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Interactive Decorations on the Cube

Interactive Decorations on the Cube
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2020-10-24 21:42
CircleSequenceSolid GeometryTransformationGeometric Construction
① This example demonstrates an interactive decorative pattern built on the surface of a 3D cube, where circles, semicircles, tangents, and mirrored elements can be dynamically adjusted by dragging points or sliders. ② Core mathematical concepts include solid geometry (cube structure), planar geometry (circles and tangents), symmetry transformations (mirroring), and the use of sequences and rotations to generate repeating patterns. ③ Construction highlights: from the summary, the GeoGebra commands used include Circle, Line, Intersect, Polygon, Vector, Midpoint, Segment, Point, CircumcircleArc, Mirror, OrthogonalLine, Semicircle, Tangent, Sequence, Rotate, and Cube, with numerous named objects (A, B_6, C, D, E, etc.) controlling geometric relationships. ④ Suitable for upper secondary or early university students exploring geometric constructions and transformations in 3D space, and also valuable as a mathematical art or interactive demonstration resource.

GeoGebra Commands & Parameters

  1. Circle(A, Zoom) → c
  2. Line(A, xAxis) → b
  3. Intersect(c, b) → B_6, C
  4. Line(A, yAxis) → d
  5. Intersect(c, d) → D, E
  6. Line(B_6, yAxis) → e
  7. Line(C, d) → f
  8. Line(D, b) → g
  9. Line(E, b) → h
  10. Intersect(g, e) → F
  11. Intersect(f, g) → G
  12. Intersect(h, f) → H
  13. Intersect(e, h) → I
  14. Polygon(F, G, H, I) → poly1, f_1, g_1, h_1, i
  15. Vector(I, H) → u
  16. Vector(I, F) → v
  17. Midpoint(F, A) → J
  18. Midpoint(A, G) → K
  19. Midpoint(F, J) → L
  20. Midpoint(L, J) → M
  21. Segment(M, A) → j
  22. Point(j) → N
  23. CircumcircleArc(D, N, B_6) → k
  24. Segment(D, E) → l
  25. Segment(B_6, C) → m
  26. Mirror(D, l) → D'
  27. Mirror(N, l) → N'_1
  28. Mirror(B_6, l) → B'
  29. CircumcircleArc(D', N'_1, B') → k'
  30. Mirror(D', m) → D''
  31. Mirror(N'_1, m) → N''_1
  32. Mirror(B', m) → B''
  33. CircumcircleArc(D'', N''_1, B'') → k''
  34. Mirror(D'', l) → D'''
  35. Mirror(N''_1, l) → N'''_1
  36. Mirror(B'', l) → B'''
  37. CircumcircleArc(D''', N'''_1, B''') → k'''
  38. Midpoint(F, D') → O
  39. Midpoint(F, B''') → P
  40. Midpoint(F, L) → Q
  41. Segment(Q, M) → p
  42. Point(p) → R_5
  43. OrthogonalLine(R_5, j) → q
  44. Intersect(q, f_1) → S
  45. Intersect(q, i) → T
  46. Mirror(S, p) → S'_1
  47. Mirror(R_5, p) → R'_1
  48. Midpoint(R_5, S) → U
  49. Mirror(U, j) → U'_1
  50. CircumcircleArc(L, U, S) → r
  51. Mirror(L, p) → L'_1
  52. Mirror(U, p) → U'_2
  53. Mirror(S, p) → S'_2
  54. CircumcircleArc(L'_1, U'_2, S'_2) → r'_1
  55. OrthogonalLine(N, j) → s
  56. Circle(N, Zoom / 2) → t
  57. Intersect(t, k) → V_5, W, ,
  58. Polygon(O, L'_1, U) → poly2, u_1, o, l'
  59. Mirror(O, p) → O'_1
  60. Mirror(L'_1, p) → L''_1
  61. Mirror(U, p) → U'_3
  62. Polygon(O'_1, L''_1, U'_3) → poly2'_1, u', o', l''
  63. CircumcircleArc(F, L''_1, O) → c_1
