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Angles of Tiles

Angles of Tiles
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2019-12-31 17:10
PolygonAngleGeometric Construction
This example demonstrates the angle relationships in Islamic geometric patterns. It involves angles, symmetry, and polygons. Using GeoGebra commands such as ConstructionStep, Rotate, Polygon, etc., it clearly shows the calculation of angles and the construction of polygons. Suitable for middle school and above students to learn geometric construction and angle calculation.

GeoGebra Commands & Parameters

  1. ConstructionStep() → stap
  2. Rotate(A, ((-(360°))) / 7) → B
  3. Polygon(B, A, 7) → veelhoek1, f, E, F, G, g, h, i, j, k, l, C, D
  4. Rotate(O, hoekb, H) → J
  5. Rotate(H, hoekb, J) → K
  6. Rotate(J, hoeka, K) → L
  7. Polygon(O, I, L, K, J, H) → veelhoek2, o, i_1, l_1, k_1, j_1, h_1
  8. Rotate(H, hoeka) → M
  9. Rotate(O, hoekd, I) → N
  10. Rotate(O, (-hoekd), M) → P
  11. Rotate(I, hoekd, N) → Q
  12. Polygon(I, N, Q, P, M, O) → veelhoek3, i_2, n, q, p, m, o_1
  13. Midpoint(q) → R
  14. Midpoint(n) → S
  15. Midpoint(i_2) → T
  16. Midpoint(p) → U
  17. Vector(P, J) → u
  18. Translate(I, u) → I'
  19. Translate(N, u) → N'
  20. Translate(Q, u) → Q'
  21. Translate(P, u) → P'
  22. Translate(M, u) → M'
  23. Translate(O, u) → O'
  24. Polygon(I', N', Q', P', M', O') → veelhoek3', i', n', q', p', m', o'
  25. Translate(O, Vector[(-u)]) → O'_1
  26. Translate(I, Vector[(-u)]) → I'_1
  27. Translate(L, Vector[(-u)]) → L'
  28. Translate(K, Vector[(-u)]) → K'
  29. Translate(J, Vector[(-u)]) → J'
  30. Translate(H, Vector[(-u)]) → H'
  31. Polygon(O'_1, I'_1, L', K', J', H') → veelhoek2', o'_1, i'_1, l', k', j', h'
  32. Rotate(I, hoeka, L) → V
  33. Rotate(L, hoekb, V) → W
  34. Rotate(V, hoekb, W) → V'
  35. Polygon(L, I, N, V', W, V) → veelhoek4, l_2, i_3, n_1, v', w, v
  36. Translate(L, Vector[(-u)]) → L'_1
  37. Translate(I, Vector[(-u)]) → I'_2
  38. Translate(N, Vector[(-u)]) → N'_1
  39. Translate(V', Vector[(-u)]) → V''
  40. Translate(W, Vector[(-u)]) → W'
  41. Translate(V, Vector[(-u)]) → V'_1
  42. Polygon(L'_1, I'_2, N'_1, V'', W', V'_1) → veelhoek4', l'_1, i'_2, n'_1, v'', w', v'_1
  43. Rotate(N, hoekb, V') → N'_2
  44. Polygon(Q, L', V'_1, N'_2, V', N) → veelhoek5, q_1, r, s, n'_2, t, n_2
  45. Translate(Q, Vector[(-u)]) → Q'_1
  46. Translate(L', Vector[(-u)]) → L''
  47. Translate(V'_1, Vector[(-u)]) → Z
  48. Translate(N'_2, Vector[(-u)]) → A_1
  49. Translate(V', Vector[(-u)]) → V''_1
  50. Translate(N, Vector[(-u)]) → N'_3
  51. Polygon(Q'_1, L'', Z, A_1, V''_1, N'_3) → veelhoek5', q'_1, l'', z_1, a_1, v''_1, n'_3
