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Axis Symmetry Patterns in a Kaleidoscope

Axis Symmetry Patterns in a Kaleidoscope
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2012-08-28 01:42
CircleTransformationGeometric ConstructionLocus
This example demonstrates the formation of axis‑symmetric patterns in a kaleidoscope, where basic shapes are reflected and rotated to create intricate symmetric designs. The core mathematical concepts include axis symmetry, reflection and rotation transformations, and the construction of circles and circular arcs. The GeoGebra construction uses commands such as CircumcircleArc, Line, Mirror, and Rotate, involving objects like points A_i, C_i and circles o. It is suitable for high‑school geometry classes, especially when teaching symmetry and transformation geometry.

GeoGebra Commands & Parameters

  1. CircumcircleArc(A_7, C_8, B_5) → c_5
  2. Line(A_7, B_5) → a_5
  3. Mirror(A_7, a_5) → A'_{15}
  4. Mirror(C_8, a_5) → C'_{15}
  5. Mirror(B_5, a_5) → B'_{15}
  6. CircumcircleArc(A'_{15}, C'_{15}, B'_{15}) → c'_{15}
  7. Rotate(A'_{15}, 72*°, B_5) → A''_{10}
  8. Rotate(C'_{15}, 72*°, B_5) → C''_{10}
  9. Rotate(B'_{15}, 72*°, B_5) → B''_{10}
  10. CircumcircleArc(A''_{10}, C''_{10}, B''_{10}) → c''_{10}
  11. Rotate(A_7, 72*°, B_5) → A'_{16}
  12. Rotate(C_8, 72*°, B_5) → C'_{16}
  13. Rotate(B_5, 72*°, B_5) → B'_{16}
  14. CircumcircleArc(A'_{16}, C'_{16}, B'_{16}) → c'_{16}
  15. Rotate(A_7, 288*°, B_5) → A'_{17}
  16. Rotate(C_8, 288*°, B_5) → C'_{17}
  17. Rotate(B_5, 288*°, B_5) → B'_{17}
  18. CircumcircleArc(A'_{17}, C'_{17}, B'_{17}) → c'_{17}
  19. Rotate(A'_{15}, 288*°, B_5) → A''_{11}
  20. Rotate(C'_{15}, 288*°, B_5) → C''_{11}
  21. Rotate(B'_{15}, 288*°, B_5) → B''_{11}
  22. CircumcircleArc(A''_{11}, C''_{11}, B''_{11}) → c''_{11}
  23. Rotate(A'_{17}, 288*°, B_5) → D_5
  24. Rotate(C'_{17}, 288*°, B_5) → E_5
  25. Rotate(B'_{17}, 288*°, B_5) → F_5
  26. CircumcircleArc(D_5, E_5, F_5) → d_5
  27. Rotate(A''_{11}, 288*°, B_5) → G_5
  28. Rotate(C''_{11}, 288*°, B_5) → H_5
  29. Rotate(B''_{11}, 288*°, B_5) → I_5
  30. CircumcircleArc(G_5, H_5, I_5) → e_5
  31. Rotate(D_5, 288*°, B_5) → D'_5
  32. Rotate(E_5, 288*°, B_5) → E'_5
  33. Rotate(F_5, 288*°, B_5) → F'_5
  34. CircumcircleArc(D'_5, E'_5, F'_5) → d'_5
  35. Rotate(G_5, 288*°, B_5) → G'_5
  36. Rotate(H_5, 288*°, B_5) → H'_5
  37. Rotate(I_5, 288*°, B_5) → I'_5
  38. CircumcircleArc(G'_5, H'_5, I'_5) → e'_5
  39. CircumcircleArc(A_8, C_9, B_2) → c_2
  40. Line(A_8, B_2) → a_2
  41. Mirror(A_8, a_2) → A'_6
  42. Mirror(C_9, a_2) → C'_6
  43. Mirror(B_2, a_2) → B'_6
  44. CircumcircleArc(A'_6, C'_6, B'_6) → c'_6
  45. Rotate(A'_6, 72*°, B_2) → A''_4
  46. Rotate(C'_6, 72*°, B_2) → C''_4
  47. Rotate(B'_6, 72*°, B_2) → B''_4
  48. CircumcircleArc(A''_4, C''_4, B''_4) → c''_4
  49. Rotate(A_8, 72*°, B_2) → A'_7
  50. Rotate(C_9, 72*°, B_2) → C'_7
  51. Rotate(B_2, 72*°, B_2) → B'_7
  52. CircumcircleArc(A'_7, C'_7, B'_7) → c'_7
  53. Rotate(A_8, 288*°, B_2) → A'_8
  54. Rotate(C_9, 288*°, B_2) → C'_8
  55. Rotate(B_2, 288*°, B_2) → B'_8
  56. CircumcircleArc(A'_8, C'_8, B'_8) → c'_8
  57. Rotate(A'_6, 288*°, B_2) → A''_5
  58. Rotate(C'_6, 288*°, B_2) → C''_5
  59. Rotate(B'_6, 288*°, B_2) → B''_5
  60. CircumcircleArc(A''_5, C''_5, B''_5) → c''_5
  61. Rotate(A'_8, 288*°, B_2) → D_2
  62. Rotate(C'_8, 288*°, B_2) → E_2
  63. Rotate(B'_8, 288*°, B_2) → F_2
  64. CircumcircleArc(D_2, E_2, F_2) → d_2
  65. Rotate(A''_5, 288*°, B_2) → G_2
  66. Rotate(C''_5, 288*°, B_2) → H_2
  67. Rotate(B''_5, 288*°, B_2) → I_2
  68. CircumcircleArc(G_2, H_2, I_2) → e_2
  69. Rotate(D_2, 288*°, B_2) → D'_2
  70. Rotate(E_2, 288*°, B_2) → E'_2
  71. Rotate(F_2, 288*°, B_2) → F'_2
  72. CircumcircleArc(D'_2, E'_2, F'_2) → d'_2