  64. Mirror(F, p) → F'_1
  65. Mirror(L''_1, p) → L'''_1
  66. Mirror(O, p) → O'_2
  67. CircumcircleArc(F'_1, L'''_1, O'_2) → d_1
  68. Intersect(t, j) → Z, A_1
  69. Midpoint(R_5, N) → B_1
  70. Segment(D', B''') → a_1
  71. Point(a_1) → C_1
  72. Mirror(C_1, j) → D_1
  73. CircumcircleArc(C_1, B_1, D_1) → e_1
  74. Midpoint(J, C_1) → E_1
  75. CircumcircleArc(B_1, E_1, R_5) → k_1
  76. Mirror(B_1, j) → F_1
  77. Mirror(E_1, j) → G_1
  78. Mirror(R_5, j) → R'_2
  79. CircumcircleArc(F_1, G_1, R'_2) → p_1
  80. Mirror(F, l) → F'_2
  81. Mirror(L''_1, l) → L'''_2
  82. Mirror(O, l) → O'_3
  83. CircumcircleArc(F'_2, L'''_2, O'_3) → q_1
  84. Mirror(F, l) → F'_3
  85. Mirror(L''_1, l) → L'''_3
  86. Mirror(O, l) → O'_4
  87. Mirror(L'_1, l) → L''_2
  88. Mirror(U'_2, l) → H_1
  89. Mirror(S'_2, l) → S''_1
  90. CircumcircleArc(L''_2, H_1, S''_1) → r''_1
  91. Mirror(L, l) → L'
  92. Mirror(U, l) → U'_4
  93. Mirror(S, l) → S'
  94. CircumcircleArc(L', U'_4, S') → r'
  95. Mirror(F, l) → F'
  96. Mirror(L''_1, l) → I_1
  97. Mirror(O, l) → O'_5
  98. Mirror(F'_1, l) → J_1
  99. Mirror(L'''_1, l) → K_1
  100. Mirror(O'_2, l) → L_1
  101. CircumcircleArc(J_1, K_1, L_1) → t_1
  102. Mirror(O, l) → O'
  103. Mirror(L'_1, l) → M_1
  104. Mirror(U, l) → U'
  105. Polygon(O', M_1, U') → poly2', u'_1, o'_1, m_1
  106. Mirror(O'_1, l) → N_1
  107. Mirror(L''_1, l) → O_1
  108. Mirror(U'_3, l) → P_1
  109. Polygon(N_1, O_1, P_1) → poly3, p_2, n_1, o_1
  110. Mirror(B_1, l) → Q_1
  111. Mirror(E_1, l) → R_1
  112. Mirror(R_5, l) → R'
  113. CircumcircleArc(Q_1, R_1, R') → c_2
  114. Mirror(F_1, l) → S_1
  115. Mirror(G_1, l) → T_1
  116. Mirror(R'_2, l) → U_1
  117. CircumcircleArc(S_1, T_1, U_1) → d_2
  118. Mirror(C_1, l) → V_1
  119. Mirror(B_1, l) → W_1
  120. Mirror(D_1, l) → Z_1
  121. CircumcircleArc(V_1, W_1, Z_1) → e_2
  122. Mirror(F'_2, m) → A_2
  123. Mirror(L'''_2, m) → B_2
  124. Mirror(O'_3, m) → C_2
  125. CircumcircleArc(A_2, B_2, C_2) → f_2
  126. Mirror(J_1, m) → D_2
  127. Mirror(K_1, m) → E_2
  128. Mirror(L_1, m) → F_2
  129. CircumcircleArc(D_2, E_2, F_2) → g_2
  130. Mirror(L''_2, m) → L'''_4
  131. Mirror(H_1, m) → G_2
  132. Mirror(S''_1, m) → S'''_1
  133. CircumcircleArc(L'''_4, G_2, S'''_1) → r'''_1
  134. Mirror(L', m) → L''
  135. Mirror(U'_4, m) → H_2
  136. Mirror(S', m) → S''
  137. CircumcircleArc(L'', H_2, S'') → r''
  138. Mirror(J_1, m) → I_2
  139. Mirror(K_1, m) → J_2
  140. Mirror(L_1, m) → K_2
  141. Mirror(J_1, m) → L_2
  142. Mirror(K_1, m) → M_2
  143. Mirror(L_1, m) → N_2
  144. Mirror(O', m) → O''
  145. Mirror(M_1, m) → O_2
  146. Mirror(U', m) → U''
  147. Polygon(O'', O_2, U'') → poly2'', u'', o'', o_2
  148. Mirror(O_1, m) → P_2
  149. Mirror(P_1, m) → Q_2
  150. Segment(P_2, Q_2) → b_1
  151. Mirror(N_1, m) → R_2
  152. Mirror(O_1, m) → S_2
  153. Mirror(P_1, m) → T_2
  154. Polygon(R_2, S_2, T_2) → poly3', t_2, r_2, s_2
  155. Mirror(Q_1, m) → U_2
  156. Mirror(R_1, m) → V_2
  157. Mirror(R', m) → R''
  158. CircumcircleArc(U_2, V_2, R'') → q_2
  159. Mirror(S_1, m) → W_2
  160. Mirror(T_1, m) → Z_2
  161. Mirror(U_1, m) → A_3
