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Kayseri Cifte Madrasah Geometric Pattern Construction

Kayseri Cifte Madrasah Geometric Pattern Construction
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2020-07-31 21:59
CirclePolygonFunctionTransformationGeometric Construction
In collections building muqarnas in GeoGebra
①This example demonstrates how to use GeoGebra's geometric transformation and construction commands to recreate the intricate geometric patterns, especially muqarnas-style symmetrical tessellations, from the architectural decoration of the Kayseri Cifte Madrasah in Turkey. ②Core mathematical concepts include rotation, scaling, polygon construction, set operations (intersection), functions and the unit circle, as well as iterative and conditional generation of repeating geometric units. ③Construction highlights: from the construction summary, commands such as Rotate, Intersect, Polygon, Dilate, Segment, and If are used, with objects like A, B, AB, BA and their rotated/scaled variants, along with composite shapes like Square1, TRhombus2, TSquare1, TAlmond14, which are combined to form symmetric decorative patterns. ④Suitable for high school and above, for teaching geometric transformations, symmetry, pattern design, or interdisciplinary lessons linking mathematics and architectural art, and as an advanced GeoGebra construction exercise.

GeoGebra Commands & Parameters

  1. Rotate(A, (-(90°)), B) → AB
  2. Rotate(B, 90°, A) → BA
  3. Rotate(B, 135°, A) → BAR
  4. Rotate(B, (-(135°)), A) → ABA
  5. Intersect(Ray[ABA, Rotate[A, 45°, ABA]], Ray[B, Rotate[A, (-(45°)), B]]) → ABAB
  6. Intersect(Ray[A, Rotate[B, 45°, A]], Ray[B, Rotate[A, (-(45°)), B]]) → ABH
  7. Intersect(Ray[A, Rotate[B, 67.5°, A]], Ray[B, Rotate[A, (-(67.5°)), B]]) → ABHR
  8. Intersect(Ray[B, Rotate[A, (-(22.5°)), B]], Ray[BA, Rotate[A, 22.5°, BA]]) → ABL
  9. Rotate(A, (-(45°)), B) → ABR
  10. Intersect(OrthogonalLine[BAR, Line[A, B]], OrthogonalLine[B, Line[A, BAR]]) → ABT
  11. Rotate(B, 135°, A) → BBA
  12. Intersect(Ray[B, Rotate[A, (-(67.5°)), B]], Ray[BBA, Rotate[A, 67.5°, BBA]]) → BAJ
  13. Intersect(OrthogonalLine[BAR, Line[A, BAR]], OrthogonalLine[B, Line[A, B]]) → BARB
  14. Intersect(OrthogonalLine[B, Line[A, B]], OrthogonalLine[BBA, Line[BBA, A]]) → BBAB
  15. Polygon(A, B, AB, BA) → Square1, a, b, ab, ba
  16. Dilate(A, 75, Centroid[Square1]) → A'
  17. Dilate(B, 75, Centroid[Square1]) → B'
  18. Dilate(AB, 75, Centroid[Square1]) → AB'
  19. Dilate(BA, 75, Centroid[Square1]) → BA'
  20. Polygon(Dilate[A, 0.75, Centroid[Square1]], Dilate[B, 0.75, Centroid[Square1]], Dilate[AB, 0.75, Centroid[Square1]], Dilate[BA, 0.75, Centroid[Square1]]) → Square1', f, g, i, j
  21. Segment(A, AB) → k
  22. Segment(B, AB) → l
  23. Segment(BA, AB) → m
  24. Segment(A, BA) → n
  25. Segment(A, B) → p
  26. Polygon(A, B, ABR, BAR) → Rhombus2, a_1, b_1, abr, bar
  27. Dilate(A, 0.75, Centroid[Rhombus2]) → A'_1
  28. Dilate(B, 0.75, Centroid[Rhombus2]) → B'_1
  29. Dilate(ABR, 0.75, Centroid[Rhombus2]) → ABR'
  30. Dilate(BAR, 0.75, Centroid[Rhombus2]) → BAR'