  73. Rotate(G_2, 288*°, B_2) → G'_2
  74. Rotate(H_2, 288*°, B_2) → H'_2
  75. Rotate(I_2, 288*°, B_2) → I'_2
  76. CircumcircleArc(G'_2, H'_2, I'_2) → e'_2
  77. CircumcircleArc(A_9, C_{10}, B_3) → c_3
  78. Line(A_9, B_3) → a_3
  79. Mirror(A_9, a_3) → A'_9
  80. Mirror(C_{10}, a_3) → C'_9
  81. Mirror(B_3, a_3) → B'_9
  82. CircumcircleArc(A'_9, C'_9, B'_9) → c'_9
  83. Rotate(A'_9, 72*°, B_3) → A''_6
  84. Rotate(C'_9, 72*°, B_3) → C''_6
  85. Rotate(B'_9, 72*°, B_3) → B''_6
  86. CircumcircleArc(A''_6, C''_6, B''_6) → c''_6
  87. Rotate(A_9, 72*°, B_3) → A'_{10}
  88. Rotate(C_{10}, 72*°, B_3) → C'_{10}
  89. Rotate(B_3, 72*°, B_3) → B'_{10}
  90. CircumcircleArc(A'_{10}, C'_{10}, B'_{10}) → c'_{10}
  91. Rotate(A_9, 288*°, B_3) → A'_{11}
  92. Rotate(C_{10}, 288*°, B_3) → C'_{11}
  93. Rotate(B_3, 288*°, B_3) → B'_{11}
  94. CircumcircleArc(A'_{11}, C'_{11}, B'_{11}) → c'_{11}
  95. Rotate(A'_9, 288*°, B_3) → A''_7
  96. Rotate(C'_9, 288*°, B_3) → C''_7
  97. Rotate(B'_9, 288*°, B_3) → B''_7
  98. CircumcircleArc(A''_7, C''_7, B''_7) → c''_7
  99. Rotate(A'_{11}, 288*°, B_3) → D_3
  100. Rotate(C'_{11}, 288*°, B_3) → E_3
  101. Rotate(B'_{11}, 288*°, B_3) → F_3
  102. CircumcircleArc(D_3, E_3, F_3) → d_3
  103. Rotate(A''_7, 288*°, B_3) → G_3
  104. Rotate(C''_7, 288*°, B_3) → H_3
  105. Rotate(B''_7, 288*°, B_3) → I_3
  106. CircumcircleArc(G_3, H_3, I_3) → e_3
  107. Rotate(D_3, 288*°, B_3) → D'_3
  108. Rotate(E_3, 288*°, B_3) → E'_3
  109. Rotate(F_3, 288*°, B_3) → F'_3
  110. CircumcircleArc(D'_3, E'_3, F'_3) → d'_3
  111. Rotate(G_3, 288*°, B_3) → G'_3
  112. Rotate(H_3, 288*°, B_3) → H'_3
  113. Rotate(I_3, 288*°, B_3) → I'_3
  114. CircumcircleArc(G'_3, H'_3, I'_3) → e'_3
  115. CircumcircleArc(A_{10}, C_{11}, B_6) → c_6
  116. Line(A_{10}, B_6) → a_6
  117. Mirror(A_{10}, a_6) → A'_1
  118. Mirror(C_{11}, a_6) → C'_1
  119. Mirror(B_6, a_6) → B'_1
  120. CircumcircleArc(A'_1, C'_1, B'_1) → c'_1
  121. Rotate(A'_1, 72*°, B_6) → A''_1
  122. Rotate(C'_1, 72*°, B_6) → C''_1
  123. Rotate(B'_1, 72*°, B_6) → B''_1
  124. CircumcircleArc(A''_1, C''_1, B''_1) → c''_1
  125. Rotate(A_{10}, 72*°, B_6) → A'_2
  126. Rotate(C_{11}, 72*°, B_6) → C'_2
  127. Rotate(B_6, 72*°, B_6) → B'_2
  128. CircumcircleArc(A'_2, C'_2, B'_2) → c'_2
  129. Rotate(A_{10}, 288*°, B_6) → A'_{18}
  130. Rotate(C_{11}, 288*°, B_6) → C'_{18}
  131. Rotate(B_6, 288*°, B_6) → B'_{18}
  132. CircumcircleArc(A'_{18}, C'_{18}, B'_{18}) → c'_{18}
  133. Rotate(A'_1, 288*°, B_6) → A''_{12}
  134. Rotate(C'_1, 288*°, B_6) → C''_{12}
  135. Rotate(B'_1, 288*°, B_6) → B''_{12}
  136. CircumcircleArc(A''_{12}, C''_{12}, B''_{12}) → c''_{12}
  137. Rotate(A'_{18}, 288*°, B_6) → D_6
  138. Rotate(C'_{18}, 288*°, B_6) → E_6
  139. Rotate(B'_{18}, 288*°, B_6) → F_6
  140. CircumcircleArc(D_6, E_6, F_6) → d_6
  141. Rotate(A''_{12}, 288*°, B_6) → G_6
  142. Rotate(C''_{12}, 288*°, B_6) → H_6
  143. Rotate(B''_{12}, 288*°, B_6) → I_6
  144. CircumcircleArc(G_6, H_6, I_6) → e_6
  145. Rotate(D_6, 288*°, B_6) → D'_6
  146. Rotate(E_6, 288*°, B_6) → E'_6
  147. Rotate(F_6, 288*°, B_6) → F'_6
  148. CircumcircleArc(D'_6, E'_6, F'_6) → d'_6
  149. Rotate(G_6, 288*°, B_6) → G'_6
  150. Rotate(H_6, 288*°, B_6) → H'_6
  151. Rotate(I_6, 288*°, B_6) → I'_6
  152. CircumcircleArc(G'_6, H'_6, I'_6) → e'_6
  153. CircumcircleArc(A_{11}, C_{12}, B_1) → c_1
  154. Line(A_{11}, B_1) → a_1
  155. Mirror(A_{11}, a_1) → A'_3
  156. Mirror(C_{12}, a_1) → C'_3
  157. Mirror(B_1, a_1) → B'_3
  158. CircumcircleArc(A'_3, C'_3, B'_3) → c'_3
  159. Rotate(A'_3, 72*°, B_1) → A''_2
  160. Rotate(C'_3, 72*°, B_1) → C''_2
  161. Rotate(B'_3, 72*°, B_1) → B''_2
  162. CircumcircleArc(A''_2, C''_2, B''_2) → c''_2
  163. Rotate(A_{11}, 72*°, B_1) → A'_4
