MathPlotAI Logo MathPlotAI

Half-Square Tessellation: Constructing Geometric Patterns with Rotation, Transla

Half-Square Tessellation: Constructing Geometric Patterns with Rotation, Transla
Loading the math board and drawing, please wait…
2023-03-22 03:26
PolygonVectorTransformationGeometric Construction
In collections Realidades de GeoGebra
① This example demonstrates how to use a half-square (half of a square) as a basic unit to construct a complex tessellation pattern through rotations, translations, and reflections, showcasing the application of geometric transformations in pattern design. ② Core mathematical concepts include polygons (squares, triangles), rotation, translation, reflection, dilation (scaling), and vector operations, along with symmetry and geometric construction. ③ Construction highlights: Based on the construction summary, GeoGebra commands such as Polygon, Midpoint, Segment, Intersect, Rotate, Translate, Mirror, Dilate, Vector, and Line are used, creating multiple points, segments, and polygon objects (e.g., A, B, C, D, poly1, poly2, poly3) to generate the tessellation by combining these transformations. ④ Suitable for middle school geometry classes, math activities, or art design teaching, helping students understand composition of transformations and pattern generation, and explore the mathematical principles of symmetry and tessellation.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, c, d, e, f, E, F
  2. Polygon(C, D, 4) → poly2, g, h, i, j, G, H
  3. Midpoint(e) → I
  4. Midpoint(c) → J
  5. Midpoint(J, B) → K
  6. Midpoint(J, A) → L
  7. Midpoint(F, I) → M
  8. Midpoint(I, E) → N
  9. Segment(M, L) → k
  10. Segment(I, J) → l
  11. Segment(N, K) → m
  12. Segment(B, F) → n
  13. Segment(E, A) → p
  14. Intersect(n, k) → O
  15. Intersect(p, m) → P
  16. Intersect(n, m) → Q
  17. Intersect(p, k) → R
  18. Polygon(F, O, P, E) → poly3, f_1, o, p_1, e_1
  19. Polygon(A, R, Q, B) → poly4, a_1, r, q, b_1
  20. Min(((a - 3) * 270), 270) → rm
  21. Rotate(R, (-(rm°)), B) → R'
  22. Rotate(Q, (-(rm°)), B) → Q'
  23. Rotate(B, (-(rm°)), B) → B'
  24. Rotate(A, rm°, B) → A'
  25. Rotate(R, rm°, B) → R'_1
  26. Rotate(Q, rm°, B) → Q'_1
  27. Rotate(B, rm°, B) → B'_1
  28. Polygon(A', R'_1, Q'_1, B'_1) → poly4', a', r'_1, q'_1, b'_1
  29. Min(((a - 4) * 270), 270) → rm2
  30. Rotate(F, rm2°, F) → F'
  31. Rotate(O, rm2°, F) → O'
  32. Rotate(P, rm2°, F) → P'
  33. Rotate(E, rm2°, F) → E'
  34. Polygon(F', O', P', E') → poly3', f', o', p', e'
  35. Polygon(O, F, E, P, O', P', A, R, Q, B, Q'_1, R'_1) → poly5, o_1, r'_2, e_2, p_2, f_2, o'_1, p'_1, a_2, r_1, q_1, b_2, q'_2
  36. Max(0.6, (8 - a) / 1.5) → rm3
  37. Dilate(O, rm3, S) → O'_1
  38. Dilate(F, rm3, S) → F'_1
  39. Dilate(O', rm3, S) → O''