  162. CircumcircleArc(W_2, Z_2, A_3) → c_3
  163. Mirror(V_1, m) → B_3
  164. Mirror(W_1, m) → C_3
  165. Mirror(Z_1, m) → D_3
  166. CircumcircleArc(B_3, C_3, D_3) → d_3
  167. Mirror(A_2, l) → E_3
  168. Mirror(B_2, l) → F_3
  169. Mirror(C_2, l) → G_3
  170. CircumcircleArc(E_3, F_3, G_3) → e_3
  171. Mirror(L'''_4, l) → H_3
  172. Mirror(G_2, l) → I_3
  173. Mirror(S'''_1, l) → J_3
  174. CircumcircleArc(H_3, I_3, J_3) → f_3
  175. Mirror(B_3, l) → K_3
  176. Mirror(C_3, l) → L_3
  177. Mirror(D_3, l) → M_3
  178. CircumcircleArc(K_3, L_3, M_3) → g_3
  179. Mirror(U_2, l) → N_3
  180. Mirror(V_2, l) → O_3
  181. Mirror(R'', l) → R'''
  182. CircumcircleArc(N_3, O_3, R''') → h_3
  183. Mirror(W_2, l) → P_3
  184. Mirror(Z_2, l) → Q_3
  185. Mirror(A_3, l) → R_3
  186. CircumcircleArc(P_3, Q_3, R_3) → k_3
  187. Mirror(L'', l) → L'''
  188. Mirror(H_2, l) → S_3
  189. Mirror(S'', l) → S'''
  190. CircumcircleArc(L''', S_3, S''') → r'''
  191. Mirror(D_2, l) → T_3
  192. Mirror(E_2, l) → U_3
  193. Mirror(F_2, l) → V_3
  194. CircumcircleArc(T_3, U_3, V_3) → p_3
  195. Mirror(A_2, l) → W_3
  196. Mirror(B_2, l) → Z_3
  197. Mirror(C_2, l) → A_4
  198. Mirror(R_2, l) → B_4
  199. Mirror(S_2, l) → C_4
  200. Mirror(T_2, l) → D_4
  201. Polygon(B_4, C_4, D_4) → poly3'', d_4, b_4, c_4
  202. Mirror(O'', l) → O'''
  203. Mirror(O_2, l) → E_4
  204. Mirror(U'', l) → U'''
  205. Polygon(O''', E_4, U''') → poly2''', u''', o''', e_4
  206. Midpoint(N, A) → F_4
  207. Circle(A, F_4) → r_3
  208. Intersect(r_3, m) → G_4, H_4
  209. Intersect(r_3, l) → I_4, J_4
  210. Semicircle(H_4, I_4) → s_3
  211. Semicircle(I_4, G_4) → t_3
  212. Semicircle(G_4, J_4) → f_4
  213. Semicircle(J_4, H_4) → g_4
  214. Segment(N, A) → i_1
  215. Intersect(r_3, i_1, 1) → K_4
  216. Midpoint(N, K_4) → L_4
  217. Midpoint(L_4, K_4) → M_4
  218. Circle(A, M_4) → h_4
  219. Tangent(M_4, h_4) → j_1, l_1
  220. Intersect(j_1, l) → N_4
  221. Polygon(N, N_4, L_4) → poly4, l_4, n_2, n_4
  222. Mirror(L_4, i_1) → O_4
  223. Mirror(N, i_1) → N'_2
  224. Segment(O_4, N'_2) → a_2
  225. Mirror(N, i_1) → N'_3
  226. Mirror(N_4, i_1) → P_4
  227. Mirror(L_4, i_1) → Q_4
  228. Polygon(N'_3, P_4, Q_4) → poly4'_1, q_4, n', p_4
  229. Mirror(N'_3, m) → N''_2
  230. Mirror(P_4, m) → R_4
  231. Mirror(Q_4, m) → S_4
  232. Polygon(N''_2, R_4, S_4) → poly4''_1, s_4, n'', r_4
  233. Mirror(N, m) → N'
  234. Mirror(N_4, m) → T_4
  235. Mirror(L_4, m) → U_4
  236. Polygon(N', T_4, U_4) → poly4', u_4, n'_1, t_4
  237. Mirror(N', l) → N''
  238. Mirror(T_4, l) → V_4
  239. Mirror(U_4, l) → W_4
  240. Polygon(N'', V_4, W_4) → poly4'', w_4, n''_1, v_4
  241. Mirror(N''_2, l) → Z_4
  242. Mirror(R_4, l) → A_5
  243. Mirror(S_4, l) → B_5
  244. Polygon(Z_4, A_5, B_5) → poly5, b_5, z_4, a_5
  245. Mirror(Z_4, m) → C_5
  246. Mirror(A_5, m) → D_5
  247. Mirror(B_5, m) → E_5
  248. Polygon(C_5, D_5, E_5) → poly5', e_5, c_5, d_5
  249. Mirror(N'', m) → N'''
  250. Mirror(V_4, m) → F_5
  251. Mirror(W_4, m) → G_5
  252. Polygon(N''', F_5, G_5) → poly4''', g_5, n''', f_5