  164. Rotate(C_{12}, 72*°, B_1) → C'_4
  165. Rotate(B_1, 72*°, B_1) → B'_4
  166. CircumcircleArc(A'_4, C'_4, B'_4) → c'_4
  167. Rotate(A_{11}, 288*°, B_1) → A'_5
  168. Rotate(C_{12}, 288*°, B_1) → C'_5
  169. Rotate(B_1, 288*°, B_1) → B'_5
  170. CircumcircleArc(A'_5, C'_5, B'_5) → c'_5
  171. Rotate(A'_3, 288*°, B_1) → A''_3
  172. Rotate(C'_3, 288*°, B_1) → C''_3
  173. Rotate(B'_3, 288*°, B_1) → B''_3
  174. CircumcircleArc(A''_3, C''_3, B''_3) → c''_3
  175. Rotate(A'_5, 288*°, B_1) → D_1
  176. Rotate(C'_5, 288*°, B_1) → E_1
  177. Rotate(B'_5, 288*°, B_1) → F_1
  178. CircumcircleArc(D_1, E_1, F_1) → d_1
  179. Rotate(A''_3, 288*°, B_1) → G_1
  180. Rotate(C''_3, 288*°, B_1) → H_1
  181. Rotate(B''_3, 288*°, B_1) → I_1
  182. CircumcircleArc(G_1, H_1, I_1) → e_1
  183. Rotate(D_1, 288*°, B_1) → D'_1
  184. Rotate(E_1, 288*°, B_1) → E'_1
  185. Rotate(F_1, 288*°, B_1) → F'_1
  186. CircumcircleArc(D'_1, E'_1, F'_1) → d'_1
  187. Rotate(G_1, 288*°, B_1) → G'_1
  188. Rotate(H_1, 288*°, B_1) → H'_1
  189. Rotate(I_1, 288*°, B_1) → I'_1
  190. CircumcircleArc(G'_1, H'_1, I'_1) → e'_1
  191. Line(B, D) → a
  192. Mirror(A_7, a) → E
  193. Mirror(C_8, a) → F
  194. Mirror(B_5, a) → G
  195. CircumcircleArc(E, F, G) → c
  196. Mirror(A'_{15}, a) → H
  197. Mirror(C'_{15}, a) → I
  198. Mirror(B'_{15}, a) → J
  199. CircumcircleArc(H, I, J) → d
  200. Mirror(A''_{10}, a) → K
  201. Mirror(C''_{10}, a) → L
  202. Mirror(B''_{10}, a) → M
  203. CircumcircleArc(K, L, M) → e
  204. Mirror(A'_{16}, a) → N
  205. Mirror(C'_{16}, a) → O
  206. Mirror(B'_{16}, a) → P
  207. CircumcircleArc(N, O, P) → f
  208. Mirror(A'_{17}, a) → Q
  209. Mirror(C'_{17}, a) → R
  210. Mirror(B'_{17}, a) → S
  211. CircumcircleArc(Q, R, S) → g
  212. Mirror(A''_{11}, a) → T
  213. Mirror(C''_{11}, a) → U
  214. Mirror(B''_{11}, a) → V
  215. CircumcircleArc(T, U, V) → h
  216. Mirror(D_5, a) → W
  217. Mirror(E_5, a) → Z
  218. Mirror(F_5, a) → J_1
  219. CircumcircleArc(W, Z, J_1) → k
  220. Mirror(G_5, a) → K_1
  221. Mirror(H_5, a) → L_1
  222. Mirror(I_5, a) → M_1
  223. CircumcircleArc(K_1, L_1, M_1) → r
  224. Mirror(D'_5, a) → N_1
  225. Mirror(E'_5, a) → O_1
  226. Mirror(F'_5, a) → P_1
  227. CircumcircleArc(N_1, O_1, P_1) → s
  228. Mirror(G'_5, a) → Q_1
  229. Mirror(H'_5, a) → R_1
  230. Mirror(I'_5, a) → S_1
  231. CircumcircleArc(Q_1, R_1, S_1) → t
  232. Mirror(A_8, a) → T_1
  233. Mirror(C_9, a) → U_1
  234. Mirror(B_2, a) → V_1
  235. CircumcircleArc(T_1, U_1, V_1) → f_1
  236. Mirror(A'_6, a) → W_1
  237. Mirror(C'_6, a) → Z_1
  238. Mirror(B'_6, a) → J_2
  239. CircumcircleArc(W_1, Z_1, J_2) → g_1
  240. Mirror(A''_4, a) → K_2
  241. Mirror(C''_4, a) → L_2
  242. Mirror(B''_4, a) → M_2
  243. CircumcircleArc(K_2, L_2, M_2) → h_1
  244. Mirror(A'_7, a) → N_2
  245. Mirror(C'_7, a) → O_2
  246. Mirror(B'_7, a) → P_2
  247. CircumcircleArc(N_2, O_2, P_2) → k_1
  248. Mirror(A'_8, a) → Q_2
  249. Mirror(C'_8, a) → R_2
  250. Mirror(B'_8, a) → S_2
  251. CircumcircleArc(Q_2, R_2, S_2) → p_1
  252. Mirror(A''_5, a) → T_2
  253. Mirror(C''_5, a) → U_2
  254. Mirror(B''_5, a) → V_2
  255. CircumcircleArc(T_2, U_2, V_2) → q_1
  256. Mirror(D_2, a) → W_2
  257. Mirror(E_2, a) → Z_2
  258. Mirror(F_2, a) → J_3
  259. CircumcircleArc(W_2, Z_2, J_3) → r_1
  260. Mirror(G_2, a) → K_3
  261. Mirror(H_2, a) → L_3
  262. Mirror(I_2, a) → M_3
  263. CircumcircleArc(K_3, L_3, M_3) → s_1
  264. Mirror(D'_2, a) → N_3
  265. Mirror(E'_2, a) → O_3
  266. Mirror(F'_2, a) → P_3
  267. CircumcircleArc(N_3, O_3, P_3) → t_1
  268. Mirror(G'_2, a) → Q_3
  269. Mirror(H'_2, a) → R_3
  270. Mirror(I'_2, a) → S_3
  271. CircumcircleArc(Q_3, R_3, S_3) → f_2
  272. Mirror(A_9, a) → T_3
  273. Mirror(C_{10}, a) → U_3
  274. Mirror(B_3, a) → V_3