  31. Polygon(A'_1, B'_1, ABR', BAR') → Rhombus2', a'_1, b'_1, abr', bar'
  32. Segment(A, BAR) → r
  33. Segment(B, BAR) → s
  34. Segment(B, ABR) → t
  35. Segment(B, A) → c
  36. Polygon(A, B, BBAB, BBA) → Almond3, a_2, b_2, bbab, bba
  37. Dilate(A, 0.75, Centroid[Almond3]) → A'_2
  38. Dilate(B, 0.75, Centroid[Almond3]) → B'_2
  39. Dilate(BBAB, 0.75, Centroid[Almond3]) → BBAB'
  40. Dilate(BBA, 0.75, Centroid[Almond3]) → BBA'
  41. Polygon(A'_2, B'_2, BBAB', BBA') → Almond3', a'_2, b'_2, bbab', bba'
  42. Segment(A, BBAB) → d
  43. Segment(B, BBAB) → e
  44. Segment(BBA, BBAB) → f_1
  45. Polygon(A, B, ABT, BAR) → SmBiped9, a_3, b_3, abt, g_1
  46. Dilate(A, 0.75, Centroid[SmBiped9]) → A'_3
  47. Dilate(B, 0.75, Centroid[SmBiped9]) → B'_3
  48. Dilate(ABT, 0.75, Centroid[SmBiped9]) → ABT'
  49. Dilate(BAR, 0.75, Centroid[SmBiped9]) → BAR'_1
  50. Polygon(A'_3, B'_3, ABT', BAR'_1) → SmBiped9', a'_3, b'_3, abt', bar'_1
  51. Segment(A, B) → h_1
  52. Segment(A, BAR) → i_1
  53. Segment(A, ABT) → j_1
  54. Polygon(A, B, BAJ, BBA) → Jug4, a_4, b_4, baj, k_1
  55. Dilate(A, 0.75, Centroid[Jug4]) → A'_4
  56. Dilate(B, 0.75, Centroid[Jug4]) → B'_4
  57. Dilate(BAJ, 0.75, Centroid[Jug4]) → BAJ'
  58. Dilate(BBA, 0.75, Centroid[Jug4]) → BBA'_1
  59. Polygon(A'_4, B'_4, BAJ', BBA'_1) → Jug4', a'_4, b'_4, baj', bba'_1
  60. Segment(A, BAJ) → l_1
  61. Segment(BBA, BAJ) → m_1
  62. Segment(B, BAJ) → n_1
  63. Polygon(A, B, ABL, BA) → LBiped10, a_5, b_5, abl, p_1
  64. Dilate(A, 0.75, Centroid[LBiped10]) → A'_5
  65. Dilate(B, 0.75, Centroid[LBiped10]) → B'_5
  66. Dilate(ABL, 0.75, Centroid[LBiped10]) → ABL'
  67. Dilate(BA, 0.75, Centroid[LBiped10]) → BA'_1
  68. Polygon(A'_5, B'_5, ABL', BA'_1) → LBiped10', a'_5, b'_5, abl', ba'_1
  69. Segment(A, B) → q_1
  70. Segment(A, BA) → r_1
  71. Segment(A, ABL) → s_1
  72. Polygon(A, B, ABH) → HSquare5, abh, a_6, b_6
  73. Dilate(A, 0.75, Centroid[HSquare5]) → A'_6
  74. Dilate(B, 0.75, Centroid[HSquare5]) → B'_6
  75. Dilate(ABH, 0.75, Centroid[HSquare5]) → ABH'
  76. Polygon(A'_6, B'_6, ABH') → HSquare5', abh', a'_6, b'_6
  77. Segment(Midpoint[A, B], ABH) → t_1
  78. Segment(A, ABH) → c_1
  79. Segment(B, ABH) → d_1
  80. Polygon(A, B, BA) → HSquare11, e_1, a_7, b_7
  81. Dilate(A, 0.75, Centroid[HSquare11]) → A'_7
  82. Dilate(B, 0.75, Centroid[HSquare11]) → B'_7
  83. Dilate(BA, 0.75, Centroid[HSquare11]) → BA'_2
  84. Polygon(A'_7, B'_7, BA'_2) → HSquare11', ba'_2, a'_7, b'_7
  85. Segment(A, Midpoint[BA, B]) → f_2
  86. Segment(A, BA) → g_2
  87. Segment(A, B) → h_2
  88. Polygon(A, B, ABHR) → HRhombus6, abhr, a_8, b_8
  89. Dilate(A, 0.75, Centroid[HRhombus6]) → A'_8
  90. Dilate(B, 0.75, Centroid[HRhombus6]) → B'_8
  91. Dilate(ABHR, 0.75, Centroid[HRhombus6]) → ABHR'
  92. Polygon(A'_8, B'_8, ABHR') → HRhombus6', abhr', a'_8, b'_8
  93. Segment(Midpoint[A, B], ABHR) → i_2
  94. Segment(A, ABHR) → j_2
  95. Segment(B, ABHR) → k_2
  96. Polygon(A, B, BAR) → HRhombus12, l_2, a_9, b_9
  97. Dilate(A, 0.75, Centroid[HRhombus12]) → A'_9
  98. Dilate(B, 0.75, Centroid[HRhombus12]) → B'_9
  99. Dilate(BAR, 0.75, Centroid[HRhombus12]) → BAR'_2