  253. Sequence(Sequence[CircumcircleArc[Translate[D, Vector[(s * u) + (t * v)]], Translate[N, Vector[(s * u) + (t * v)]], Translate[B_6, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste1
  254. Sequence(Sequence[CircumcircleArc[Translate[D', Vector[(s * u) + (t * v)]], Translate[N'_1, Vector[(s * u) + (t * v)]], Translate[B', Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste2
  255. Sequence(Sequence[Polygon[Translate[F, Vector[(s * u) + (t * v)]], Translate[G, Vector[(s * u) + (t * v)]], Translate[H, Vector[(s * u) + (t * v)]], Translate[I, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste3
  256. Sequence(Sequence[CircumcircleArc[Translate[D'', Vector[(s * u) + (t * v)]], Translate[N''_1, Vector[(s * u) + (t * v)]], Translate[B'', Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste4
  257. Sequence(Sequence[CircumcircleArc[Translate[D''', Vector[(s * u) + (t * v)]], Translate[N'''_1, Vector[(s * u) + (t * v)]], Translate[B''', Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste5
  258. Sequence(Sequence[CircumcircleArc[Translate[F, Vector[(s * u) + (t * v)]], Translate[L''_1, Vector[(s * u) + (t * v)]], Translate[O, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste6
  259. Sequence(Sequence[CircumcircleArc[Translate[F'_1, Vector[(s * u) + (t * v)]], Translate[L'''_1, Vector[(s * u) + (t * v)]], Translate[O'_2, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste7
  260. Sequence(Sequence[CircumcircleArc[Translate[J_1, Vector[(s * u) + (t * v)]], Translate[K_1, Vector[(s * u) + (t * v)]], Translate[L_1, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste8
  261. Sequence(Sequence[CircumcircleArc[Translate[F'_2, Vector[(s * u) + (t * v)]], Translate[L'''_2, Vector[(s * u) + (t * v)]], Translate[O'_3, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste9
  262. Sequence(Sequence[CircumcircleArc[Translate[L'''_4, Vector[(s * u) + (t * v)]], Translate[G_2, Vector[(s * u) + (t * v)]], Translate[S'''_1, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste10
  263. Sequence(Sequence[CircumcircleArc[Translate[L''_2, Vector[(s * u) + (t * v)]], Translate[H_1, Vector[(s * u) + (t * v)]], Translate[S''_1, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste11
  264. Sequence(Sequence[CircumcircleArc[Translate[L', Vector[(s * u) + (t * v)]], Translate[U'_4, Vector[(s * u) + (t * v)]], Translate[S', Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste12
  265. Sequence(Sequence[CircumcircleArc[Translate[L, Vector[(s * u) + (t * v)]], Translate[U, Vector[(s * u) + (t * v)]], Translate[S, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste13
  266. Sequence(Sequence[CircumcircleArc[Translate[L'_1, Vector[(s * u) + (t * v)]], Translate[U'_2, Vector[(s * u) + (t * v)]], Translate[S'_2, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste14
  267. Sequence(Sequence[CircumcircleArc[Translate[L'', Vector[(s * u) + (t * v)]], Translate[H_2, Vector[(s * u) + (t * v)]], Translate[S'', Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste15
  268. Sequence(Sequence[CircumcircleArc[Translate[A_2, Vector[(s * u) + (t * v)]], Translate[B_2, Vector[(s * u) + (t * v)]], Translate[C_2, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste16