  275. CircumcircleArc(T_3, U_3, V_3) → g_2
  276. Mirror(A'_9, a) → W_3
  277. Mirror(C'_9, a) → Z_3
  278. Mirror(B'_9, a) → B_4
  279. CircumcircleArc(W_3, Z_3, B_4) → h_2
  280. Mirror(A''_6, a) → D_4
  281. Mirror(C''_6, a) → E_4
  282. Mirror(B''_6, a) → F_4
  283. CircumcircleArc(D_4, E_4, F_4) → k_2
  284. Mirror(A'_{10}, a) → G_4
  285. Mirror(C'_{10}, a) → H_4
  286. Mirror(B'_{10}, a) → I_4
  287. CircumcircleArc(G_4, H_4, I_4) → p_2
  288. Mirror(A'_{11}, a) → J_4
  289. Mirror(C'_{11}, a) → K_4
  290. Mirror(B'_{11}, a) → L_4
  291. CircumcircleArc(J_4, K_4, L_4) → q_2
  292. Mirror(A''_7, a) → M_4
  293. Mirror(C''_7, a) → N_4
  294. Mirror(B''_7, a) → O_4
  295. CircumcircleArc(M_4, N_4, O_4) → r_2
  296. Mirror(D_3, a) → P_4
  297. Mirror(E_3, a) → Q_4
  298. Mirror(F_3, a) → R_4
  299. CircumcircleArc(P_4, Q_4, R_4) → s_2
  300. Mirror(G_3, a) → S_4
  301. Mirror(H_3, a) → T_4
  302. Mirror(I_3, a) → U_4
  303. CircumcircleArc(S_4, T_4, U_4) → t_2
  304. Mirror(D'_3, a) → V_4
  305. Mirror(E'_3, a) → W_4
  306. Mirror(F'_3, a) → Z_4
  307. CircumcircleArc(V_4, W_4, Z_4) → f_3
  308. Mirror(G'_3, a) → J_5
  309. Mirror(H'_3, a) → K_5
  310. Mirror(I'_3, a) → L_5
  311. CircumcircleArc(J_5, K_5, L_5) → g_3
  312. Mirror(A_{10}, a) → M_5
  313. Mirror(C_{11}, a) → N_5
  314. Mirror(B_6, a) → O_5
  315. CircumcircleArc(M_5, N_5, O_5) → h_3
  316. Mirror(A'_1, a) → P_5
  317. Mirror(C'_1, a) → Q_5
  318. Mirror(B'_1, a) → R_5
  319. CircumcircleArc(P_5, Q_5, R_5) → k_3
  320. Mirror(A''_1, a) → S_5
  321. Mirror(C''_1, a) → T_5
  322. Mirror(B''_1, a) → U_5
  323. CircumcircleArc(S_5, T_5, U_5) → p_3
  324. Mirror(A'_2, a) → V_5
  325. Mirror(C'_2, a) → W_5
  326. Mirror(B'_2, a) → Z_5
  327. CircumcircleArc(V_5, W_5, Z_5) → q_3
  328. Mirror(A'_{18}, a) → J_6
  329. Mirror(C'_{18}, a) → K_6
  330. Mirror(B'_{18}, a) → L_6
  331. CircumcircleArc(J_6, K_6, L_6) → r_3
  332. Mirror(A''_{12}, a) → M_6
  333. Mirror(C''_{12}, a) → N_6
  334. Mirror(B''_{12}, a) → O_6
  335. CircumcircleArc(M_6, N_6, O_6) → s_3
  336. Mirror(D_6, a) → P_6
  337. Mirror(E_6, a) → Q_6
  338. Mirror(F_6, a) → R_6
  339. CircumcircleArc(P_6, Q_6, R_6) → t_3
  340. Mirror(G_6, a) → S_6
  341. Mirror(H_6, a) → T_6
  342. Mirror(I_6, a) → U_6
  343. CircumcircleArc(S_6, T_6, U_6) → c_4
  344. Mirror(D'_6, a) → V_6
  345. Mirror(E'_6, a) → W_6
  346. Mirror(F'_6, a) → Z_6
  347. CircumcircleArc(V_6, W_6, Z_6) → d_4
  348. Mirror(G'_6, a) → B_7
  349. Mirror(H'_6, a) → D_7
  350. Mirror(I'_6, a) → E_7
  351. CircumcircleArc(B_7, D_7, E_7) → e_4
  352. Mirror(A_{11}, a) → F_7
  353. Mirror(C_{12}, a) → G_7
  354. Mirror(B_1, a) → H_7
  355. CircumcircleArc(F_7, G_7, H_7) → f_4
  356. Mirror(A'_3, a) → I_7
  357. Mirror(C'_3, a) → J_7
  358. Mirror(B'_3, a) → K_7
  359. CircumcircleArc(I_7, J_7, K_7) → g_4
  360. Mirror(A''_2, a) → L_7
  361. Mirror(C''_2, a) → M_7
  362. Mirror(B''_2, a) → N_7
  363. CircumcircleArc(L_7, M_7, N_7) → h_4
  364. Mirror(A'_4, a) → O_7
  365. Mirror(C'_4, a) → P_7
  366. Mirror(B'_4, a) → Q_7
  367. CircumcircleArc(O_7, P_7, Q_7) → k_4
  368. Mirror(A'_5, a) → R_7
  369. Mirror(C'_5, a) → S_7
  370. Mirror(B'_5, a) → T_7
  371. CircumcircleArc(R_7, S_7, T_7) → p_4
  372. Mirror(A''_3, a) → U_7
  373. Mirror(C''_3, a) → V_7
  374. Mirror(B''_3, a) → W_7
  375. CircumcircleArc(U_7, V_7, W_7) → q_4
  376. Mirror(D_1, a) → Z_7
  377. Mirror(E_1, a) → B_8
  378. Mirror(F_1, a) → D_8
  379. CircumcircleArc(Z_7, B_8, D_8) → r_4
  380. Mirror(G_1, a) → E_8
  381. Mirror(H_1, a) → F_8
  382. Mirror(I_1, a) → G_8
  383. CircumcircleArc(E_8, F_8, G_8) → s_4
  384. Mirror(D'_1, a) → H_8
  385. Mirror(E'_1, a) → I_8
  386. Mirror(F'_1, a) → J_8
  387. CircumcircleArc(H_8, I_8, J_8) → t_4
  388. Mirror(G'_1, a) → K_8