  100. Polygon(A'_9, B'_9, BAR'_2) → HRhombus12', bar'_2, a'_9, b'_9
  101. Segment(A, Midpoint[BAR, B]) → m_2
  102. Segment(A, BAR) → n_2
  103. Segment(A, B) → p_2
  104. Polygon(ABA, A, B, ABAB) → SmBiped13, aba, a_{10}, b_{10}, abab
  105. Dilate(ABA, 0.75, Centroid[SmBiped13]) → ABA'
  106. Dilate(A, 0.75, Centroid[SmBiped13]) → A'_{10}
  107. Dilate(B, 0.75, Centroid[SmBiped13]) → B'_{10}
  108. Dilate(ABAB, 0.75, Centroid[SmBiped13]) → ABAB'
  109. Polygon(ABA', A'_{10}, B'_{10}, ABAB') → SmBiped13', aba', a'_{10}, b'_{10}, abab'
  110. Segment(ABA, ABAB) → q_2
  111. Segment(A, ABAB) → r_2
  112. Segment(B, ABAB) → s_2
  113. Polygon(A, B, BARB, BAR) → Almond14, a_{11}, b_{11}, barb, t_2
  114. Dilate(A, 0.75, Centroid[Almond14]) → A'_{11}
  115. Dilate(B, 0.75, Centroid[Almond14]) → B'_{11}
  116. Dilate(BARB, 0.75, Centroid[Almond14]) → BARB'
  117. Dilate(BAR, 0.75, Centroid[Almond14]) → BAR'_3
  118. Polygon(A'_{11}, B'_{11}, BARB', BAR'_3) → Almond14', a'_{11}, b'_{11}, barb', bar'_3
  119. Segment(A, B) → c_2
  120. Segment(A, BARB) → d_2
  121. Segment(A, BAR) → e_2
  122. If(toon_{max}, "3D only", "layer = " + toon_{lagen}) → toon_{lagen-tekst}
  123. Segment(BAR, ABR) → q
  124. Segment(A, ABR) → g_3
  125. Segment(A, B) → h_3
  126. Segment(A, BAR) → i_3
  127. Polygon(D, E, EE, DD) → achter1, d_3, e_3, ee, dd
  128. Polygon(C, CC, DD, D) → achter2, c_3, cc, j_3, d_4
  129. Polygon(EE, EC, DD) → Square1boven1, k_3, l_3, ec
  130. Polygon(CC, EC, DD) → Square1boven2, m_3, n_3, p_3
  131. Polygon(EE, ECA, DD) → Almond3boven1, q_3, r_3, eca
  132. Polygon(CC, ECA, DD) → Almond3boven2, s_3, t_3, f_4
  133. Polygon(EE, ECJ, DD) → Jug4boven1, g_4, h_4, ecj
  134. Polygon(CC, ECJ, DD) → Jug4boven2, i_4, j_4, k_4
  135. Polygon(CC, DD, CDHS) → HSquare5boven, cdhs, l_4, m_4
  136. Polygon(CC, DD, CDHR) → HRhombusboven, cdhr, n_4, p_4
  137. Polygon(EE, ECSB, DD) → SmBiped2boven1, q_4, r_4, ecsb
  138. Polygon(DD, ECSB, CC) → SmBiped2boven2, s_4, t_4, c_4
  139. Intersect(Line[C, Line[D, E]], Line[E, Line[D, C]]) → CE
  140. Polygon(DU, E, CE) → Square7boven1, ce, du, e_4
  141. Polygon(DU, CE, C) → Square7boven2, c_5, f_5, g_5
  142. Intersect(Line[C, Rotate[D, 45°, Line[C, C + (0, 0, 1)]]], Line[E, Rotate[D, (-(45°)), Line[E, E + (0, 0, 1)]]]) → CESB
  143. Polygon(DU, E, CESB) → SmBiped9boven1, cesb, h_5, e_5
  144. Polygon(DU, CESB, C) → SmBiped9boven2, c_6, i_5, j_5
  145. Intersect(Line[C, Rotate[D, 22.5°, Line[C, C + (0, 0, 1)]]], Line[E, Rotate[D, (-(22.5°)), Line[E, E + (0, 0, 1)]]]) → CELB
  146. Polygon(DU, E, CELB) → LBiped10boven1, celb, k_5, e_6
  147. Polygon(DU, CELB, C) → LBiped10boven2, c_7, l_5, m_5
  148. Intersect(Line[C, Rotate[D, 90°, Line[C, C + (0, 0, 1)]]], Line[E, Rotate[D, (-(90°)), Line[E, E + (0, 0, 1)]]]) → CEA
  149. Polygon(DU, E, CEA) → Almond14onder1, cea, p_5, e_8
  150. Polygon(DU, CEA, C) → Almond14onder2, c_9, q_5, r_5
  151. Left1(F) → G
  152. LeftSqrt2(G) → H
  153. Left1(H) → I
  154. TRhombus2(J, I) → K, L, h_6, vierhoek1, vierhoek2, n_5, s_5, t_5, d_5, f_6, g_6
  155. Up1(L) → M