  52. Translate(Q, u) → Q'_2
  53. Translate(L', u) → L''_1
  54. Translate(V'_1, u) → B_1
  55. Translate(N'_2, u) → C_1
  56. Translate(V', u) → V''_2
  57. Translate(N, u) → N'_4
  58. Polygon(Q'_2, L''_1, B_1, C_1, V''_2, N'_4) → veelhoek5'_1, q'_2, l''_1, b_1, c_1, v''_2, n'_4
  59. Translate(I, Vector[(-u)]) → I'_3
  60. Translate(N, Vector[(-u)]) → N'_5
  61. Translate(Q, Vector[(-u)]) → Q'_3
  62. Translate(P, Vector[(-u)]) → P'_1
  63. Translate(M, Vector[(-u)]) → M'_1
  64. Translate(O, Vector[(-u)]) → O'_2
  65. Polygon(I'_3, N'_5, Q'_3, P'_1, M'_1, O'_2) → veelhoek3'_1, i'_3, n'_5, q'_3, p'_1, m'_1, o'_2
  66. Translate(Q, uu) → Q'_4
  67. Translate(L', uu) → L''_2
  68. Translate(V'_1, uu) → D_1
  69. Translate(N'_2, uu) → E_1
  70. Translate(V', uu) → V''_3
  71. Translate(N, uu) → N'_6
  72. Polygon(Q'_4, L''_2, D_1, E_1, V''_3, N'_6) → veelhoek5'_2, q'_4, l''_2, d_1, e_1, v''_3, n'_6
  73. Translate(L'_1, uu) → F_1
  74. Translate(I'_2, uu) → G_1
  75. Translate(N'_1, uu) → H_1
  76. Translate(V'', uu) → V'''
  77. Translate(W', uu) → W''
  78. Translate(V'_1, uu) → I_1
  79. Polygon(F_1, G_1, H_1, V''', W'', I_1) → veelhoek4'', f_1, g_1, a, v''', w'', b
  80. Translate(L, uu) → L'_2
  81. Translate(I, uu) → I'_4
  82. Translate(N, uu) → N'_7
  83. Translate(V', uu) → V''_4
  84. Translate(W, uu) → W'_1
  85. Translate(V, uu) → V'_2
  86. Polygon(L'_2, I'_4, N'_7, V''_4, W'_1, V'_2) → veelhoek4'_1, l'_2, i'_4, n'_7, v''_4, w'_1, v'_2
  87. Translate(I, uu) → I'_5
  88. Translate(N, uu) → N'_8
  89. Translate(Q, uu) → Q'_5
  90. Translate(P, uu) → P'_2
  91. Translate(M, uu) → M'_2
  92. Translate(O, uu) → O'_3
  93. Polygon(I'_5, N'_8, Q'_5, P'_2, M'_2, O'_3) → veelhoek3'_2, i'_5, n'_8, q'_5, p'_2, m'_2, o'_3
  94. Translate(L, u) → L'_3
  95. Translate(I, u) → I'_6
  96. Translate(N, u) → N'_9
  97. Translate(V', u) → V''_5
  98. Translate(W, u) → W'_2
  99. Translate(V, u) → V'_3
  100. Polygon(L'_3, I'_6, N'_9, V''_5, W'_2, V'_3) → veelhoek4'_2, l'_3, i'_6, n'_9, v''_5, w'_2, v'_3
  101. Translate(I, Vector[(-uu)]) → I'_7
  102. Translate(N, Vector[(-uu)]) → N'_{10}
  103. Translate(Q, Vector[(-uu)]) → Q'_6
  104. Translate(P, Vector[(-uu)]) → P'_3
  105. Translate(M, Vector[(-uu)]) → M'_3
  106. Translate(O, Vector[(-uu)]) → O'_4
  107. Polygon(I'_7, N'_{10}, Q'_6, P'_3, M'_3, O'_4) → veelhoek3'_3, i'_7, n'_{10}, q'_6, p'_3, m'_3, o'_4
  108. Translate(Q, Vector[(-uu)]) → Q'_7
  109. Translate(L', Vector[(-uu)]) → L''_3
  110. Translate(V'_1, Vector[(-uu)]) → J_1
  111. Translate(N'_2, Vector[(-uu)]) → K_1
  112. Translate(V', Vector[(-uu)]) → V''_6
  113. Translate(N, Vector[(-uu)]) → N'_{11}