  269. Sequence(Sequence[CircumcircleArc[Translate[D_2, Vector[(s * u) + (t * v)]], Translate[E_2, Vector[(s * u) + (t * v)]], Translate[F_2, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste17
  270. Sequence(Sequence[CircumcircleArc[Translate[T_3, Vector[(s * u) + (t * v)]], Translate[U_3, Vector[(s * u) + (t * v)]], Translate[V_3, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste18
  271. Sequence(Sequence[CircumcircleArc[Translate[E_3, Vector[(s * u) + (t * v)]], Translate[F_3, Vector[(s * u) + (t * v)]], Translate[G_3, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste19
  272. Sequence(Sequence[CircumcircleArc[Translate[L''', Vector[(s * u) + (t * v)]], Translate[S_3, Vector[(s * u) + (t * v)]], Translate[S''', Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste20
  273. Sequence(Sequence[CircumcircleArc[Translate[H_3, Vector[(s * u) + (t * v)]], Translate[I_3, Vector[(s * u) + (t * v)]], Translate[J_3, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste21
  274. Sequence(Sequence[CircumcircleArc[Translate[B_1, Vector[(s * u) + (t * v)]], Translate[E_1, Vector[(s * u) + (t * v)]], Translate[R_5, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste22
  275. Sequence(Sequence[CircumcircleArc[Translate[F_1, Vector[(s * u) + (t * v)]], Translate[G_1, Vector[(s * u) + (t * v)]], Translate[R'_2, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste23
  276. Sequence(Sequence[CircumcircleArc[Translate[C_1, Vector[(s * u) + (t * v)]], Translate[B_1, Vector[(s * u) + (t * v)]], Translate[D_1, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste24
  277. Sequence(Sequence[CircumcircleArc[Translate[V_1, Vector[(s * u) + (t * v)]], Translate[W_1, Vector[(s * u) + (t * v)]], Translate[Z_1, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste25
  278. Sequence(Sequence[CircumcircleArc[Translate[Q_1, Vector[(s * u) + (t * v)]], Translate[R_1, Vector[(s * u) + (t * v)]], Translate[R', Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste26
  279. Sequence(Sequence[CircumcircleArc[Translate[S_1, Vector[(s * u) + (t * v)]], Translate[T_1, Vector[(s * u) + (t * v)]], Translate[U_1, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste27
  280. Sequence(Sequence[CircumcircleArc[Translate[W_2, Vector[(s * u) + (t * v)]], Translate[Z_2, Vector[(s * u) + (t * v)]], Translate[A_3, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste28
  281. Sequence(Sequence[CircumcircleArc[Translate[U_2, Vector[(s * u) + (t * v)]], Translate[V_2, Vector[(s * u) + (t * v)]], Translate[R'', Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste29
  282. Sequence(Sequence[CircumcircleArc[Translate[B_3, Vector[(s * u) + (t * v)]], Translate[C_3, Vector[(s * u) + (t * v)]], Translate[D_3, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste30
  283. Sequence(Sequence[CircumcircleArc[Translate[K_3, Vector[(s * u) + (t * v)]], Translate[L_3, Vector[(s * u) + (t * v)]], Translate[M_3, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste31