  156. UpSqrt2(K) → N
  157. TRhombus2(M, L) → O, P, p_6, vierhoek3, vierhoek4, i_6, j_6, k_6, l_6, m_6, n_6
  158. TRhombus2(Q, P) → R, S, g_7, vierhoek5, vierhoek6, q_6, r_6, s_6, t_6, d_6, f_7
  159. Right1(S) → T
  160. TRhombus2(T, S) → U, V, n_7, vierhoek7, vierhoek8, h_7, i_7, j_7, k_7, l_7, m_7
  161. TRhombus2(W, V) → Z, A_1, e_7, vierhoek9, vierhoek10, p_7, q_7, r_7, s_7, t_7, d_7
  162. Right1(A_1) → B_1
  163. TRhombus2(B_1, A_1) → C_1, D_1, l_8, vierhoek11, vierhoek12, f_8, g_8, h_8, i_8, j_8, k_8
  164. TRhombus2(E_1, D_1) → F_1, G_1, t_8, vierhoek13, vierhoek14, m_8, n_8, p_8, q_8, r_8, s_8
  165. Down1(G_1) → H_1
  166. TRhombus2(H_1, G_1) → I_1, J_1, j_9, vierhoek15, vierhoek16, c_8, d_8, f_9, g_9, h_9, i_9
  167. TSquare1(L, K) → K_1, L_1, r_9, vierhoek17, vierhoek18, k_9, l_9, m_9, n_9, p_9, q_9
  168. TSquare1(P, N) → M_1, N_1, h_{10}, vierhoek19, vierhoek20, s_9, t_9, d_9, e_9, f_{10}, g_{10}
  169. TSquare1(S, R) → O_1, P_1, p_{10}, vierhoek21, vierhoek22, i_{10}, j_{10}, k_{10}, l_{10}, m_{10}, n_{10}
  170. TSquare1(A_1, Z) → Q_1, R_1, e_{10}, vierhoek23, vierhoek24, q_{10}, r_{10}, s_{10}, t_{10}, c_{10}, d_{10}
  171. TSquare1(D_1, C_1) → S_1, T_1, l_{11}, vierhoek25, vierhoek26, f_{11}, g_{11}, h_{11}, i_{11}, j_{11}, k_{11}
  172. TSquare1(G_1, F_1) → U_1, V_1, t_{11}, vierhoek27, vierhoek28, m_{11}, n_{11}, p_{11}, q_{11}, r_{11}, s_{11}
  173. TAlmond14(I_1, U_1) → W_1, Z_1, vierhoek29, vierhoek30, c_{11}, d_{11}, e_{11}, f_{12}, g_{12}, h_{12}
  174. TAlmond14(F_1, S_1) → A_2, B_2, vierhoek31, vierhoek32, i_{12}, j_{12}, k_{12}, l_{12}, m_{12}, n_{12}
  175. TAlmond14(C_1, Q_1) → C_2, D_2, vierhoek33, vierhoek34, p_{12}, q_{12}, r_{12}, s_{12}, t_{12}, a_{12}
  176. Down1(Z) → E_2
  177. TAlmond14(Z, E_2) → F_2, G_2, vierhoek35, vierhoek36, b_{12}, c_{12}, d_{12}, e_{12}, f_{13}, g_{13}
  178. TAlmond14(U, O_1) → H_2, I_2, vierhoek37, vierhoek38, h_{13}, i_{13}, j_{13}, k_{13}, l_{13}, m_{13}
  179. TAlmond14(R, M_1) → J_2, K_2, vierhoek39, vierhoek40, n_{13}, p_{13}, q_{13}, r_{13}, s_{13}, t_{13}
  180. TAlmond14(N, K_1) → L_2, M_2, vierhoek41, vierhoek42, a_{13}, b_{13}, c_{13}, d_{13}, e_{13}, f_{14}
  181. Right1(K) → N_2
  182. TAlmond14(K, N_2) → O_2, P_2, vierhoek43, vierhoek44, g_{14}, h_{14}, i_{14}, j_{14}, k_{14}, l_{14}
  183. TRhombus2(N_2, H) → Q_2, R_2, t_{14}, vierhoek45, vierhoek46, m_{14}, n_{14}, p_{14}, q_{14}, r_{14}, s_{14}
  184. TSmBiped13(P_2, N_2) → S_2, T_2, g_{15}, vierhoek47, vierhoek48, a_{14}, b_{14}, c_{14}, d_{14}, e_{14}, f_{15}
  185. TSmBiped13(M_2, K_1) → U_2, V_2, n_{15}, vierhoek49, vierhoek50, h_{15}, i_{15}, j_{15}, k_{15}, l_{15}, m_{15}
  186. TSmBiped13(K_2, M_1) → W_2, Z_2, b_{15}, vierhoek51, vierhoek52, p_{15}, q_{15}, r_{15}, s_{15}, t_{15}, a_{15}
  187. TSmBiped13(I_2, O_1) → A_3, B_3, i_{16}, vierhoek53, vierhoek54, c_{15}, d_{15}, e_{15}, f_{16}, g_{16}, h_{16}
  188. TSmBiped13(G_2, E_2) → C_3, D_3, q_{16}, vierhoek55, vierhoek56, j_{16}, k_{16}, l_{16}, m_{16}, n_{16}, p_{16}
  189. TSmBiped13(D_2, Q_1) → E_3, F_3, d_{16}, vierhoek57, vierhoek58, r_{16}, s_{16}, t_{16}, a_{16}, b_{16}, c_{16}