  40. Dilate(P', rm3, S) → P''
  41. Dilate(A, rm3, S) → A'_1
  42. Dilate(R, rm3, S) → R'_2
  43. Dilate(Q, rm3, S) → Q'_2
  44. Dilate(B, rm3, S) → B'_2
  45. Dilate(Q'_1, rm3, S) → T
  46. Dilate(R'_1, rm3, S) → U
  47. Dilate(E, rm3, S) → E'_1
  48. Dilate(P, rm3, S) → P'_1
  49. Polygon(O'_1, F'_1, E'_1, P'_1, O'', P'', A'_1, R'_2, Q'_2, B'_2, T, U) → poly5', o'_2, u, e'_1, p'_2, f'_1, o'', p'', a'_1, r'_3, q'_3, b'_2, t
  50. Vector(B'_2, F'_1) → v
  51. Vector(A'_1, E'_1) → w
  52. Translate(O'_1, w) → V
  53. Translate(F'_1, w) → W
  54. Translate(O'', w) → O'''
  55. Translate(P'', w) → P'''
  56. Translate(A'_1, w) → Z
  57. Translate(R'_2, w) → A1
  58. Translate(Q'_2, w) → B1
  59. Translate(B'_2, w) → C1
  60. Translate(T, w) → T'
  61. Translate(U, w) → U'
  62. Translate(E'_1, w) → D1
  63. Translate(P'_1, w) → E1
  64. Polygon(V, W, D1, E1, O''', P''', Z, A1, B1, C1, T', U') → poly5'', v_1, u', d1, e1, w_1, o''', p''', z, a1, b1, c1, t'
  65. Translate(O'_1, v) → F1
  66. Translate(F'_1, v) → G1
  67. Translate(O'', v) → O'''_1
  68. Translate(P'', v) → P'''_1
  69. Translate(A'_1, v) → H1
  70. Translate(R'_2, v) → I1
  71. Translate(Q'_2, v) → J1
  72. Translate(B'_2, v) → K1
  73. Translate(T, v) → T'_1
  74. Translate(U, v) → U'_1
  75. Translate(E'_1, v) → L1
  76. Translate(P'_1, v) → M1
  77. Polygon(F1, G1, L1, M1, O'''_1, P'''_1, H1, I1, J1, K1, T'_1, U'_1) → poly5''_1, f1, u'_1, l1, m1, g1, o'''_1, p'''_1, h1, i1, j1, k1, t'_1
  78. Translate(F1, w) → F1'
  79. Translate(G1, w) → G1'
  80. Translate(O'''_1, w) → O1
  81. Translate(P'''_1, w) → P1
  82. Translate(H1, w) → H1'
  83. Translate(I1, w) → I1'
  84. Translate(J1, w) → J1'
  85. Translate(K1, w) → K1'
  86. Translate(T'_1, w) → Q1
  87. Translate(U'_1, w) → R1
  88. Translate(L1, w) → L1'
  89. Translate(M1, w) → M1'
  90. Polygon(F1', G1', L1', M1', O1, P1, H1', I1', J1', K1', Q1, R1) → poly6, f1', r1, l1', m1', g1', o1, p1, h1', i1', j1', k1', q1
  91. Translate(V, w) → V'
  92. Translate(W, w) → W'
  93. Translate(O''', w) → S1
  94. Translate(P''', w) → T1
  95. Translate(Z, w) → Z'
  96. Translate(A1, w) → A1'
  97. Translate(B1, w) → B1'
  98. Translate(C1, w) → C1'
  99. Translate(T', w) → T''
  100. Translate(U', w) → U''
  101. Translate(D1, w) → D1'
  102. Translate(E1, w) → E1'
  103. Polygon(V', W', D1', E1', S1, T1, Z', A1', B1', C1', T'', U'') → poly5''', v', u'', d1', e1', w', s1, t1, z', a1', b1', c1', t''
  104. Vector(G1, F'_1) → s
  105. Vector(L1, H1) → u1
  106. Translate(O'_1, s) → U1
  107. Translate(F'_1, s) → V1
  108. Translate(O'', s) → O'''_2
  109. Translate(P'', s) → P'''_2
  110. Translate(A'_1, s) → W1
  111. Translate(R'_2, s) → Z1
  112. Translate(Q'_2, s) → A2
  113. Translate(B'_2, s) → B2
  114. Translate(T, s) → T'_2