  389. Mirror(H'_1, a) → L_8
  390. Mirror(I'_1, a) → M_8
  391. CircumcircleArc(K_8, L_8, M_8) → f_5
  392. Line(N_8, O_8) → b
  393. Mirror(A_7, b) → P_8
  394. Mirror(C_8, b) → Q_8
  395. Mirror(B_5, b) → R_8
  396. CircumcircleArc(P_8, Q_8, R_8) → g_5
  397. Mirror(A'_{15}, b) → S_8
  398. Mirror(C'_{15}, b) → T_8
  399. Mirror(B'_{15}, b) → U_8
  400. CircumcircleArc(S_8, T_8, U_8) → h_5
  401. Mirror(A''_{10}, b) → V_8
  402. Mirror(C''_{10}, b) → W_8
  403. Mirror(B''_{10}, b) → Z_8
  404. CircumcircleArc(V_8, W_8, Z_8) → k_5
  405. Mirror(A'_{16}, b) → B_9
  406. Mirror(C'_{16}, b) → D_9
  407. Mirror(B'_{16}, b) → E_9
  408. CircumcircleArc(B_9, D_9, E_9) → p_5
  409. Mirror(A'_{17}, b) → F_9
  410. Mirror(C'_{17}, b) → G_9
  411. Mirror(B'_{17}, b) → H_9
  412. CircumcircleArc(F_9, G_9, H_9) → q_5
  413. Mirror(A''_{11}, b) → I_9
  414. Mirror(C''_{11}, b) → J_9
  415. Mirror(B''_{11}, b) → K_9
  416. CircumcircleArc(I_9, J_9, K_9) → r_5
  417. Mirror(D_5, b) → L_9
  418. Mirror(E_5, b) → M_9
  419. Mirror(F_5, b) → N_9
  420. CircumcircleArc(L_9, M_9, N_9) → s_5
  421. Mirror(G_5, b) → O_9
  422. Mirror(H_5, b) → P_9
  423. Mirror(I_5, b) → Q_9
  424. CircumcircleArc(O_9, P_9, Q_9) → t_5
  425. Mirror(D'_5, b) → R_9
  426. Mirror(E'_5, b) → S_9
  427. Mirror(F'_5, b) → T_9
  428. CircumcircleArc(R_9, S_9, T_9) → f_6
  429. Mirror(G'_5, b) → U_9
  430. Mirror(H'_5, b) → V_9
  431. Mirror(I'_5, b) → W_9
  432. CircumcircleArc(U_9, V_9, W_9) → g_6
  433. Mirror(A_8, b) → Z_9
  434. Mirror(C_9, b) → B_{10}
  435. Mirror(B_2, b) → D_{10}
  436. CircumcircleArc(Z_9, B_{10}, D_{10}) → h_6
  437. Mirror(A'_6, b) → E_{10}
  438. Mirror(C'_6, b) → F_{10}
  439. Mirror(B'_6, b) → G_{10}
  440. CircumcircleArc(E_{10}, F_{10}, G_{10}) → k_6
  441. Mirror(A''_4, b) → H_{10}
  442. Mirror(C''_4, b) → I_{10}
  443. Mirror(B''_4, b) → J_{10}
  444. CircumcircleArc(H_{10}, I_{10}, J_{10}) → p_6
  445. Mirror(A'_7, b) → K_{10}
  446. Mirror(C'_7, b) → L_{10}
  447. Mirror(B'_7, b) → M_{10}
  448. CircumcircleArc(K_{10}, L_{10}, M_{10}) → q_6
  449. Mirror(A'_8, b) → N_{10}
  450. Mirror(C'_8, b) → O_{10}
  451. Mirror(B'_8, b) → P_{10}
  452. CircumcircleArc(N_{10}, O_{10}, P_{10}) → r_6
  453. Mirror(A''_5, b) → Q_{10}
  454. Mirror(C''_5, b) → R_{10}
  455. Mirror(B''_5, b) → S_{10}
  456. CircumcircleArc(Q_{10}, R_{10}, S_{10}) → s_6
  457. Mirror(D_2, b) → T_{10}
  458. Mirror(E_2, b) → U_{10}
  459. Mirror(F_2, b) → V_{10}
  460. CircumcircleArc(T_{10}, U_{10}, V_{10}) → t_6
  461. Mirror(G_2, b) → W_{10}
  462. Mirror(H_2, b) → Z_{10}
  463. Mirror(I_2, b) → B_{11}
  464. CircumcircleArc(W_{10}, Z_{10}, B_{11}) → c_7
  465. Mirror(D'_2, b) → D_{11}
  466. Mirror(E'_2, b) → E_{11}
  467. Mirror(F'_2, b) → F_{11}
  468. CircumcircleArc(D_{11}, E_{11}, F_{11}) → d_7
  469. Mirror(G'_2, b) → G_{11}
  470. Mirror(H'_2, b) → H_{11}
  471. Mirror(I'_2, b) → I_{11}
  472. CircumcircleArc(G_{11}, H_{11}, I_{11}) → e_7
  473. Mirror(A_9, b) → J_{11}
  474. Mirror(C_{10}, b) → K_{11}
  475. Mirror(B_3, b) → L_{11}
  476. CircumcircleArc(J_{11}, K_{11}, L_{11}) → f_7
  477. Mirror(A'_9, b) → M_{11}
  478. Mirror(C'_9, b) → N_{11}
  479. Mirror(B'_9, b) → O_{11}
  480. CircumcircleArc(M_{11}, N_{11}, O_{11}) → g_7
  481. Mirror(A''_6, b) → P_{11}
  482. Mirror(C''_6, b) → Q_{11}
  483. Mirror(B''_6, b) → R_{11}
  484. CircumcircleArc(P_{11}, Q_{11}, R_{11}) → h_7
  485. Mirror(A'_{10}, b) → S_{11}
  486. Mirror(C'_{10}, b) → T_{11}
  487. Mirror(B'_{10}, b) → U_{11}
  488. CircumcircleArc(S_{11}, T_{11}, U_{11}) → k_7
  489. Mirror(A'_{11}, b) → V_{11}
  490. Mirror(C'_{11}, b) → W_{11}
  491. Mirror(B'_{11}, b) → Z_{11}
  492. CircumcircleArc(V_{11}, W_{11}, Z_{11}) → p_7
  493. Mirror(A''_7, b) → B_{12}
  494. Mirror(C''_7, b) → D_{12}
