + (Segment[G_4, H_4], 0), Angle[H_4 - G_4] + Angle[G_7 - F_7] - Angle[G_4 - F_4], G_7) → H_7
  179. Polygon(E_7, F_7, G_7, H_7) → q44, e_7, g_7, h_7, i_7
  180. Point(Circle[I_7, Segment[E_4, F_4]]) → J_7
  181. Rotate(J_7 + (Segment[F_4, G_4], 0), Angle[G_4 - F_4] + Angle[J_7 - I_7] - Angle[F_4 - E_4], J_7) → K_7
  182. Rotate(K_7 + (Segment[G_4, H_4], 0), Angle[H_4 - G_4] + Angle[K_7 - J_7] - Angle[G_4 - F_4], K_7) → L_7
  183. Polygon(I_7, J_7, K_7, L_7) → q45, j_7, k_7, l_7, m_7
  184. Point(Circle[M_7, Segment[E_4, F_4]]) → N_7
  185. Rotate(N_7 + (Segment[F_4, G_4], 0), Angle[G_4 - F_4] + Angle[N_7 - M_7] - Angle[F_4 - E_4], N_7) → O_7
  186. Rotate(O_7 + (Segment[G_4, H_4], 0), Angle[H_4 - G_4] + Angle[O_7 - N_7] - Angle[G_4 - F_4], O_7) → P_7
  187. Polygon(M_7, N_7, O_7, P_7) → q46, n_7, p_7, o_7, q_7
  188. Point(Circle[Q_7, Segment[E_4, F_4]]) → R_7
  189. Rotate(R_7 + (Segment[F_4, G_4], 0), Angle[G_4 - F_4] + Angle[R_7 - Q_7] - Angle[F_4 - E_4], R_7) → S_7
  190. Rotate(S_7 + (Segment[G_4, H_4], 0), Angle[H_4 - G_4] + Angle[S_7 - R_7] - Angle[G_4 - F_4], S_7) → T_7
  191. Polygon(Q_7, R_7, S_7, T_7) → q47, r_7, s_7, t_7, f_8
  192. Point(Circle[U_7, Segment[E_4, F_4]]) → V_7
  193. Rotate(V_7 + (Segment[F_4, G_4], 0), Angle[G_4 - F_4] + Angle[V_7 - U_7] - Angle[F_4 - E_4], V_7) → W_7
  194. Rotate(W_7 + (Segment[G_4, H_4], 0), Angle[H_4 - G_4] + Angle[W_7 - V_7] - Angle[G_4 - F_4], W_7) → Z_7
  195. Polygon(U_7, V_7, W_7, Z_7) → q48, u_7, v_7, w_7, z_7
  196. Point(Circle[A_8, Segment[E_4, F_4]]) → B_8
  197. Rotate(B_8 + (Segment[F_4, G_4], 0), Angle[G_4 - F_4] + Angle[B_8 - A_8] - Angle[F_4 - E_4], B_8) → C_8
  198. Rotate(C_8 + (Segment[G_4, H_4], 0), Angle[H_4 - G_4] + Angle[C_8 - B_8] - Angle[G_4 - F_4], C_8) → D_8
  199. Polygon(A_8, B_8, C_8, D_8) → q49, a_8, b_8, c_8, d_8
  200. Point(Circle[E_8, Segment[E_4, F_4]]) → F_8
  201. Rotate(F_8 + (Segment[F_4, G_4], 0), Angle[G_4 - F_4] + Angle[F_8 - E_8] - Angle[F_4 - E_4], F_8) → G_8
  202. Rotate(G_8 + (Segment[G_4, H_4], 0), Angle[H_4 - G_4] + Angle[G_8 - F_8] - Angle[G_4 - F_4], G_8) → H_8
  203. Polygon(E_8, F_8, G_8, H_8) → q50, e_8, g_8, h_8, i_8
  204. Point(Circle[I_8, Segment[E_4, F_4]]) → J_8
  205. Rotate(J_8 + (Segment[F_4, G_4], 0), Angle[G_4 - F_4] + Angle[J_8 - I_8] - Angle[F_4 - E_4], J_8) → K_8
  206. Rotate(K_8 + (Segment[G_4, H_4], 0), Angle[H_4 - G_4] + Angle[K_8 - J_8] - Angle[G_4 - F_4], K_8) → L_8
  207. Polygon(I_8, J_8, K_8, L_8) → q51, j_8, k_8, l_8, m_8
  208. Point(Circle[M_8, Segment[E_4, F_4]]) → N_8
  209. Rotate(N_8 + (Segment[F_4, G_4], 0), Angle[G_4 - F_4] + Angle[N_8 - M_8] - Angle[F_4 - E_4], N_8) → O_8
  210. Rotate(O_8 + (Segment[G_4, H_4], 0), Angle[H_4 - G_4] + Angle[O_8 - N_8] - Angle[G_4 - F_4], O_8) → P_8
  211. Polygon(M_8, N_8, O_8, P_8) → q52, n_8, p_8, o_8, q_8