  115. Translate(U, s) → U'_2
  116. Translate(E'_1, s) → C2
  117. Translate(P'_1, s) → D2
  118. Polygon(U1, V1, C2, D2, O'''_2, P'''_2, W1, Z1, A2, B2, T'_2, U'_2) → poly5''_2, u1_1, u'_2, c2, d2, v1, o'''_2, p'''_2, w1, z1, a2, b2, t'_2
  119. Translate(V, s) → V'_1
  120. Translate(W, s) → W'_1
  121. Translate(O''', s) → E2
  122. Translate(P''', s) → F2
  123. Translate(Z, s) → Z'_1
  124. Translate(A1, s) → A1'_1
  125. Translate(B1, s) → B1'_1
  126. Translate(C1, s) → C1'_1
  127. Translate(T', s) → T''_1
  128. Translate(U', s) → U''_1
  129. Translate(D1, s) → D1'_1
  130. Translate(E1, s) → E1'_1
  131. Polygon(V'_1, W'_1, D1'_1, E1'_1, E2, F2, Z'_1, A1'_1, B1'_1, C1'_1, T''_1, U''_1) → poly5'''_1, v'_1, u''_1, d1'_1, e1'_1, w'_1, e2, f2, z'_1, a1'_1, b1'_1, c1'_1, t''_1
  132. Translate(O'_1, u1) → G2
  133. Translate(F'_1, u1) → H2
  134. Translate(O'', u1) → O'''_3
  135. Translate(P'', u1) → P'''_3
  136. Translate(A'_1, u1) → I2
  137. Translate(R'_2, u1) → J2
  138. Translate(Q'_2, u1) → K2
  139. Translate(B'_2, u1) → L2
  140. Translate(T, u1) → T'_3
  141. Translate(U, u1) → U'_3
  142. Translate(E'_1, u1) → M2
  143. Translate(P'_1, u1) → N2
  144. Polygon(G2, H2, M2, N2, O'''_3, P'''_3, I2, J2, K2, L2, T'_3, U'_3) → poly5''_3, g2, u'_3, m2, n2, h2, o'''_3, p'''_3, i2, j2, k2, l2, t'_3
  145. Translate(V', s) → V''
  146. Translate(W', s) → W''
  147. Translate(S1, s) → S1'
  148. Translate(T1, s) → T1'
  149. Translate(Z', s) → Z''
  150. Translate(A1', s) → A1''
  151. Translate(B1', s) → B1''
  152. Translate(C1', s) → C1''
  153. Translate(T'', s) → T'''
  154. Translate(U'', s) → U'''
  155. Translate(D1', s) → D1''
  156. Translate(E1', s) → E1''
  157. Polygon(V'', W'', D1'', E1'', S1', T1', Z'', A1'', B1'', C1'', T''', U''') → poly7, v'', u''', d1'', e1'', w'', s1', t1', z'', a1'', b1'', c1'', t'''
  158. Translate(V'_1, s) → O2
  159. Translate(W'_1, s) → P2
  160. Translate(E2, s) → E2'
  161. Translate(F2, s) → F2'
  162. Translate(Z'_1, s) → Q2
  163. Translate(A1'_1, s) → R2
  164. Translate(B1'_1, s) → S2
  165. Translate(C1'_1, s) → T2
  166. Translate(T''_1, s) → U2
  167. Translate(U''_1, s) → V2
  168. Translate(D1'_1, s) → W2
  169. Translate(E1'_1, s) → Z2
  170. Polygon(O2, P2, W2, Z2, E2', F2', Q2, R2, S2, T2, U2, V2) → poly8, o2, v2, w2, z2, p2, e2', f2', q2, r2, s2, t2, u2
  171. Segment(C, G) → n1
  172. Segment(H, D) → a3
  173. Intersect(a3, n1) → A3
  174. Midpoint(G, A3) → B3
  175. Midpoint(G, H) → C3
  176. Midpoint(C3, G) → D3
  177. Segment(A3, B3) → b3
  178. Segment(B3, D3) → c3
  179. Min(90, (90 * (b - 1))) → sm1
  180. Rotate(A3, sm1°, A3) → A3'
  181. Rotate(B3, sm1°, A3) → B3'
  182. Segment(A3', B3') → b3'
  183. Rotate(B3, sm1°, A3) → B3'_1
  184. Rotate(D3, sm1°, A3) → D3'