  114. Polygon(Q'_7, L''_3, J_1, K_1, V''_6, N'_{11}) → veelhoek5'_3, q'_7, l''_3, c, d, v''_6, n'_{11}
  115. Translate(O'_1, Vector[(-uu)]) → L_1
  116. Translate(I'_1, Vector[(-uu)]) → M_1
  117. Translate(L', Vector[(-uu)]) → L''_4
  118. Translate(K', Vector[(-uu)]) → K''
  119. Translate(J', Vector[(-uu)]) → J''
  120. Translate(H', Vector[(-uu)]) → H''
  121. Polygon(L_1, M_1, L''_4, K'', J'', H'') → veelhoek2'', e, m_1, l''_4, k'', j'', h''
  122. Translate(O, Vector[(-uu)]) → O'_5
  123. Translate(I, Vector[(-uu)]) → I'_8
  124. Translate(L, Vector[(-uu)]) → L'_4
  125. Translate(K, Vector[(-uu)]) → K'_1
  126. Translate(J, Vector[(-uu)]) → J'_1
  127. Translate(H, Vector[(-uu)]) → H'_1
  128. Polygon(O'_5, I'_8, L'_4, K'_1, J'_1, H'_1) → veelhoek2'_1, o'_5, i'_8, l'_4, k'_1, j'_1, h'_1
  129. Translate(L, Vector[(-uu)]) → L'_5
  130. Translate(I, Vector[(-uu)]) → I'_9
  131. Translate(N, Vector[(-uu)]) → N'_{12}
  132. Translate(V', Vector[(-uu)]) → V''_7
  133. Translate(W, Vector[(-uu)]) → W'_3
  134. Translate(V, Vector[(-uu)]) → V'_4
  135. Polygon(L'_5, I'_9, N'_{12}, V''_7, W'_3, V'_4) → veelhoek4'_3, l'_5, i'_9, n'_{12}, v''_7, w'_3, v'_4
  136. Translate(I', Vector[(-uu)]) → I''
  137. Translate(N', Vector[(-uu)]) → N''
  138. Translate(Q', Vector[(-uu)]) → Q''
  139. Translate(P', Vector[(-uu)]) → P''
  140. Translate(M', Vector[(-uu)]) → M''
  141. Translate(O', Vector[(-uu)]) → O''
  142. Polygon(I'', N'', Q'', P'', M'', O'') → veelhoek3'', i'', n'', q'', p'', m'', o''
  143. Translate(O'_5, u) → N_1
  144. Translate(I'_8, u) → O_1
  145. Translate(L'_4, u) → P_1
  146. Translate(K'_1, u) → Q_1
  147. Translate(J'_1, u) → R_1
  148. Translate(H'_1, u) → S_1
  149. Polygon(N_1, O_1, P_1, Q_1, R_1, S_1) → veelhoek6, p_1, r_1, s_1, t_1, f_2, g_2
  150. Translate(Q'_7, u) → T_1
  151. Translate(L''_3, u) → U_1
  152. Translate(J_1, u) → V_1
  153. Translate(K_1, u) → W_1
  154. Translate(V''_6, u) → Z_1
  155. Translate(N'_{11}, u) → A_2
  156. Polygon(T_1, U_1, V_1, W_1, Z_1, A_2) → veelhoek7, h_2, u_1, v_1, w_1, j_2, a_2
  157. Translate(I'_3, Vector[(-uu)]) → B_2
  158. Translate(N'_5, Vector[(-uu)]) → C_2
  159. Translate(Q'_3, Vector[(-uu)]) → D_2
  160. Translate(P'_1, Vector[(-uu)]) → E_2
  161. Translate(M'_1, Vector[(-uu)]) → F_2
  162. Translate(O'_2, Vector[(-uu)]) → G_2
  163. Polygon(B_2, C_2, D_2, E_2, F_2, G_2) → veelhoek8, b_2, c_2, d_2, e_2, k_2, m_2
  164. Translate(L'_1, Vector[(-u)]) → H_2
  165. Translate(I'_2, Vector[(-u)]) → I_2
  166. Translate(N'_1, Vector[(-u)]) → J_2
  167. Translate(V'', Vector[(-u)]) → V'''_1
  168. Translate(W', Vector[(-u)]) → W''_1
  169. Translate(V'_1, Vector[(-u)]) → K_2