  284. Sequence(Sequence[CircumcircleArc[Translate[P_3, Vector[(s * u) + (t * v)]], Translate[Q_3, Vector[(s * u) + (t * v)]], Translate[R_3, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste32
  285. Sequence(Sequence[CircumcircleArc[Translate[N_3, Vector[(s * u) + (t * v)]], Translate[O_3, Vector[(s * u) + (t * v)]], Translate[R''', Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste33
  286. Sequence(Sequence[Translate[h_4, Vector[(s * u) + (t * v)]], s, 0, n], t, 0, n) → liste34
  287. Sequence(Sequence[Translate[r_3, Vector[(s * u) + (t * v)]], s, 0, n], t, 0, n) → liste35
  288. Sequence(Sequence[Semicircle[Translate[H_4, Vector[(s * u) + (t * v)]], Translate[I_4, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste36
  289. Sequence(Sequence[Semicircle[Translate[J_4, Vector[(s * u) + (t * v)]], Translate[H_4, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste37
  290. Sequence(Sequence[Semicircle[Translate[I_4, Vector[(s * u) + (t * v)]], Translate[G_4, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste38
  291. Sequence(Sequence[Semicircle[Translate[G_4, Vector[(s * u) + (t * v)]], Translate[J_4, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste39
  292. Sequence(Sequence[Polygon[Translate[O, Vector[(s * u) + (t * v)]], Translate[L'_1, Vector[(s * u) + (t * v)]], Translate[U, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste40
  293. Sequence(Sequence[Polygon[Translate[O'_1, Vector[(s * u) + (t * v)]], Translate[L''_1, Vector[(s * u) + (t * v)]], Translate[U'_3, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste41
  294. Sequence(Sequence[Polygon[Translate[O', Vector[(s * u) + (t * v)]], Translate[M_1, Vector[(s * u) + (t * v)]], Translate[U', Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste42
  295. Sequence(Sequence[Polygon[Translate[N_1, Vector[(s * u) + (t * v)]], Translate[O_1, Vector[(s * u) + (t * v)]], Translate[P_1, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste43
  296. Sequence(Sequence[Polygon[Translate[R_2, Vector[(s * u) + (t * v)]], Translate[S_2, Vector[(s * u) + (t * v)]], Translate[T_2, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste44
  297. Sequence(Sequence[Polygon[Translate[O'', Vector[(s * u) + (t * v)]], Translate[O_2, Vector[(s * u) + (t * v)]], Translate[U'', Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste45
  298. Sequence(Sequence[Polygon[Translate[B_4, Vector[(s * u) + (t * v)]], Translate[C_4, Vector[(s * u) + (t * v)]], Translate[D_4, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste46
  299. Sequence(Sequence[Polygon[Translate[O''', Vector[(s * u) + (t * v)]], Translate[E_4, Vector[(s * u) + (t * v)]], Translate[U''', Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste47
  300. Sequence(Sequence[Polygon[Translate[N''', Vector[(s * u) + (t * v)]], Translate[F_5, Vector[(s * u) + (t * v)]], Translate[G_5, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste48
  301. Sequence(Sequence[Polygon[Translate[Z_4, Vector[(s * u) + (t * v)]], Translate[A_5, Vector[(s * u) + (t * v)]], Translate[B_5, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste49