  185. Segment(B3'_1, D3') → c3'
  186. Min(90, (90 * (b - 2))) → sm2
  187. Min(90, (90 * (b - 3))) → sm3
  188. Rotate(A3', sm2°, A3) → A3''
  189. Rotate(B3', sm2°, A3) → B3''
  190. Segment(A3'', B3'') → b3''
  191. Rotate(B3'_1, sm2°, A3) → E3
  192. Rotate(D3', sm2°, A3) → D3''
  193. Segment(E3, D3'') → c3''
  194. Rotate(A3'', sm3°, A3) → A3'''
  195. Rotate(B3'', sm3°, A3) → B3'''
  196. Segment(A3''', B3''') → b3'''
  197. Rotate(E3, sm3°, A3) → E3'
  198. Rotate(D3'', sm3°, A3) → D3'''
  199. Segment(E3', D3''') → c3'''
  200. Polygon(G, D3, B3, A3, B3''', D3''') → poly9, g_1, d3, b3_1, a3_1, b3'''_1, d3'''
  201. Polygon(D3'', B3'', A3, B3', D3', C) → poly10, d3'', b3''_1, a3_2, b3'_1, d3', c_1
  202. Max(0.6, (8 - b) / 1.5) → sm4
  203. Dilate(D3'', sm4, F3) → D3'''_1
  204. Dilate(B3'', sm4, F3) → B3'''_1
  205. Dilate(A3, sm4, F3) → A3'_1
  206. Dilate(B3', sm4, F3) → B3''_1
  207. Dilate(D3', sm4, F3) → D3''_1
  208. Dilate(C, sm4, F3) → C'
  209. Polygon(D3'''_1, B3'''_1, A3'_1, B3''_1, D3''_1, C') → poly10', d3'''_1, b3'''_2, a3'_1, b3''_2, d3''_1, c'
  210. Dilate(G, sm4, F3) → G'
  211. Dilate(D3, sm4, F3) → D3'_1
  212. Dilate(B3, sm4, F3) → B3'_2
  213. Dilate(A3, sm4, F3) → A3'_2
  214. Dilate(B3''', sm4, F3) → G3
  215. Dilate(D3''', sm4, F3) → H3
  216. Polygon(G', D3'_1, B3'_2, A3'_2, G3, H3) → poly9', g', d3'_1, b3'_2, a3'_2, g3, h3
  217. Mirror(D3'''_1, h3) → I3
  218. Mirror(B3'''_1, h3) → J3
  219. Mirror(A3'_1, h3) → K3
  220. Mirror(B3''_1, h3) → L3
  221. Mirror(D3''_1, h3) → M3
  222. Mirror(C', h3) → C''
  223. Polygon(I3, J3, K3, L3, M3, C'') → poly10'', i3, j3, k3, l3, m3, c''
  224. Mirror(G', h3) → G''
  225. Mirror(D3'_1, h3) → N3
  226. Mirror(B3'_2, h3) → O3
  227. Mirror(A3'_2, h3) → P3
  228. Mirror(G3, h3) → G3'
  229. Mirror(H3, h3) → H3'
  230. Polygon(G'', N3, O3, P3, G3', H3') → poly9'', g'', n3, o3, p3, g3', h3'
  231. Mirror(D3'''_1, g') → Q3
  232. Mirror(B3'''_1, g') → R3
  233. Mirror(A3'_1, g') → S3
  234. Mirror(B3''_1, g') → T3
  235. Mirror(D3''_1, g') → U3
  236. Mirror(C', g') → C''_1
  237. Polygon(Q3, R3, S3, T3, U3, C''_1) → poly10''_1, q3, r3, s3, t3, u3, c''_1
  238. Mirror(G', g') → G''_1
  239. Mirror(D3'_1, g') → V3
  240. Mirror(B3'_2, g') → W3
  241. Mirror(A3'_2, g') → Z3
  242. Mirror(G3, g') → G3'_1
  243. Mirror(H3, g') → H3'_1
  244. Polygon(G''_1, V3, W3, Z3, G3'_1, H3'_1) → poly9''_1, g''_1, v3, w3, z3, g3'_1, h3'_1
  245. Mirror(D3'''_1, d3''_1) → A4
  246. Mirror(B3'''_1, d3''_1) → B4
  247. Mirror(A3'_1, d3''_1) → C4
  248. Mirror(B3''_1, d3''_1) → D4
  249. Mirror(D3''_1, d3''_1) → E4
  250. Mirror(C', d3''_1) → C''_2
  251. Polygon(A4, B4, C4, D4, E4, C''_2) → poly10''_2, a4, b4, c4, d4, e4, c''_2
  252. Mirror(G', e4) → G''_2