  170. Polygon(H_2, I_2, J_2, V'''_1, W''_1, K_2) → veelhoek4''_1, p_2, q_2, r_2, v'''_1, w''_1, s_2
  171. Translate(L'_1, Vector[(-uu)]) → L_2
  172. Translate(I'_2, Vector[(-uu)]) → M_2
  173. Translate(N'_1, Vector[(-uu)]) → N_2
  174. Translate(V'', Vector[(-uu)]) → V'''_2
  175. Translate(W', Vector[(-uu)]) → W''_2
  176. Translate(V'_1, Vector[(-uu)]) → O_2
  177. Polygon(L_2, M_2, N_2, V'''_2, W''_2, O_2) → veelhoek4''_2, t_2, f_3, g_3, v'''_2, w''_2, o_2
  178. Translate(I'_7, Vector[(-uu)]) → P_2
  179. Translate(N'_{10}, Vector[(-uu)]) → Q_2
  180. Translate(Q'_6, Vector[(-uu)]) → R_2
  181. Translate(P'_3, Vector[(-uu)]) → S_2
  182. Translate(M'_3, Vector[(-uu)]) → T_2
  183. Translate(O'_4, Vector[(-uu)]) → U_2
  184. Polygon(P_2, Q_2, R_2, S_2, T_2, U_2) → veelhoek9, h_3, j_3, k_3, l_3, m_3, u_2
  185. Translate(O'_5, Vector[(-uu)]) → V_2
  186. Translate(I'_8, Vector[(-uu)]) → W_2
  187. Translate(L'_4, Vector[(-uu)]) → Z_2
  188. Translate(K'_1, Vector[(-uu)]) → A_3
  189. Translate(J'_1, Vector[(-uu)]) → B_3
  190. Translate(H'_1, Vector[(-uu)]) → C_3
  191. Polygon(V_2, W_2, Z_2, A_3, B_3, C_3) → veelhoek10, v_2, w_2, z_2, a_3, b_3, c_3
  192. OrthogonalLine(G, o) → n_3
  193. Mirror(F, n_3) → F'
  194. Mirror(G, n_3) → G'
  195. Segment(F', G') → k'_2
  196. OrthogonalLine(D, m) → p_3
  197. Mirror(D, p_3) → D'
  198. Mirror(E, p_3) → E'
  199. Segment(D', E') → i'_{10}
  200. Midpoint(i_2) → D_3
  201. Midpoint(p) → E_3
  202. Line(D_3, E_3) → q_3
  203. Mirror(F', q_3) → F''
  204. Mirror(G', q_3) → G''
  205. Segment(F'', G'') → r_3
  206. Mirror(F, q_3) → F'_1
  207. Mirror(G, q_3) → G'_1
  208. Segment(F'_1, G'_1) → k'_3
  209. Mirror(E, q_3) → E'_1
  210. Mirror(F, q_3) → F'_2
  211. Segment(E'_1, F'_2) → j'_2
  212. Mirror(D, q_3) → D'_1
  213. Mirror(E, q_3) → E'_2
  214. Segment(D'_1, E'_2) → i'_{11}
  215. Mirror(E', q_3) → E''
  216. PolyLine(D_3, F', E'_1, F'_1, G'', F'', D_3, G, F, E, D, E', E_3, E'', D'_1) → recht
  217. Centroid(veelhoek2) → F_3
  218. Mirror(B, F_3) → B'
  219. Midpoint(k_1) → G_3
  220. Midpoint(l_1) → H_3
  221. Intersect(o, h_1) → I_3
  222. Angle(C, A, I_3) → snij
  223. Midpoint(i_1) → J_3
  224. Midpoint(j_1) → K_3
  225. Intersect(k_1, j_1) → L_3
  226. Rotate(L_3, (-snij), K_3) → M_3
  227. Ray(K_3, M_3) → e_3
  228. Rotate(L_3, snij, G_3) → N_3
  229. Ray(G_3, N_3) → f_4
  230. Intersect(e_3, f_4) → O_3
  231. Mirror(O_3, Line[K_3, J_3]) → P_3
  232. Intersect(l_1, k_1) → Q_3
  233. Mirror(O_3, Line[Q_3, I_3]) → R_3
  234. Mirror(P_3, Line[Q_3, I_3]) → S_3
  235. PolyLine(H_3, B', J_3, R_3, H_3, G_3, O_3, K_3, P_3, A, B, G, S_3) → kringLB
