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Çorum Osmancık Muqarnas Geometry: Polygon & Segment Construction

Çorum Osmancık Muqarnas Geometry: Polygon & Segment Construction
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2020-08-16 03:50
PolygonGeometric ConstructionGraphing
In collections building muqarnas in GeoGebra
This example demonstrates a Muqarnas (Muqarnas) style architectural pattern by constructing a complex, continuously blended geometric outline from many modules. The key math ideas are geometric construction, piecewise boundary building via polygons and segments, and the visual intuition of continuity across adjacent elements. Construction-wise, the GeoGebra setup uses conditional logic with If to decide which geometric parts to display or assemble, and relies on Polygon and Segment to create the face-like regions and their connecting edges. The remaining objects in the construction summary focus on interface/visualization support (title, status/info panels, and layout/view toggles such as wireframe/floorplan/topview/frontview) to clearly present the stepwise construction in the final rendering. Suitable for upper-secondary to early university learners for geometry modeling, constructive geometry demonstrations, and visualization-oriented math lessons.

GeoGebra Commands & Parameters

  1. If(toon_{wireframe}, "wireframe only", If[toon_{max}, "3D only", "layer = " + toon_{lagen}]) → toon_{lagen-tekst}
  2. Polygon({(2.19203, 0.70711), (2.75772, 0.14142), (2.75772, 0.70711), (2.75772, 1.27279)}) → E_{6-1-P}
  3. Segment((2.82843, 0), (2.12132, 0.70711)) → E_{6-1-S-1}
  4. Segment((2.82843, 0.70711), (2.12132, 0.70711)) → E_{6-1-S-2}
  5. Segment((2.82843, 1.41421), (2.12132, 0.70711)) → E_{6-1-S-3}
  6. Segment((2.82843, 0), (2.82843, 0.70711)) → E_{6-1-W-1}
  7. Segment((2.82843, 1.41421), (2.82843, 0.70711)) → E_{6-1-W-3}
  8. Polygon({(2.82843, 0, 0), (2.82843, 0.70711, 0), (2.82843, 0.70711, 0.35), (2.82843, 0, 0.35)}) → E_{6-1-F-1}
  9. Polygon({(2.82843, 0.70711, 0), (2.82843, 1.41421, 0), (2.82843, 1.41421, 0.35), (2.82843, 0.70711, 0.35)}) → E_{6-1-F-2}
  10. Polygon({(2.12132, 0.70711, 1.4), (2.82843, 0, 0.35), (2.82843, 0.70711, 0.35)}) → E_{6-1-R-1}
  11. Polygon({(2.12132, 0.70711, 1.4), (2.82843, 1.41421, 0.35), (2.82843, 0.70711, 0.35)}) → E_{6-1-R-3}
  12. Polygon({(2.19203, 2.12132), (2.75772, 1.55563), (2.75772, 2.12132), (2.75772, 2.68701)}) → E_{6-3-P}
  13. Segment((2.82843, 1.41421), (2.12132, 2.12132)) → E_{6-3-S-1}
  14. Segment((2.82843, 2.12132), (2.12132, 2.12132)) → E_{6-3-S-2}
  15. Segment((2.82843, 2.82843), (2.12132, 2.12132)) → E_{6-3-S-3}
  16. Segment((2.82843, 1.41421), (2.82843, 2.12132)) → E_{6-3-W-1}
  17. Segment((2.82843, 2.82843), (2.82843, 2.12132)) → E_{6-3-W-3}
  18. Polygon({(2.82843, 1.41421, 0), (2.82843, 2.12132, 0), (2.82843, 2.12132, 0.35), (2.82843, 1.41421, 0.35)}) → E_{6-3-F-1}
  19. Polygon({(2.82843, 2.12132, 0), (2.82843, 2.82843, 0), (2.82843, 2.82843, 0.35), (2.82843, 2.12132, 0.35)}) → E_{6-3-F-2}