  253. Mirror(D3'_1, e4) → F4
  254. Mirror(B3'_2, e4) → G4
  255. Mirror(A3'_2, e4) → H4
  256. Mirror(G3, e4) → G3'_2
  257. Mirror(H3, e4) → H3'_2
  258. Polygon(G''_2, F4, G4, H4, G3'_2, H3'_2) → poly9''_2, g''_2, f4, g4, h4, g3'_2, h3'_2
  259. Mirror(D3'''_1, c') → I4
  260. Mirror(B3'''_1, c') → J4
  261. Mirror(A3'_1, c') → K4
  262. Mirror(B3''_1, c') → L4
  263. Mirror(D3''_1, c') → M4
  264. Mirror(C', c') → C''_3
  265. Polygon(I4, J4, K4, L4, M4, C''_3) → poly10''_3, i4, j4, k4, l4, m4, c''_3
  266. Mirror(G', c') → G''_3
  267. Mirror(D3'_1, c') → N4
  268. Mirror(B3'_2, c') → O4
  269. Mirror(A3'_2, c') → P4
  270. Mirror(G3, c') → G3'_3
  271. Mirror(H3, c') → H3'_3
  272. Polygon(G''_3, N4, O4, P4, G3'_3, H3'_3) → poly9''_3, g''_3, n4, o4, p4, g3'_3, h3'_3
  273. Mirror(Q3, u3) → Q3'
  274. Mirror(R3, u3) → R3'
  275. Mirror(S3, u3) → S3'
  276. Mirror(T3, u3) → T3'
  277. Mirror(U3, u3) → U3'
  278. Mirror(C''_1, u3) → Q4
  279. Polygon(Q3', R3', S3', T3', U3', Q4) → poly11, q3', r3', s3', t3', u3', q4
  280. Mirror(G''_1, u3) → R4
  281. Mirror(V3, u3) → V3'
  282. Mirror(W3, u3) → W3'
  283. Mirror(Z3, u3) → Z3'
  284. Mirror(G3'_1, u3) → S4
  285. Mirror(H3'_1, u3) → T4
  286. Polygon(R4, V3', W3', Z3', S4, T4) → poly12, r4, v3', w3', z3', s4, t4
  287. Mirror(G''_1, h3'_1) → U4
  288. Mirror(V3, h3'_1) → V3'_1
  289. Mirror(W3, h3'_1) → W3'_1
  290. Mirror(Z3, h3'_1) → Z3'_1
  291. Mirror(G3'_1, h3'_1) → V4
  292. Mirror(H3'_1, h3'_1) → W4
  293. Polygon(U4, V3'_1, W3'_1, Z3'_1, V4, W4) → poly13, u4, v3'_1, w3'_1, z3'_1, v4, w4
  294. Mirror(Q3, w4) → Q3'_1
  295. Mirror(R3, w4) → R3'_1
  296. Mirror(S3, w4) → S3'_1
  297. Mirror(T3, w4) → T3'_1
  298. Mirror(U3, w4) → U3'_1
  299. Mirror(C''_1, w4) → Z4
  300. Polygon(Q3'_1, R3'_1, S3'_1, T3'_1, U3'_1, Z4) → poly14, q3'_1, r3'_1, s3'_1, t3'_1, u3'_1, z4
  301. Mirror(G''_3, h3'_3) → A5
  302. Mirror(N4, h3'_3) → N4'
  303. Mirror(O4, h3'_3) → O4'
  304. Mirror(P4, h3'_3) → P4'
  305. Mirror(G3'_3, h3'_3) → B5
  306. Mirror(H3'_3, h3'_3) → C5
  307. Polygon(A5, N4', O4', P4', B5, C5) → poly15, a5, n4', o4', p4', b5, c5
  308. Mirror(I4, c5) → I4'
  309. Mirror(J4, c5) → J4'
  310. Mirror(K4, c5) → K4'
  311. Mirror(L4, c5) → L4'
  312. Mirror(M4, c5) → M4'
  313. Mirror(C''_3, c5) → D5
  314. Polygon(I4', J4', K4', L4', M4', D5) → poly16, i4', j4', k4', l4', m4', d5
  315. Mirror(I4, m4) → I4'_1
  316. Mirror(J4, m4) → J4'_1
  317. Mirror(K4, m4) → K4'_1
  318. Mirror(L4, m4) → L4'_1
  319. Mirror(M4, m4) → M4'_1
  320. Mirror(C''_3, m4) → E5
  321. Polygon(I4'_1, J4'_1, K4'_1, L4'_1, M4'_1, E5) → poly17, i4'_1, j4'_1, k4'_1, l4'_1, m4'_1, e5
  322. Mirror(G''_3, m4) → F5
  323. Mirror(N4, m4) → N4'_1
  324. Mirror(O4, m4) → O4'_1
  325. Mirror(P4, m4) → P4'_1