  236. Centroid(veelhoek4) → T_3
  237. Mirror(H_3, h_1) → U_3
  238. Mirror(B', h_1) → B''
  239. Mirror(G_3, h_1) → V_3
  240. Mirror(O_3, h_1) → W_3
  241. Mirror(K_3, h_1) → Z_3
  242. Mirror(P_3, h_1) → A_4
  243. Mirror(A, h_1) → A'
  244. Mirror(B, h_1) → B'_1
  245. Mirror(G, h_1) → G'_2
  246. Mirror(S_3, h_1) → B_4
  247. Mirror(J_3, h_1) → C_4
  248. Mirror(R_3, h_1) → D_4
  249. Mirror(H_3, h_1) → E_4
  250. PolyLine(U_3, B'', C_4, D_4, E_4, V_3, W_3, Z_3, A_4, A', B'_1, G'_2, B_4) → kringLO
  251. Mirror(H_3, q_3) → F_4
  252. Mirror(B', q_3) → B''_1
  253. Mirror(G_3, q_3) → G_4
  254. Mirror(O_3, q_3) → H_4
  255. Mirror(K_3, q_3) → I_4
  256. Mirror(P_3, q_3) → J_4
  257. Mirror(A, q_3) → A'_1
  258. Mirror(B, q_3) → B'_2
  259. Mirror(G, q_3) → G'_3
  260. Mirror(S_3, q_3) → K_4
  261. Mirror(J_3, q_3) → L_4
  262. Mirror(R_3, q_3) → M_4
  263. Mirror(H_3, q_3) → N_4
  264. PolyLine(F_4, B''_1, L_4, M_4, N_4, G_4, H_4, I_4, J_4, A'_1, B'_2, G'_3, K_4) → kringRB
  265. Mirror(U_3, q_3) → O_4
  266. Mirror(B'', q_3) → B'''
  267. Mirror(V_3, q_3) → P_4
  268. Mirror(W_3, q_3) → Q_4
  269. Mirror(Z_3, q_3) → R_4
  270. Mirror(A_4, q_3) → S_4
  271. Mirror(A', q_3) → A''
  272. Mirror(B'_1, q_3) → T_4
  273. Mirror(G'_2, q_3) → U_4
  274. Mirror(B_4, q_3) → V_4
  275. Mirror(C_4, q_3) → W_4
  276. Mirror(D_4, q_3) → Z_4
  277. Mirror(E_4, q_3) → A_5
  278. PolyLine(O_4, B''', W_4, Z_4, A_5, P_4, Q_4, R_4, S_4, A'', T_4, U_4, V_4) → kringRO
  279. Ray(E'', E_3) → s_3
  280. Ray(D_4, C_4) → t_3
  281. Ray(E', E_3) → d_3
  282. Ray(Z_4, W_4) → g_4
  283. Intersect(s_3, t_3) → B_5
  284. Intersect(d_3, g_4) → C_5
  285. Ray(B_4, C_4) → h_4
  286. Ray(V_4, W_4) → i_4
  287. Intersect(q_3, g_1) → D_5
  288. Centroid(veelhoek4'') → E_5
  289. Mirror(B_5, E_5) → F_5
  290. Mirror(C_5, E_5) → G_5
  291. Midpoint(f_1) → H_5
  292. Midpoint(a) → I_5
  293. Segment(H_5, G_5) → j_4
  294. Segment(G_5, D_5) → k_4
  295. Segment(D_5, F_5) → l_4
  296. Segment(F_5, I_5) → m_4
  297. Segment(E_3, B_5) → n_4
  298. Segment(B_5, C_4) → p_4
  299. Segment(E_3, C_5) → q_4
  300. Segment(W_4, C_5) → r_4
  301. Ray(B_4, C_4) → s_4
  302. Ray(V_4, W_4) → t_4
  303. Intersect(q'_4, l''_2) → K_5
  304. Intersect(j', a) → L_5
  305. Segment(K_5, L_5) → a_4
  306. Intersect(s_4, a_4) → M_5
  307. Intersect(t_4, a_4) → N_5
  308. PolyLine(E_3, B_5, W_4, C_5, E_3, C_4, M_5, H_5, G_5, D_5, F_5, I_5, N_5) → kringhor
  309. Translate(E_3, Vector[E_5, T_3]) → O_5
  310. Translate(B_5, Vector[E_5, T_3]) → P_5
  311. Translate(C_4, Vector[E_5, T_3]) → Q_5
  312. Translate(M_5, Vector[E_5, T_3]) → R_5
  313. Translate(H_5, Vector[E_5, T_3]) → S_5