  495. Mirror(B''_7, b) → E_{12}
  496. CircumcircleArc(B_{12}, D_{12}, E_{12}) → q_7
  497. Mirror(D_3, b) → F_{12}
  498. Mirror(E_3, b) → G_{12}
  499. Mirror(F_3, b) → H_{12}
  500. CircumcircleArc(F_{12}, G_{12}, H_{12}) → r_7
  501. Mirror(G_3, b) → I_{12}
  502. Mirror(H_3, b) → J_{12}
  503. Mirror(I_3, b) → K_{12}
  504. CircumcircleArc(I_{12}, J_{12}, K_{12}) → s_7
  505. Mirror(D'_3, b) → L_{12}
  506. Mirror(E'_3, b) → M_{12}
  507. Mirror(F'_3, b) → N_{12}
  508. CircumcircleArc(L_{12}, M_{12}, N_{12}) → t_7
  509. Mirror(G'_3, b) → O_{12}
  510. Mirror(H'_3, b) → P_{12}
  511. Mirror(I'_3, b) → Q_{12}
  512. CircumcircleArc(O_{12}, P_{12}, Q_{12}) → c_8
  513. Mirror(A_{10}, b) → R_{12}
  514. Mirror(C_{11}, b) → S_{12}
  515. Mirror(B_6, b) → T_{12}
  516. CircumcircleArc(R_{12}, S_{12}, T_{12}) → d_8
  517. Mirror(A'_1, b) → U_{12}
  518. Mirror(C'_1, b) → V_{12}
  519. Mirror(B'_1, b) → W_{12}
  520. CircumcircleArc(U_{12}, V_{12}, W_{12}) → e_8
  521. Mirror(A''_1, b) → Z_{12}
  522. Mirror(C''_1, b) → B_{13}
  523. Mirror(B''_1, b) → D_{13}
  524. CircumcircleArc(Z_{12}, B_{13}, D_{13}) → f_8
  525. Mirror(A'_2, b) → E_{13}
  526. Mirror(C'_2, b) → F_{13}
  527. Mirror(B'_2, b) → G_{13}
  528. CircumcircleArc(E_{13}, F_{13}, G_{13}) → g_8
  529. Mirror(A'_{18}, b) → H_{13}
  530. Mirror(C'_{18}, b) → I_{13}
  531. Mirror(B'_{18}, b) → J_{13}
  532. CircumcircleArc(H_{13}, I_{13}, J_{13}) → h_8
  533. Mirror(A''_{12}, b) → K_{13}
  534. Mirror(C''_{12}, b) → L_{13}
  535. Mirror(B''_{12}, b) → M_{13}
  536. CircumcircleArc(K_{13}, L_{13}, M_{13}) → k_8
  537. Mirror(D_6, b) → N_{13}
  538. Mirror(E_6, b) → O_{13}
  539. Mirror(F_6, b) → P_{13}
  540. CircumcircleArc(N_{13}, O_{13}, P_{13}) → p_8
  541. Mirror(G_6, b) → Q_{13}
  542. Mirror(H_6, b) → R_{13}
  543. Mirror(I_6, b) → S_{13}
  544. CircumcircleArc(Q_{13}, R_{13}, S_{13}) → q_8
  545. Mirror(D'_6, b) → T_{13}
  546. Mirror(E'_6, b) → U_{13}
  547. Mirror(F'_6, b) → V_{13}
  548. CircumcircleArc(T_{13}, U_{13}, V_{13}) → r_8
  549. Mirror(G'_6, b) → W_{13}
  550. Mirror(H'_6, b) → Z_{13}
  551. Mirror(I'_6, b) → B_{14}
  552. CircumcircleArc(W_{13}, Z_{13}, B_{14}) → s_8
  553. Mirror(A_{11}, b) → D_{14}
  554. Mirror(C_{12}, b) → E_{14}
  555. Mirror(B_1, b) → F_{14}
  556. CircumcircleArc(D_{14}, E_{14}, F_{14}) → t_8
  557. Mirror(A'_3, b) → G_{14}
  558. Mirror(C'_3, b) → H_{14}
  559. Mirror(B'_3, b) → I_{14}
  560. CircumcircleArc(G_{14}, H_{14}, I_{14}) → c_9
  561. Mirror(A''_2, b) → J_{14}
  562. Mirror(C''_2, b) → K_{14}
  563. Mirror(B''_2, b) → L_{14}
  564. CircumcircleArc(J_{14}, K_{14}, L_{14}) → d_9
  565. Mirror(A'_4, b) → M_{14}
  566. Mirror(C'_4, b) → N_{14}
  567. Mirror(B'_4, b) → O_{14}
  568. CircumcircleArc(M_{14}, N_{14}, O_{14}) → e_9
  569. Mirror(A'_5, b) → P_{14}
  570. Mirror(C'_5, b) → Q_{14}
  571. Mirror(B'_5, b) → R_{14}
  572. CircumcircleArc(P_{14}, Q_{14}, R_{14}) → f_9
  573. Mirror(A''_3, b) → S_{14}
  574. Mirror(C''_3, b) → T_{14}
  575. Mirror(B''_3, b) → U_{14}
  576. CircumcircleArc(S_{14}, T_{14}, U_{14}) → g_9
  577. Mirror(D_1, b) → V_{14}
  578. Mirror(E_1, b) → W_{14}
  579. Mirror(F_1, b) → Z_{14}
  580. CircumcircleArc(V_{14}, W_{14}, Z_{14}) → h_9
  581. Mirror(G_1, b) → B_{15}
  582. Mirror(H_1, b) → D_{15}
  583. Mirror(I_1, b) → E_{15}
  584. CircumcircleArc(B_{15}, D_{15}, E_{15}) → k_9
  585. Mirror(D'_1, b) → F_{15}
  586. Mirror(E'_1, b) → G_{15}
  587. Mirror(F'_1, b) → H_{15}
  588. CircumcircleArc(F_{15}, G_{15}, H_{15}) → p_9
  589. Mirror(G'_1, b) → I_{15}
  590. Mirror(H'_1, b) → J_{15}
  591. Mirror(I'_1, b) → K_{15}
  592. CircumcircleArc(I_{15}, J_{15}, K_{15}) → q_9
  593. Mirror(E, b) → E'
  594. Mirror(F, b) → F'
  595. Mirror(G, b) → G'