  326. Mirror(G3'_3, m4) → G5
  327. Mirror(H3'_3, m4) → H5
  328. Polygon(F5, N4'_1, O4'_1, P4'_1, G5, H5) → poly18, f5, n4'_1, o4'_1, p4'_1, g5, h5
  329. Segment(C', D3'''_1) → e3
  330. Mirror(Q3'_1, u3'_1) → I5
  331. Mirror(R3'_1, u3'_1) → J5
  332. Mirror(S3'_1, u3'_1) → K5
  333. Mirror(T3'_1, u3'_1) → L5
  334. Mirror(U3'_1, u3'_1) → M5
  335. Mirror(Z4, u3'_1) → Z4'
  336. Polygon(I5, J5, K5, L5, M5, Z4') → poly14', i5, j5, k5, l5, m5, z4'
  337. Mirror(U4, u3'_1) → U4'
  338. Mirror(V3'_1, u3'_1) → N5
  339. Mirror(W3'_1, u3'_1) → O5
  340. Mirror(Z3'_1, u3'_1) → P5
  341. Mirror(V4, u3'_1) → V4'
  342. Mirror(W4, u3'_1) → W4'
  343. Polygon(U4', N5, O5, P5, V4', W4') → poly13', u4', n5, o5, p5, v4', w4'
  344. Mirror(Q3'_1, w4') → Q5
  345. Mirror(R3'_1, w4') → R5
  346. Mirror(S3'_1, w4') → S5
  347. Mirror(T3'_1, w4') → T5
  348. Mirror(U3'_1, w4') → U5
  349. Mirror(Z4, w4') → Z4'_1
  350. Polygon(Q5, R5, S5, T5, U5, Z4'_1) → poly14'_1, q5, r5, s5, t5, u5, z4'_1
  351. Mirror(I5, w4') → I5'
  352. Mirror(J5, w4') → J5'
  353. Mirror(K5, w4') → K5'
  354. Mirror(L5, w4') → L5'
  355. Mirror(M5, w4') → M5'
  356. Mirror(Z4', w4') → Z4''
  357. Polygon(I5', J5', K5', L5', M5', Z4'') → poly14'', i5', j5', k5', l5', m5', z4''
  358. Mirror(U4', w4') → U4''
  359. Mirror(N5, w4') → N5'
  360. Mirror(O5, w4') → O5'
  361. Mirror(P5, w4') → P5'
  362. Mirror(V4', w4') → V4''
  363. Mirror(W4', w4') → W4''
  364. Polygon(U4'', N5', O5', P5', V4'', W4'') → poly13'', u4'', n5', o5', p5', v4'', w4''
  365. Mirror(G', m3) → G''_4
  366. Mirror(D3'_1, m3) → V5
  367. Mirror(B3'_2, m3) → W5
  368. Mirror(A3'_2, m3) → Z5
  369. Mirror(G3, m3) → G3'_4
  370. Mirror(H3, m3) → H3'_4
  371. Polygon(G''_4, V5, W5, Z5, G3'_4, H3'_4) → poly9''_4, g''_4, v5, w5, z5, g3'_4, h3'_4
  372. Mirror(G'', m3) → G'''
  373. Mirror(N3, m3) → N3'
  374. Mirror(O3, m3) → O3'
  375. Mirror(P3, m3) → P3'
  376. Mirror(G3', m3) → G3''
  377. Mirror(H3', m3) → H3''
  378. Polygon(G''', N3', O3', P3', G3'', H3'') → poly9''', g''', n3', o3', p3', g3'', h3''
  379. Mirror(D3'''_1, m3) → A6
  380. Mirror(B3'''_1, m3) → B6
  381. Mirror(A3'_1, m3) → C6
  382. Mirror(B3''_1, m3) → D6
  383. Mirror(D3''_1, m3) → E6
  384. Mirror(C', m3) → C''_4
  385. Polygon(A6, B6, C6, D6, E6, C''_4) → poly10''_4, a6, b6, c6, d6, e6, c''_4
  386. Mirror(A4, m3) → A4'
  387. Mirror(B4, m3) → B4'
  388. Mirror(C4, m3) → C4'
  389. Mirror(D4, m3) → D4'
  390. Mirror(E4, m3) → E4'
  391. Mirror(C''_2, m3) → F6
  392. Polygon(A4', B4', C4', D4', E4', F6) → poly19, a4', b4', c4', d4', e4', f6
  393. Mirror(I3, m3) → I3'
  394. Mirror(J3, m3) → J3'
  395. Mirror(K3, m3) → K3'
  396. Mirror(L3, m3) → L3'
  397. Mirror(M3, m3) → M3'
  398. Mirror(C'', m3) → C'''