  314. Translate(G_5, Vector[E_5, T_3]) → T_5
  315. Translate(D_5, Vector[E_5, T_3]) → U_5
  316. Translate(F_5, Vector[E_5, T_3]) → V_5
  317. Translate(I_5, Vector[E_5, T_3]) → W_5
  318. Translate(N_5, Vector[E_5, T_3]) → Z_5
  319. Translate(W_4, Vector[E_5, T_3]) → A_6
  320. Translate(C_5, Vector[E_5, T_3]) → B_6
  321. Translate(E_3, Vector[E_5, T_3]) → C_6
  322. PolyLine(O_5, P_5, A_6, B_6, C_6, Q_5, R_5, S_5, T_5, U_5, V_5, W_5, Z_5) → kringhor'
  323. Translate(D_3, Vector[(-uu)]) → D_6
  324. Translate(F', Vector[(-uu)]) → F''_1
  325. Translate(G, Vector[(-uu)]) → G'_4
  326. Translate(F, Vector[(-uu)]) → F'_3
  327. Translate(E, Vector[(-uu)]) → E'_3
  328. Translate(D, Vector[(-uu)]) → D'_2
  329. Translate(E', Vector[(-uu)]) → E''_1
  330. Translate(E_3, Vector[(-uu)]) → E_6
  331. Translate(E'', Vector[(-uu)]) → E'''
  332. Translate(D'_1, Vector[(-uu)]) → F_6
  333. Translate(E'_1, Vector[(-uu)]) → G_6
  334. Translate(F'_1, Vector[(-uu)]) → H_6
  335. Translate(G'', Vector[(-uu)]) → G'''
  336. Translate(F'', Vector[(-uu)]) → F'''
  337. Translate(D_3, Vector[(-uu)]) → I_6
  338. Translate(D_3, u) → J_6
  339. Translate(F', u) → F''_2
  340. Translate(G, u) → G'_5
  341. Translate(F, u) → F'_4
  342. Translate(E, u) → E'_4
  343. Translate(D, u) → D'_3
  344. Translate(E', u) → E''_2
  345. Translate(E_3, u) → K_6
  346. Translate(E'', u) → E'''_1
  347. Translate(D'_1, u) → L_6
  348. Translate(E'_1, u) → M_6
  349. Translate(F'_1, u) → N_6
  350. Translate(G'', u) → G'''_1
  351. Translate(F'', u) → F'''_1
  352. Translate(D_3, u) → O_6
  353. Translate(D_6, u) → P_6
  354. Translate(F''_1, u) → Q_6
  355. Translate(G'_4, u) → R_6
  356. Translate(F'_3, u) → S_6
  357. Translate(E'_3, u) → T_6
  358. Translate(D'_2, u) → U_6
  359. Translate(E''_1, u) → V_6
  360. Translate(E_6, u) → W_6
  361. Translate(E''', u) → Z_6
  362. Translate(F_6, u) → A_7
  363. Translate(G_6, u) → B_7
  364. Translate(H_6, u) → C_7
  365. Translate(G''', u) → D_7
  366. Translate(F''', u) → E_7
  367. Translate(I_6, u) → F_7
  368. Translate(D_6, Vector[(-u)]) → G_7
  369. Translate(F''_1, Vector[(-u)]) → H_7
  370. Translate(G'_4, Vector[(-u)]) → I_7
  371. Translate(F'_3, Vector[(-u)]) → J_7
  372. Translate(E'_3, Vector[(-u)]) → K_7
  373. Translate(D'_2, Vector[(-u)]) → L_7
  374. Translate(E''_1, Vector[(-u)]) → M_7
  375. Translate(E_6, Vector[(-u)]) → N_7
  376. Translate(E''', Vector[(-u)]) → O_7
  377. Translate(F_6, Vector[(-u)]) → P_7
  378. Translate(G_6, Vector[(-u)]) → Q_7
  379. Translate(H_6, Vector[(-u)]) → R_7
  380. Translate(G''', Vector[(-u)]) → S_7
  381. Translate(F''', Vector[(-u)]) → T_7
  382. Translate(I_6, Vector[(-u)]) → U_7