  190. TSmBiped13(B_2, S_1) → G_3, H_3, k_{17}, vierhoek59, vierhoek60, e_{16}, f_{17}, g_{17}, h_{17}, i_{17}, j_{17}
  191. TSmBiped13(Z_1, U_1) → I_3, J_3, s_{17}, vierhoek61, vierhoek62, l_{17}, m_{17}, n_{17}, p_{17}, q_{17}, r_{17}
  192. TRhombus2(W_1, D_3) → K_3, L_3, f_{18}, vierhoek63, vierhoek64, t_{17}, a_{17}, b_{17}, c_{17}, d_{17}, e_{17}
  193. TRhombus2(H_2, R_2) → M_3, N_3, m_{18}, vierhoek65, vierhoek66, g_{18}, h_{18}, i_{18}, j_{18}, k_{18}, l_{18}
  194. TRhombus2(E_2, N_3) → O_3, P_3, a_{18}, vierhoek67, vierhoek68, n_{18}, p_{18}, q_{18}, r_{18}, s_{18}, t_{18}
  195. TSquare1(R_2, Q_2) → Q_3, R_3, h_{19}, vierhoek69, vierhoek70, b_{18}, c_{18}, d_{18}, e_{18}, f_{19}, g_{19}
  196. TSquare1(N_3, M_3) → S_3, T_3, p_{19}, vierhoek71, vierhoek72, i_{19}, j_{19}, k_{19}, l_{19}, m_{19}, n_{19}
  197. TSquare1(D_3, O_3) → U_3, V_3, c_{19}, vierhoek73, vierhoek74, q_{19}, r_{19}, s_{19}, t_{19}, a_{19}, b_{19}
  198. TAlmond14(O_3, S_3) → W_3, Z_3, vierhoek75, vierhoek76, d_{19}, e_{19}, f_{20}, g_{20}, h_{20}, i_{20}
  199. TAlmond14(M_3, Q_3) → A_4, B_4, vierhoek77, vierhoek78, j_{20}, k_{20}, l_{20}, m_{20}, n_{20}, p_{20}
  200. TAlmond14(Q_2, G) → C_4, D_4, vierhoek79, vierhoek80, q_{20}, r_{20}, s_{20}, t_{20}, a_{20}, b_{20}
  201. TAlmond14(K_3, U_3) → E_4, F_4, vierhoek81, vierhoek82, c_{20}, d_{20}, e_{20}, f_{21}, g_{21}, h_{21}
  202. TSmBiped13(D_4, G) → G_4, H_4, p_{21}, vierhoek83, vierhoek84, i_{21}, j_{21}, k_{21}, l_{21}, m_{21}, n_{21}
  203. TSmBiped13(B_4, Q_3) → I_4, J_4, c_{21}, vierhoek85, vierhoek86, q_{21}, r_{21}, s_{21}, t_{21}, a_{21}, b_{21}
  204. TSmBiped13(Z_3, S_3) → K_4, L_4, j_{22}, vierhoek87, vierhoek88, d_{21}, e_{21}, f_{22}, g_{22}, h_{22}, i_{22}
  205. TSmBiped13(F_4, U_3) → M_4, N_4, r_{22}, vierhoek89, vierhoek90, k_{22}, l_{22}, m_{22}, n_{22}, p_{22}, q_{22}
  206. THSquare5(K, I) → O_4, driehoek1, driehoek2, s_{22}, t_{22}, a_{22}, b_{22}, c_{22}, d_{22}
  207. THSquare5(V, U) → P_4, driehoek3, driehoek4, e_{22}, f_{23}, g_{23}, h_{23}, i_{23}, j_{23}
  208. THSquare5(Z, V) → Q_4, driehoek5, driehoek6, k_{23}, l_{23}, m_{23}, n_{23}, p_{23}, q_{23}
  209. THSquare5(J_1, I_1) → R_4, driehoek7, driehoek8, r_{23}, s_{23}, t_{23}, a_{23}, b_{23}, c_{23}
  210. ERhombus2(J_1, H_1, G_1) → S_4, T_4, U_4, vierhoek91, vierhoek92, driehoek9, driehoek10
  211. ERhombus2(G_1, E_1, D_1) → V_4, W_4, Z_4, vierhoek93, vierhoek94, driehoek11, driehoek12
  212. ERhombus2(D_1, B_1, A_1) → A_5, B_5, C_5, vierhoek95, vierhoek96, driehoek13, driehoek14
  213. ERhombus2(A_1, W, V) → D_5, E_5, F_5, vierhoek97, vierhoek98, driehoek15, driehoek16
  214. ERhombus2(V, T, S) → G_5, H_5, I_5, vierhoek99, vierhoek100, driehoek17, driehoek18
  215. ERhombus2(S, Q, P) → J_5, K_5, L_5, vierhoek101, vierhoek102, driehoek19, driehoek20
  216. ERhombus2(P, M, L) → M_5, N_5, O_5, vierhoek103, vierhoek104, driehoek21, driehoek22
  217. ERhombus2(L, J, I) → P_5, Q_5, R_5, vierhoek105, vierhoek106, driehoek23, driehoek24
  218. Polygon(C_6, T_4, S_4) → driehoek25, d_{23}, e_{23}, f_{24}