  596. CircumcircleArc(E', F', G') → c'
  597. Mirror(H, b) → H'
  598. Mirror(I, b) → I'
  599. Mirror(J, b) → J'
  600. CircumcircleArc(H', I', J') → d'
  601. Mirror(K, b) → K'
  602. Mirror(L, b) → L'
  603. Mirror(M, b) → M'
  604. CircumcircleArc(K', L', M') → e'
  605. Mirror(N, b) → N'
  606. Mirror(O, b) → O'
  607. Mirror(P, b) → P'
  608. CircumcircleArc(N', O', P') → f'
  609. Mirror(Q, b) → Q'
  610. Mirror(R, b) → R'
  611. Mirror(S, b) → S'
  612. CircumcircleArc(Q', R', S') → g'
  613. Mirror(T, b) → T'
  614. Mirror(U, b) → U'
  615. Mirror(V, b) → V'
  616. CircumcircleArc(T', U', V') → h'
  617. Mirror(W, b) → W'
  618. Mirror(Z, b) → Z'
  619. Mirror(J_1, b) → L_{15}
  620. CircumcircleArc(W', Z', L_{15}) → k'
  621. Mirror(K_1, b) → M_{15}
  622. Mirror(L_1, b) → N_{15}
  623. Mirror(M_1, b) → O_{15}
  624. CircumcircleArc(M_{15}, N_{15}, O_{15}) → r'
  625. Mirror(N_1, b) → P_{15}
  626. Mirror(O_1, b) → Q_{15}
  627. Mirror(P_1, b) → R_{15}
  628. CircumcircleArc(P_{15}, Q_{15}, R_{15}) → s'
  629. Mirror(Q_1, b) → S_{15}
  630. Mirror(R_1, b) → T_{15}
  631. Mirror(S_1, b) → U_{15}
  632. CircumcircleArc(S_{15}, T_{15}, U_{15}) → t'
  633. Mirror(T_1, b) → V_{15}
  634. Mirror(U_1, b) → W_{15}
  635. Mirror(V_1, b) → Z_{15}
  636. CircumcircleArc(V_{15}, W_{15}, Z_{15}) → r_9
  637. Mirror(W_1, b) → B_{16}
  638. Mirror(Z_1, b) → D_{16}
  639. Mirror(J_2, b) → E_{16}
  640. CircumcircleArc(B_{16}, D_{16}, E_{16}) → s_9
  641. Mirror(K_2, b) → F_{16}
  642. Mirror(L_2, b) → G_{16}
  643. Mirror(M_2, b) → H_{16}
  644. CircumcircleArc(F_{16}, G_{16}, H_{16}) → t_9
  645. Mirror(N_2, b) → I_{16}
  646. Mirror(O_2, b) → J_{16}
  647. Mirror(P_2, b) → K_{16}
  648. CircumcircleArc(I_{16}, J_{16}, K_{16}) → c_{10}
  649. Mirror(Q_2, b) → L_{16}
  650. Mirror(R_2, b) → M_{16}
  651. Mirror(S_2, b) → N_{16}
  652. CircumcircleArc(L_{16}, M_{16}, N_{16}) → d_{10}
  653. Mirror(T_2, b) → O_{16}
  654. Mirror(U_2, b) → P_{16}
  655. Mirror(V_2, b) → Q_{16}
  656. CircumcircleArc(O_{16}, P_{16}, Q_{16}) → e_{10}
  657. Mirror(W_2, b) → R_{16}
  658. Mirror(Z_2, b) → S_{16}
  659. Mirror(J_3, b) → T_{16}
  660. CircumcircleArc(R_{16}, S_{16}, T_{16}) → f_{10}
  661. Mirror(K_3, b) → U_{16}
  662. Mirror(L_3, b) → V_{16}
  663. Mirror(M_3, b) → W_{16}
  664. CircumcircleArc(U_{16}, V_{16}, W_{16}) → g_{10}
  665. Mirror(N_3, b) → Z_{16}
  666. Mirror(O_3, b) → A_{17}
  667. Mirror(P_3, b) → B_{17}
  668. CircumcircleArc(Z_{16}, A_{17}, B_{17}) → h_{10}
  669. Mirror(Q_3, b) → D_{17}
  670. Mirror(R_3, b) → E_{17}
  671. Mirror(S_3, b) → F_{17}
  672. CircumcircleArc(D_{17}, E_{17}, F_{17}) → k_{10}
  673. Mirror(T_3, b) → G_{17}
  674. Mirror(U_3, b) → H_{17}
  675. Mirror(V_3, b) → I_{17}
  676. CircumcircleArc(G_{17}, H_{17}, I_{17}) → p_{10}
  677. Mirror(W_3, b) → J_{17}
  678. Mirror(Z_3, b) → K_{17}
  679. Mirror(B_4, b) → L_{17}
  680. CircumcircleArc(J_{17}, K_{17}, L_{17}) → q_{10}
  681. Mirror(D_4, b) → M_{17}
  682. Mirror(E_4, b) → N_{17}
  683. Mirror(F_4, b) → O_{17}
  684. CircumcircleArc(M_{17}, N_{17}, O_{17}) → r_{10}
  685. Mirror(G_4, b) → P_{17}
  686. Mirror(H_4, b) → Q_{17}
  687. Mirror(I_4, b) → R_{17}
  688. CircumcircleArc(P_{17}, Q_{17}, R_{17}) → s_{10}
  689. Mirror(J_4, b) → S_{17}
  690. Mirror(K_4, b) → T_{17}
  691. Mirror(L_4, b) → U_{17}
  692. CircumcircleArc(S_{17}, T_{17}, U_{17}) → t_{10}
  693. Mirror(M_4, b) → V_{17}
  694. Mirror(N_4, b) → W_{17}
  695. Mirror(O_4, b) → Z_{17}
  696. CircumcircleArc(V_{17}, W_{17}, Z_{17}) → c_{11}
  697. Mirror(P_4, b) → A_{18}
  698. Mirror(Q_4, b) → B_{18}
  699. Mirror(R_4, b) → C_{18}
  700. CircumcircleArc(A_{18}, B_{18}, C_{18}) → d_{11}
  701. Mirror(S_4, b) → D_{18}
  702. Mirror(T_4, b) → E_{18}
  703. Mirror(U_4, b) → F_{18}