  383. Translate(D_6, Vector[(-uu)]) → V_7
  384. Translate(F''_1, Vector[(-uu)]) → W_7
  385. Translate(G'_4, Vector[(-uu)]) → Z_7
  386. Translate(F'_3, Vector[(-uu)]) → A_8
  387. Translate(E'_3, Vector[(-uu)]) → B_8
  388. Translate(D'_2, Vector[(-uu)]) → C_8
  389. Translate(E''_1, Vector[(-uu)]) → D_8
  390. Translate(E_6, Vector[(-uu)]) → E_8
  391. Translate(E''', Vector[(-uu)]) → F_8
  392. Translate(F_6, Vector[(-uu)]) → G_8
  393. Translate(G_6, Vector[(-uu)]) → H_8
  394. Translate(H_6, Vector[(-uu)]) → I_8
  395. Translate(G''', Vector[(-uu)]) → J_8
  396. Translate(F''', Vector[(-uu)]) → K_8
  397. Translate(I_6, Vector[(-uu)]) → L_8
  398. Translate(D_3, Vector[(-u)]) → M_8
  399. Translate(F', Vector[(-u)]) → F''_3
  400. Translate(G, Vector[(-u)]) → G'_6
  401. Translate(F, Vector[(-u)]) → F'_5
  402. Translate(E, Vector[(-u)]) → E'_5
  403. Translate(D, Vector[(-u)]) → D'_4
  404. Translate(E', Vector[(-u)]) → E''_3
  405. Translate(E_3, Vector[(-u)]) → N_8
  406. Translate(E'', Vector[(-u)]) → E'''_2
  407. Translate(D'_1, Vector[(-u)]) → O_8
  408. Translate(E'_1, Vector[(-u)]) → P_8
  409. Translate(F'_1, Vector[(-u)]) → Q_8
  410. Translate(G'', Vector[(-u)]) → G'''_2
  411. Translate(F'', Vector[(-u)]) → F'''_2
  412. Translate(D_3, Vector[(-u)]) → R_8
  413. Translate(D_3, uu) → S_8
  414. Translate(F', uu) → F''_4
  415. Translate(G, uu) → G'_7
  416. Translate(F, uu) → F'_6
  417. Translate(E, uu) → E'_6
  418. Translate(D, uu) → D'_5
  419. Translate(E', uu) → E''_4
  420. Translate(E_3, uu) → T_8
  421. Translate(E'', uu) → E'''_3
  422. Translate(D'_1, uu) → U_8
  423. Translate(E'_1, uu) → V_8
  424. Translate(F'_1, uu) → W_8
  425. Translate(G'', uu) → G'''_3
  426. Translate(F'', uu) → F'''_3
  427. Translate(D_3, uu) → Z_8
  428. Angle(G, O, A) → α
  429. FractionText(2 / 7) → tekst1
  430. Angle(J, K, L) → β
  431. FractionText(2 / 7) → tekst2
  432. Angle(K, L, I) → γ
  433. Angle(H, J, G_3) → δ
  434. Angle(O, H, J) → ε
  435. Angle(L, I, O) → ζ
  436. FractionText(5 / 14) → tekst3
  437. FractionText(5 / 14) → tekst4
  438. FractionText(5 / 14) → tekst5
  439. FractionText(5 / 14) → tekst6
  440. Angle(H, O, M) → η
  441. FractionText(2 / 7) → tekst7
  442. Angle(N, I, L) → ξ
  443. FractionText(5 / 14) → tekst8
  444. Angle(M, O, I) → θ
  445. FractionText(3 / 7) → tekst9
  446. Angle(N, Q, P) → ι
  447. FractionText(3 / 7) → tekst10
  448. Angle(O, I, N) → κ
  449. Angle(I, N, Q) → λ
  450. Angle(P, M, D) → μ
  451. Angle(R, P, U) → ν
  452. FractionText(2 / 7) → tekst11
  453. FractionText(2 / 7) → tekst12
  454. FractionText(2 / 7) → tekst13
  455. FractionText(2 / 7) → tekst14