  212. Point(Circle[Q_8, Segment[E_4, F_4]]) → R_8
  213. Rotate(R_8 + (Segment[F_4, G_4], 0), Angle[G_4 - F_4] + Angle[R_8 - Q_8] - Angle[F_4 - E_4], R_8) → S_8
  214. Rotate(S_8 + (Segment[G_4, H_4], 0), Angle[H_4 - G_4] + Angle[S_8 - R_8] - Angle[G_4 - F_4], S_8) → T_8
  215. Polygon(Q_8, R_8, S_8, T_8) → q53, r_8, s_8, t_8, f_9
  216. Point(Circle[U_8, Segment[E_4, F_4]]) → V_8
  217. Rotate(V_8 + (Segment[F_4, G_4], 0), Angle[G_4 - F_4] + Angle[V_8 - U_8] - Angle[F_4 - E_4], V_8) → W_8
  218. Rotate(W_8 + (Segment[G_4, H_4], 0), Angle[H_4 - G_4] + Angle[W_8 - V_8] - Angle[G_4 - F_4], W_8) → Z_8
  219. Polygon(U_8, V_8, W_8, Z_8) → q54, u_8, v_8, w_8, z_8
  220. Point(Circle[A_9, Segment[E_4, F_4]]) → B_9
  221. Rotate(B_9 + (Segment[F_4, G_4], 0), Angle[G_4 - F_4] + Angle[B_9 - A_9] - Angle[F_4 - E_4], B_9) → C_9
  222. Rotate(C_9 + (Segment[G_4, H_4], 0), Angle[H_4 - G_4] + Angle[C_9 - B_9] - Angle[G_4 - F_4], C_9) → D_9
  223. Polygon(A_9, B_9, C_9, D_9) → q55, a_9, b_9, c_9, d_9
  224. Point(Circle[E_9, Segment[E_4, F_4]]) → F_9
  225. Rotate(F_9 + (Segment[F_4, G_4], 0), Angle[G_4 - F_4] + Angle[F_9 - E_9] - Angle[F_4 - E_4], F_9) → G_9
  226. Rotate(G_9 + (Segment[G_4, H_4], 0), Angle[H_4 - G_4] + Angle[G_9 - F_9] - Angle[G_4 - F_4], G_9) → H_9
  227. Polygon(E_9, F_9, G_9, H_9) → q56, e_9, g_9, h_9, i_9
  228. Point(Circle[I_9, Segment[E_4, F_4]]) → J_9
  229. Rotate(J_9 + (Segment[F_4, G_4], 0), Angle[G_4 - F_4] + Angle[J_9 - I_9] - Angle[F_4 - E_4], J_9) → K_9
  230. Rotate(K_9 + (Segment[G_4, H_4], 0), Angle[H_4 - G_4] + Angle[K_9 - J_9] - Angle[G_4 - F_4], K_9) → L_9
  231. Polygon(I_9, J_9, K_9, L_9) → q57, j_9, k_9, l_9, m_9
  232. Point(Circle[M_9, Segment[E_4, F_4]]) → N_9
  233. Rotate(N_9 + (Segment[F_4, G_4], 0), Angle[G_4 - F_4] + Angle[N_9 - M_9] - Angle[F_4 - E_4], N_9) → O_9
  234. Rotate(O_9 + (Segment[G_4, H_4], 0), Angle[H_4 - G_4] + Angle[O_9 - N_9] - Angle[G_4 - F_4], O_9) → P_9
  235. Polygon(M_9, N_9, O_9, P_9) → q58, n_9, p_9, o_9, q_9
  236. Point(Circle[Q_9, Segment[E_4, F_4]]) → R_9
  237. Rotate(R_9 + (Segment[F_4, G_4], 0), Angle[G_4 - F_4] + Angle[R_9 - Q_9] - Angle[F_4 - E_4], R_9) → S_9
  238. Rotate(S_9 + (Segment[G_4, H_4], 0), Angle[H_4 - G_4] + Angle[S_9 - R_9] - Angle[G_4 - F_4], S_9) → T_9
  239. Polygon(Q_9, R_9, S_9, T_9) → q59, r_9, s_9, t_9, f_{10}
  240. Point(Circle[U_9, Segment[E_4, F_4]]) → V_9
  241. Rotate(V_9 + (Segment[F_4, G_4], 0), Angle[G_4 - F_4] + Angle[V_9 - U_9] - Angle[F_4 - E_4], V_9) → W_9
  242. Rotate(W_9 + (Segment[G_4, H_4], 0), Angle[H_4 - G_4] + Angle[W_9 - V_9] - Angle[G_4 - F_4], W_9) → Z_9
  243. Polygon(U_9, V_9, W_9, Z_9) → q60, u_9, v_9, w_9, z_9

AI 绘图提示语参考

绘制一个由五边形和等腰三角形组成的准周期性铺砖图案。首先创建一个圆并标记其与圆心的交点，然后利用旋转和线段连接这些点，形成多个相似的几何形状。通过旋转和连接这些形状的中心点，构建出复杂的铺砖结构。整个图案通过旋转和比例控制，展现出有序而非严格周期性的美感。
以上提示语为根据原始绘图命令整理而来，仅供参考。