  219. Polygon(D_6, T_4, V_4) → driehoek26, v_4, g_{24}, h_{24}
  220. Polygon(D_6, W_4, V_4) → driehoek27, i_{24}, j_{24}, w_4
  221. Polygon(V_5, A_5, W_4) → driehoek28, k_{24}, v_5, l_{24}
  222. Polygon(V_5, B_5, A_5) → driehoek29, m_{24}, n_{24}, p_{24}
  223. Polygon(W_5, B_5, D_5) → driehoek30, q_{24}, w_5, r_{24}
  224. Polygon(W_5, E_5, D_5) → driehoek31, s_{24}, t_{24}, a_{24}
  225. Polygon(G_5, Z_5, E_5) → driehoek32, b_{24}, c_{24}, z_5
  226. Polygon(Z_5, G_5, H_5) → driehoek33, d_{24}, e_{24}, f_{25}
  227. Polygon(A_6, H_5, J_5) → driehoek34, g_{25}, h_{25}, i_{25}
  228. Polygon(A_6, J_5, K_5) → driehoek35, j_{25}, k_{25}, l_{25}
  229. Polygon(B_6, R_5, Q_5) → driehoek36, m_{25}, n_{25}, p_{25}
  230. Polygon(S_5, Q_5, P_5) → driehoek37, q_{25}, r_{25}, s_{25}
  231. Polygon(S_5, P_5, N_5) → driehoek38, t_{25}, a_{25}, b_{25}
  232. Polygon(T_5, M_5, K_5) → driehoek39, c_{25}, d_{25}, e_{25}
  233. Polygon(T_5, N_5, M_5) → driehoek40, f_{26}, g_{26}, h_{26}
  234. ESquare1(T_4, D_6, W_4) → U_5, E_6, F_6, vierhoek107, vierhoek108, driehoek41, driehoek42
  235. ESquare1(W_4, V_5, B_5) → G_6, H_6, I_6, vierhoek109, vierhoek110, driehoek43, driehoek44
  236. ESquare1(B_5, W_5, E_5) → J_6, K_6, L_6, vierhoek111, vierhoek112, driehoek45, driehoek46
  237. ESquare1(H_5, A_6, K_5) → M_6, N_6, O_6, vierhoek113, vierhoek114, driehoek47, driehoek48
  238. ESquare1(K_5, T_5, N_5) → P_6, Q_6, R_6, vierhoek115, vierhoek116, driehoek49, driehoek50
  239. ESquare1(N_5, S_5, Q_5) → S_6, T_6, U_6, vierhoek117, vierhoek118, driehoek51, driehoek52
  240. EHSquare5(E_5, Z_5) → V_6, W_6, Z_6, vierhoek119, driehoek53
  241. EHSquare5(Z_5, H_5) → A_7, B_7, C_7, vierhoek120, driehoek54
  242. EHSquare5(Q_5, B_6) → D_7, E_7, F_7, vierhoek121, driehoek55
  243. EHSquare5(C_6, T_4) → G_7, H_7, I_7, vierhoek122, driehoek56
  244. EAlmond14(F_6, R_7, I_6) → V_7, driehoek59, driehoek60
  245. EAlmond14(I_6, Q_7, L_6) → W_7, driehoek61, driehoek62
  246. EAlmond14(O_6, L_7, R_6) → Z_7, driehoek63, driehoek64
  247. EAlmond14(R_6, K_7, U_6) → A_8, driehoek65, driehoek66
  248. EAlmond14(D_8, S_7, F_6) → E_8, driehoek57, driehoek58
  249. EAlmond14(U_6, J_7, U_7) → F_8, driehoek67, driehoek68
  250. EAlmond14(B_8, O_7, O_6) → G_8, driehoek69, driehoek70
  251. EAlmond14(L_6, P_7, C_8) → H_8, driehoek71, driehoek72
  252. Polygon(B_7, C_7, B_8) → driehoek73, i_{26}, j_{26}, k_{26}
  253. Polygon(C_8, V_6, Z_6) → driehoek74, z_6, l_{26}, v_6
  254. Polygon(A_7, C_7, I_8) → driehoek75, m_{26}, n_{26}, p_{26}
  255. Polygon(A_7, I_8, Z_6) → driehoek76, q_{26}, r_{26}, s_{26}
  256. Polygon(D_7, F_7, U_7) → driehoek77, t_{26}, a_{26}, e_{26}
  257. Polygon(H_7, I_7, D_8) → driehoek78, b_{26}, c_{26}, d_{26}
  258. ESmBiped13(B_8, G_8, O_6) → J_8, K_8, L_8, vierhoek123, vierhoek124, driehoek79, driehoek80
  259. ESmBiped13(O_6, Z_7, R_6) → M_8, N_8, O_8, vierhoek125, vierhoek126, driehoek81, driehoek82
  260. ESmBiped13(R_6, A_8, U_6) → P_8, Q_8, R_8, vierhoek127, vierhoek128, driehoek83, driehoek84
  261. ESmBiped13(U_6, F_8, U_7) → S_8, T_8, U_8, vierhoek129, vierhoek130, driehoek85, driehoek86