  302. Sequence(Sequence[Polygon[Translate[C_5, Vector[(s * u) + (t * v)]], Translate[D_5, Vector[(s * u) + (t * v)]], Translate[E_5, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste50
  303. Sequence(Sequence[Polygon[Translate[N'', Vector[(s * u) + (t * v)]], Translate[V_4, Vector[(s * u) + (t * v)]], Translate[W_4, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste51
  304. Sequence(Sequence[Polygon[Translate[N', Vector[(s * u) + (t * v)]], Translate[T_4, Vector[(s * u) + (t * v)]], Translate[U_4, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste52
  305. Sequence(Sequence[Polygon[Translate[N''_2, Vector[(s * u) + (t * v)]], Translate[R_4, Vector[(s * u) + (t * v)]], Translate[S_4, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste53
  306. Sequence(Sequence[Polygon[Translate[N'_3, Vector[(s * u) + (t * v)]], Translate[P_4, Vector[(s * u) + (t * v)]], Translate[Q_4, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste54
  307. Sequence(Sequence[Polygon[Translate[N, Vector[(s * u) + (t * v)]], Translate[N_4, Vector[(s * u) + (t * v)]], Translate[L_4, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste55
  308. Sequence(Sequence[Polygon[Translate[F, Vector[(s * u) + (t * v)]], Translate[G, Vector[(s * u) + (t * v)]], Translate[H, Vector[(s * u) + (t * v)]], Translate[I, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste56
  309. Sequence(Sequence[CircumcircleArc[Translate[D', Vector[(s * u) + (t * v)]], Translate[N'_1, Vector[(s * u) + (t * v)]], Translate[B', Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste57
  310. Sequence(Sequence[CircumcircleArc[Translate[D, Vector[(s * u) + (t * v)]], Translate[N, Vector[(s * u) + (t * v)]], Translate[B_6, Vector[(s * u) + (t * v)]]], s, 0, n], t, 0, n) → liste58
  311. Line(I, H) → r_1
  312. Rotate(l1, 90°, r_1) → l1'
  313. Line(Mid, zAxis) → s_1
  314. Sequence(Rotate[l1', i, s_1], i, 0, (2 * π), (2 * π / 4)) → l2
  315. Cube(I, H_5, s_1) → w, I_5, face4, face5, face6, arête2, arête1, arête4, arête6, arête3, arête8, arête10, J_5, arête9, arête5, arête11, arête7, arête12, K_5, L_5, M_5, N_5, face1, face3, face2
  316. Rotate(l1', 90°, Line[K_5, L_5]) → l1''

AI Drawing Prompt Reference

Draw a decorative 2D pattern based on a circle centered at a draggable point A, with two perpendicular axes through A. Create intersection points where the circle meets each axis, then draw lines from these points aligned with the axes to generate additional intersection points and form a closed quadrilateral. Use vectors and several midpoints from key vertices to guide construction. Construct circumcircle arcs using three relevant points, then reflect these arc-defining elements across a chosen base line to obtain mirrored copies, repeating the reflection to build a multi-segment symmetric decoration. Finally, drop an orthogonal line from a constructed point to a chosen segment, intersect it with polygon edges, and use the resulting points to add localized mirrored details.
The prompt above was compiled from the original drawing commands and is for reference only.