  399. Polygon(I3', J3', K3', L3', M3', C''') → poly10''', i3', j3', k3', l3', m3', c'''
  400. Mirror(I4'_1, m4') → G6
  401. Mirror(J4'_1, m4') → H6
  402. Mirror(K4'_1, m4') → I6
  403. Mirror(L4'_1, m4') → J6
  404. Mirror(M4'_1, m4') → K6
  405. Mirror(E5, m4') → E5'
  406. Polygon(G6, H6, I6, J6, K6, E5') → poly17', g6, h6, i6, j6, k6, e5'
  407. Mirror(I4, m4') → I4'_2
  408. Mirror(J4, m4') → J4'_2
  409. Mirror(K4, m4') → K4'_2
  410. Mirror(L4, m4') → L4'_2
  411. Mirror(M4, m4') → M4'_2
  412. Mirror(C''_3, m4') → L6
  413. Polygon(I4'_2, J4'_2, K4'_2, L4'_2, M4'_2, L6) → poly20, i4'_2, j4'_2, k4'_2, l4'_2, m4'_2, l6
  414. Mirror(G''_3, m4') → M6
  415. Mirror(N4, m4') → N4'_2
  416. Mirror(O4, m4') → O4'_2
  417. Mirror(P4, m4') → P4'_2
  418. Mirror(G3'_3, m4') → N6
  419. Mirror(H3'_3, m4') → O6
  420. Polygon(M6, N4'_2, O4'_2, P4'_2, N6, O6) → poly21, m6, n4'_2, o4'_2, p4'_2, n6, o6
  421. Mirror(A5, m4') → A5'
  422. Mirror(N4', m4') → N4''
  423. Mirror(O4', m4') → O4''
  424. Mirror(P4', m4') → P4''
  425. Mirror(B5, m4') → B5'
  426. Mirror(C5, m4') → C5'
  427. Polygon(A5', N4'', O4'', P4'', B5', C5') → poly15', a5', n4'', o4'', p4'', b5', c5'
  428. Mirror(I4', m4') → I4''
  429. Mirror(J4', m4') → J4''
  430. Mirror(K4', m4') → K4''
  431. Mirror(L4', m4') → L4''
  432. Mirror(M4', m4') → M4''
  433. Mirror(D5, m4') → D5'
  434. Polygon(I4'', J4'', K4'', L4'', M4'', D5') → poly16', i4'', j4'', k4'', l4'', m4'', d5'
  435. Mirror(R4, q4) → R4'
  436. Mirror(V3', q4) → V3''
  437. Mirror(W3', q4) → W3''
  438. Mirror(Z3', q4) → Z3''
  439. Mirror(S4, q4) → S4'
  440. Mirror(T4, q4) → T4'
  441. Polygon(R4', V3'', W3'', Z3'', S4', T4') → poly12', r4', v3'', w3'', z3'', s4', t4'
  442. Mirror(Q3', q4) → Q3''
  443. Mirror(R3', q4) → R3''
  444. Mirror(S3', q4) → S3''
  445. Mirror(T3', q4) → T3''
  446. Mirror(U3', q4) → U3''
  447. Mirror(Q4, q4) → Q4'
  448. Polygon(Q3'', R3'', S3'', T3'', U3'', Q4') → poly11', q3'', r3'', s3'', t3'', u3'', q4'
  449. Mirror(G''_1, z4) → P6
  450. Mirror(V3, z4) → V3'_2
  451. Mirror(W3, z4) → W3'_2
  452. Mirror(Z3, z4) → Z3'_2
  453. Mirror(G3'_1, z4) → Q6
  454. Mirror(H3'_1, z4) → R6
  455. Polygon(P6, V3'_2, W3'_2, Z3'_2, Q6, R6) → poly22, p6, v3'_2, w3'_2, z3'_2, q6, r6
  456. Mirror(Q3, z4) → Q3'_2
  457. Mirror(R3, z4) → R3'_2
  458. Mirror(S3, z4) → S3'_2
  459. Mirror(T3, z4) → T3'_2
  460. Mirror(U3, z4) → U3'_2
  461. Mirror(C''_1, z4) → S6
  462. Polygon(Q3'_2, R3'_2, S3'_2, T3'_2, U3'_2, S6) → poly23, q3'_2, r3'_2, s3'_2, t3'_2, u3'_2, s6
  463. Mirror(U4, z4) → U4'_1
  464. Mirror(V3'_1, z4) → T6
  465. Mirror(W3'_1, z4) → U6
  466. Mirror(Z3'_1, z4) → V6
  467. Mirror(V4, z4) → V4'_1
  468. Mirror(W4, z4) → W4'_1
  469. Polygon(U4'_1, T6, U6, V6, V4'_1, W4'_1) → poly13'_1, u4'_1, t6, u6, v6, v4'_1, w4'_1