  262. ESmBiped13(L_6, H_8, C_8) → V_8, W_8, Z_8, vierhoek131, vierhoek132, driehoek87, driehoek88
  263. ESmBiped13(I_6, W_7, L_6) → A_9, B_9, C_9, vierhoek133, vierhoek134, driehoek89, driehoek90
  264. ESmBiped13(F_6, V_7, I_6) → D_9, E_9, F_9, vierhoek135, vierhoek136, driehoek91, driehoek92
  265. ESmBiped13(D_8, E_8, F_6) → G_9, H_9, I_9, vierhoek137, vierhoek138, driehoek93, driehoek94
  266. EJug4(I_8, C_7, B_8) → J_9, K_9, L_9, vierhoek139, vierhoek140, driehoek95, driehoek96
  267. EJug4(C_8, Z_6, I_8) → M_9, N_9, O_9, vierhoek141, vierhoek142, driehoek97, driehoek98
  268. ERhombus2(Q_9, P_9, I_9) → R_9, S_9, T_9, vierhoek143, vierhoek144, driehoek99, driehoek100
  269. Polygon(P_9, G_9, I_9) → driehoek101, f_{27}, g_{27}, h_{27}
  270. Polygon(W_9, I_9, M_9) → driehoek102, i_{27}, w_9, j_{27}
  271. Polygon(B_{10}, T_8, U_8) → driehoek103, u_8, k_{27}, l_{27}
  272. Polygon(U_9, K_9, U_8) → driehoek104, m_{27}, u_9, n_{27}
  273. Polygon(D_{10}, V_9, W_9) → driehoek105, p_{27}, q_{27}, v_9
  274. Polygon(D_{10}, M_9, W_9) → driehoek106, r_{27}, s_{27}, t_{27}
  275. Polygon(D_{10}, N_9, V_9) → driehoek107, a_{27}, b_{27}, c_{27}
  276. Polygon(C_{10}, N_9, V_9) → driehoek108, d_{27}, e_{27}, f_{28}
  277. Polygon(C_{10}, K_9, U_9) → driehoek109, g_{28}, h_{28}, i_{28}
  278. Polygon(U_9, V_9, C_{10}) → driehoek110, j_{28}, k_{28}, l_{28}
  279. ERhombus2(I_9, W_9, V_9) → E_{10}, F_{10}, G_{10}, vierhoek145, vierhoek146, driehoek111, driehoek112
  280. ERhombus2(V_9, U_9, U_8) → H_{10}, I_{10}, J_{10}, vierhoek147, vierhoek148, driehoek113, driehoek114
  281. ERhombus2(U_8, B_{10}, A_{10}) → K_{10}, L_{10}, M_{10}, vierhoek149, vierhoek150, driehoek115, driehoek116
  282. Polygon(N_{10}, M_{10}, L_{10}) → driehoek117, m_{28}, n_{28}, p_{28}
  283. Polygon(L_{10}, O_{10}, K_{10}) → driehoek118, q_{28}, r_{28}, o_{10}
  284. Polygon(O_{10}, I_{10}, K_{10}) → driehoek119, s_{28}, t_{28}, a_{28}
  285. Polygon(H_{10}, P_{10}, I_{10}) → driehoek120, b_{28}, c_{28}, d_{28}
  286. Polygon(P_{10}, F_{10}, H_{10}) → driehoek121, e_{28}, f_{29}, g_{29}
  287. Polygon(Q_{10}, F_{10}, E_{10}) → driehoek122, h_{29}, i_{29}, j_{29}
  288. Polygon(Q_{10}, S_9, E_{10}) → driehoek123, k_{29}, l_{29}, m_{29}
  289. Polygon(R_{10}, R_9, S_9) → driehoek124, n_{29}, p_{29}, q_{29}
  290. ESquare1(S_9, Q_{10}, F_{10}) → S_{10}, T_{10}, U_{10}, vierhoek151, vierhoek152, driehoek125, driehoek126
  291. ESquare1(F_{10}, P_{10}, I_{10}) → V_{10}, W_{10}, Z_{10}, vierhoek153, vierhoek154, driehoek127, driehoek128
  292. ESquare1(I_{10}, O_{10}, L_{10}) → A_{11}, B_{11}, C_{11}, vierhoek155, vierhoek156, driehoek129, driehoek130
  293. EAlmond14(Z_{10}, D_{11}, C_{11}) → F_{11}, driehoek131, driehoek132
  294. EAlmond14(U_{10}, E_{11}, Z_{10}) → G_{11}, driehoek133, driehoek134
  295. Polygon(F_7, H_{11}, E_7) → driehoek135, r_{29}, s_{29}, t_{29}
  296. Polygon(G_7, I_{11}, I_7) → driehoek136, a_{29}, b_{29}, c_{29}
  297. EJug4(U_7, F_7, H_{11}) → J_{11}, K_{11}, L_{11}, vierhoek157, vierhoek158, driehoek137, driehoek138