  704. CircumcircleArc(D_{18}, E_{18}, F_{18}) → e_{11}
  705. Mirror(V_4, b) → G_{18}
  706. Mirror(W_4, b) → H_{18}
  707. Mirror(Z_4, b) → I_{18}
  708. CircumcircleArc(G_{18}, H_{18}, I_{18}) → f_{11}
  709. Mirror(J_5, b) → J_{18}
  710. Mirror(K_5, b) → K_{18}
  711. Mirror(L_5, b) → L_{18}
  712. CircumcircleArc(J_{18}, K_{18}, L_{18}) → g_{11}
  713. Mirror(M_5, b) → M_{18}
  714. Mirror(N_5, b) → N_{18}
  715. Mirror(O_5, b) → O_{18}
  716. CircumcircleArc(M_{18}, N_{18}, O_{18}) → h_{11}
  717. Mirror(P_5, b) → P_{18}
  718. Mirror(Q_5, b) → Q_{18}
  719. Mirror(R_5, b) → R_{18}
  720. CircumcircleArc(P_{18}, Q_{18}, R_{18}) → k_{11}
  721. Mirror(S_5, b) → S_{18}
  722. Mirror(T_5, b) → T_{18}
  723. Mirror(U_5, b) → U_{18}
  724. CircumcircleArc(S_{18}, T_{18}, U_{18}) → p_{11}
  725. Mirror(V_5, b) → V_{18}
  726. Mirror(W_5, b) → W_{18}
  727. Mirror(Z_5, b) → Z_{18}
  728. CircumcircleArc(V_{18}, W_{18}, Z_{18}) → q_{11}
  729. Mirror(J_6, b) → A_{19}
  730. Mirror(K_6, b) → B_{19}
  731. Mirror(L_6, b) → C_{19}
  732. CircumcircleArc(A_{19}, B_{19}, C_{19}) → r_{11}
  733. Mirror(M_6, b) → D_{19}
  734. Mirror(N_6, b) → E_{19}
  735. Mirror(O_6, b) → F_{19}
  736. CircumcircleArc(D_{19}, E_{19}, F_{19}) → s_{11}
  737. Mirror(P_6, b) → G_{19}
  738. Mirror(Q_6, b) → H_{19}
  739. Mirror(R_6, b) → I_{19}
  740. CircumcircleArc(G_{19}, H_{19}, I_{19}) → t_{11}
  741. Mirror(S_6, b) → J_{19}
  742. Mirror(T_6, b) → K_{19}
  743. Mirror(U_6, b) → L_{19}
  744. CircumcircleArc(J_{19}, K_{19}, L_{19}) → c_{12}
  745. Mirror(V_6, b) → M_{19}
  746. Mirror(W_6, b) → N_{19}
  747. Mirror(Z_6, b) → O_{19}
  748. CircumcircleArc(M_{19}, N_{19}, O_{19}) → d_{12}
  749. Mirror(B_7, b) → P_{19}
  750. Mirror(D_7, b) → Q_{19}
  751. Mirror(E_7, b) → R_{19}
  752. CircumcircleArc(P_{19}, Q_{19}, R_{19}) → e_{12}
  753. Mirror(F_7, b) → S_{19}
  754. Mirror(G_7, b) → T_{19}
  755. Mirror(H_7, b) → U_{19}
  756. CircumcircleArc(S_{19}, T_{19}, U_{19}) → f_{12}
  757. Mirror(I_7, b) → V_{19}
  758. Mirror(J_7, b) → W_{19}
  759. Mirror(K_7, b) → Z_{19}
  760. CircumcircleArc(V_{19}, W_{19}, Z_{19}) → g_{12}
  761. Mirror(L_7, b) → A_{20}
  762. Mirror(M_7, b) → B_{20}
  763. Mirror(N_7, b) → C_{20}
  764. CircumcircleArc(A_{20}, B_{20}, C_{20}) → h_{12}
  765. Mirror(O_7, b) → D_{20}
  766. Mirror(P_7, b) → E_{20}
  767. Mirror(Q_7, b) → F_{20}
  768. CircumcircleArc(D_{20}, E_{20}, F_{20}) → k_{12}
  769. Mirror(R_7, b) → G_{20}
  770. Mirror(S_7, b) → H_{20}
  771. Mirror(T_7, b) → I_{20}
  772. CircumcircleArc(G_{20}, H_{20}, I_{20}) → p_{12}
  773. Mirror(U_7, b) → J_{20}
  774. Mirror(V_7, b) → K_{20}
  775. Mirror(W_7, b) → L_{20}
  776. CircumcircleArc(J_{20}, K_{20}, L_{20}) → q_{12}
  777. Mirror(Z_7, b) → M_{20}
  778. Mirror(B_8, b) → N_{20}
  779. Mirror(D_8, b) → O_{20}
  780. CircumcircleArc(M_{20}, N_{20}, O_{20}) → r_{12}
  781. Mirror(E_8, b) → P_{20}
  782. Mirror(F_8, b) → Q_{20}
  783. Mirror(G_8, b) → R_{20}
  784. CircumcircleArc(P_{20}, Q_{20}, R_{20}) → s_{12}
  785. Mirror(H_8, b) → S_{20}
  786. Mirror(I_8, b) → T_{20}
  787. Mirror(J_8, b) → U_{20}
  788. CircumcircleArc(S_{20}, T_{20}, U_{20}) → t_{12}
  789. Mirror(K_8, b) → V_{20}
  790. Mirror(L_8, b) → W_{20}
  791. Mirror(M_8, b) → Z_{20}
  792. CircumcircleArc(V_{20}, W_{20}, Z_{20}) → c_{13}

AI Drawing Prompt Reference

Draw a symmetric pattern starting from an initial point. Reflect and rotate to create multiple symmetric points. Connect these points and draw arcs to form a complex symmetric design. The pattern consists of multiple arcs and symmetric points, illustrating the principles of axis symmetry and rotation transformations.
The prompt above was compiled from the original drawing commands and is for reference only.