  470. Mirror(Q3'_1, z4') → W6
  471. Mirror(R3'_1, z4') → Z6
  472. Mirror(S3'_1, z4') → A7
  473. Mirror(T3'_1, z4') → B7
  474. Mirror(U3'_1, z4') → C7
  475. Mirror(Z4, z4') → Z4'_2
  476. Polygon(W6, Z6, A7, B7, C7, Z4'_2) → poly14'_2, w6, z6, a7, b7, c7, z4'_2
  477. Mirror(I5, z4') → I5'_1
  478. Mirror(J5, z4') → J5'_1
  479. Mirror(K5, z4') → K5'_1
  480. Mirror(L5, z4') → L5'_1
  481. Mirror(M5, z4') → M5'_1
  482. Mirror(Z4', z4') → Z4''_1
  483. Polygon(I5'_1, J5'_1, K5'_1, L5'_1, M5'_1, Z4''_1) → poly14''_1, i5'_1, j5'_1, k5'_1, l5'_1, m5'_1, z4''_1
  484. Mirror(U4', z4'') → U4''_1
  485. Mirror(N5, z4'') → N5'_1
  486. Mirror(O5, z4'') → O5'_1
  487. Mirror(P5, z4'') → P5'_1
  488. Mirror(V4', z4'') → V4''_1
  489. Mirror(W4', z4'') → W4''_1
  490. Polygon(U4''_1, N5'_1, O5'_1, P5'_1, V4''_1, W4''_1) → poly13''_1, u4''_1, n5'_1, o5'_1, p5'_1, v4''_1, w4''_1
  491. Mirror(U4'', z4'') → U4'''
  492. Mirror(N5', z4'') → N5''
  493. Mirror(O5', z4'') → O5''
  494. Mirror(P5', z4'') → P5''
  495. Mirror(V4'', z4'') → V4'''
  496. Mirror(W4'', z4'') → W4'''
  497. Polygon(U4''', N5'', O5'', P5'', V4''', W4''') → poly13''', u4''', n5'', o5'', p5'', v4''', w4'''
  498. Mirror(Q5, z4'') → Q5'
  499. Mirror(R5, z4'') → R5'
  500. Mirror(S5, z4'') → S5'
  501. Mirror(T5, z4'') → T5'
  502. Mirror(U5, z4'') → U5'
  503. Mirror(Z4'_1, z4'') → D7
  504. Polygon(Q5', R5', S5', T5', U5', D7) → poly24, q5', r5', s5', t5', u5', d7
  505. Mirror(I5', z4'') → I5''
  506. Mirror(J5', z4'') → J5''
  507. Mirror(K5', z4'') → K5''
  508. Mirror(L5', z4'') → L5''
  509. Mirror(M5', z4'') → M5''
  510. Mirror(Z4'', z4'') → Z4'''
  511. Polygon(I5'', J5'', K5'', L5'', M5'', Z4''') → poly14''', i5'', j5'', k5'', l5'', m5'', z4'''
  512. Line(A, b3'_1) → f3
  513. Polygon(A, F, O, P, E, B, Q, R) → poly25, a_3, f_3, o_2, p_3, e_3, b_3, q_2, r_2

AI Drawing Prompt Reference

Start by constructing two square-based half-square units from the same set of corner points, forming matching polygonal pieces. Compute the midpoints of key segments, draw the connecting segments between these midpoints, and determine their intersection points. Use the original corners together with those intersections to form a couple of quadrilateral regions. Then rotate the corresponding key points and quadrilateral boundaries around a chosen endpoint by a computed angle, producing mirrored/rotated copies. Repeat the rotation with a related angle to extend the pattern. Finally, dilate (scale) selected points and the rotated copies outward by the same factor to assemble a cohesive tessellation composed of multiple interlocking quadrilateral polygons and their overlaps.
The prompt above was compiled from the original drawing commands and is for reference only.