  298. EJug4(I_{11}, I_7, D_8) → M_{11}, N_{11}, O_{11}, vierhoek159, vierhoek160, driehoek139, driehoek140
  299. Polygon(P_{11}, J_{11}, B_{10}) → driehoek141, d_{29}, e_{29}, f_{30}
  300. Polygon(P_{11}, B_{10}, A_{10}) → driehoek142, g_{30}, h_{30}, i_{30}
  301. Polygon(P_{11}, K_{11}, A_{10}) → driehoek143, j_{30}, k_{30}, l_{30}
  302. Polygon(Q_{11}, N_{11}, Z_9) → driehoek144, z_9, m_{30}, n_{30}
  303. Polygon(Q_9, Z_9, Q_{11}) → driehoek145, p_{30}, q_{30}, r_{30}
  304. Polygon(M_{11}, Q_9, Q_{11}) → driehoek146, s_{30}, t_{30}, a_{30}
  305. EAlmond14(C_{11}, U_{11}, R_{11}) → V_{11}, driehoek147, driehoek148
  306. EAlmond14(S_{11}, T_{11}, U_{10}) → W_{11}, driehoek149, driehoek150
  307. EHRhombus6(L_{10}, N_{10}) → Z_{11}, A_{12}, B_{12}, vierhoek161, driehoek151
  308. EHRhombus6(R_{10}, S_9) → C_{12}, D_{12}, E_{12}, vierhoek162, driehoek152
  309. Polygon(A_{12}, R_{11}, Z_{11}) → driehoek153, z_{11}, b_{30}, c_{30}
  310. Polygon(S_{11}, C_{12}, D_{12}) → driehoek154, d_{30}, e_{30}, f_{31}
  311. ESmBiped13(U_{10}, G_{11}, Z_{10}) → F_{12}, G_{12}, H_{12}, vierhoek163, vierhoek164, driehoek155, driehoek156
  312. ESmBiped13(Z_{10}, F_{11}, C_{11}) → I_{12}, J_{12}, K_{12}, vierhoek165, vierhoek166, driehoek157, driehoek158
  313. ESmBiped13(C_{11}, V_{11}, R_{11}) → L_{12}, M_{12}, N_{12}, vierhoek167, vierhoek168, driehoek159, driehoek160
  314. ESmBiped13(S_{11}, W_{11}, U_{10}) → O_{12}, P_{12}, Q_{12}, vierhoek169, vierhoek170, driehoek161, driehoek162
  315. Segment(I, H) → g_{31}
  316. Segment(O_4, H) → h_{31}
  317. Segment(O_4, N_2) → i_{31}
  318. Segment(P_4, H_2) → j_{31}
  319. Segment(P_4, N_3) → k_{31}
  320. Segment(V, N_3) → l_{31}
  321. Segment(Q_4, N_3) → m_{31}
  322. Segment(Q_4, E_2) → n_{31}
  323. Segment(J_1, L_3) → p_{31}
  324. Segment(R_4, L_3) → q_{31}
  325. Segment(R_4, W_1) → r_{31}
  326. Segment(H, G) → s_{31}
  327. Segment(L_3, E_4) → t_{31}
  328. Segment(Q_2, G) → a_{31}
  329. Segment(K_3, E_4) → b_{31}
  330. Segment(O_4, H) → c_{31}
  331. Segment(O_4, N_2) → d_{31}
  332. Segment(R_4, W_1) → e_{31}
  333. Segment(R_4, L_3) → f_{32}
  334. Segment(L_3, K_3) → g_{32}
  335. Segment(H, Q_2) → h_{32}
  336. Segment(I, H) → i_{32}
  337. Segment(J_1, L_3) → j_{32}
  338. Segment(P_4, H_2) → k_{32}
  339. Segment(Q_4, N_3) → l_{32}
  340. Segment(P_4, N_3) → m_{32}
  341. Segment(Q_4, E_2) → n_{32}
  342. Segment(L_3, W_1) → p_{32}
  343. Segment(H, N_2) → q_{32}
  344. Segment(H_2, E_2) → r_{32}
  345. Segment(H, G) → s_{32}
  346. Segment(Q_2, G) → t_{32}
  347. Segment(K_3, E_4) → a_{32}
  348. Segment(L_3, E_4) → b_{32}

AI Drawing Prompt Reference

Draw the geometric pattern of the Kayseri Cifte Madrasah, starting by creating points A and B, then rotate A around B to form AB and BA. Use intersection commands to generate basic symmetric units like ABAB, ABH, and ABHR. Construct squares and rhombuses, then scale them around their centroids. Finally, use these basic units to construct more complex symmetric patterns such as Almond3 and SmBiped9.
The prompt above was compiled from the original drawing commands and is for reference only.