  20. Polygon({(2.12132, 2.12132, 1.4), (2.82843, 1.41421, 0.35), (2.82843, 2.12132, 0.35)}) → E_{6-3-R-1}
  21. Polygon({(2.12132, 2.12132, 1.4), (2.82843, 2.82843, 0.35), (2.82843, 2.12132, 0.35)}) → E_{6-3-R-3}
  22. Polygon({(2.12132, 2.19203), (2.68701, 2.75772), (2.12132, 2.75772), (1.55563, 2.75772)}) → E_{6-4-P}
  23. Segment((2.82843, 2.82843), (2.12132, 2.12132)) → E_{6-4-S-1}
  24. Segment((2.12132, 2.82843), (2.12132, 2.12132)) → E_{6-4-S-2}
  25. Segment((1.41421, 2.82843), (2.12132, 2.12132)) → E_{6-4-S-3}
  26. Segment((2.82843, 2.82843), (2.12132, 2.82843)) → E_{6-4-W-1}
  27. Segment((1.41421, 2.82843), (2.12132, 2.82843)) → E_{6-4-W-3}
  28. Polygon({(2.82843, 2.82843, 0), (2.12132, 2.82843, 0), (2.12132, 2.82843, 0.35), (2.82843, 2.82843, 0.35)}) → E_{6-4-F-1}
  29. Polygon({(2.12132, 2.82843, 0), (1.41421, 2.82843, 0), (1.41421, 2.82843, 0.35), (2.12132, 2.82843, 0.35)}) → E_{6-4-F-2}
  30. Polygon({(2.12132, 2.12132, 1.4), (2.82843, 2.82843, 0.35), (2.12132, 2.82843, 0.35)}) → E_{6-4-R-1}
  31. Polygon({(2.12132, 2.12132, 1.4), (1.41421, 2.82843, 0.35), (2.12132, 2.82843, 0.35)}) → E_{6-4-R-3}
  32. Polygon({(0.70711, 2.19203), (1.27279, 2.75772), (0.70711, 2.75772), (0.14142, 2.75772)}) → E_{6-6-P}
  33. Segment((1.41421, 2.82843), (0.70711, 2.12132)) → E_{6-6-S-1}
  34. Segment((0.70711, 2.82843), (0.70711, 2.12132)) → E_{6-6-S-2}
  35. Segment((0, 2.82843), (0.70711, 2.12132)) → E_{6-6-S-3}
  36. Segment((1.41421, 2.82843), (0.70711, 2.82843)) → E_{6-6-W-1}
  37. Segment((0, 2.82843), (0.70711, 2.82843)) → E_{6-6-W-3}
  38. Polygon({(1.41421, 2.82843, 0), (0.70711, 2.82843, 0), (0.70711, 2.82843, 0.35), (1.41421, 2.82843, 0.35)}) → E_{6-6-F-1}
  39. Polygon({(0.70711, 2.82843, 0), (0, 2.82843, 0), (0, 2.82843, 0.35), (0.70711, 2.82843, 0.35)}) → E_{6-6-F-2}
  40. Polygon({(0.70711, 2.12132, 1.4), (1.41421, 2.82843, 0.35), (0.70711, 2.82843, 0.35)}) → E_{6-6-R-1}
  41. Polygon({(0.70711, 2.12132, 1.4), (0, 2.82843, 0.35), (0.70711, 2.82843, 0.35)}) → E_{6-6-R-3}
  42. Polygon({(-0.70711, 2.19203), (-0.14142, 2.75772), (-0.70711, 2.75772), (-1.27279, 2.75772)}) → E_{6-8-P}
  43. Segment((0, 2.82843), (-0.70711, 2.12132)) → E_{6-8-S-1}
  44. Segment((-0.70711, 2.82843), (-0.70711, 2.12132)) → E_{6-8-S-2}
  45. Segment((-1.41421, 2.82843), (-0.70711, 2.12132)) → E_{6-8-S-3}
  46. Segment((0, 2.82843), (-0.70711, 2.82843)) → E_{6-8-W-1}
  47. Segment((-1.41421, 2.82843), (-0.70711, 2.82843)) → E_{6-8-W-3}
  48. Polygon({(0, 2.82843, 0), (-0.70711, 2.82843, 0), (-0.70711, 2.82843, 0.35), (0, 2.82843, 0.35)}) → E_{6-8-F-1}
  49. Polygon({(-0.70711, 2.82843, 0), (-1.41421, 2.82843, 0), (-1.41421, 2.82843, 0.35), (-0.70711, 2.82843, 0.35)}) → E_{6-8-F-2}
  50. Polygon({(-0.70711, 2.12132, 1.4), (0, 2.82843, 0.35), (-0.70711, 2.82843, 0.35)}) → E_{6-8-R-1}
  51. Polygon({(-0.70711, 2.12132, 1.4), (-1.41421, 2.82843, 0.35), (-0.70711, 2.82843, 0.35)}) → E_{6-8-R-3}
  52. Polygon({(-2.12132, 2.19203), (-1.55563, 2.75772), (-2.12132, 2.75772), (-2.68701, 2.75772)}) → E_{6-10-P}
  53. Segment((-1.41421, 2.82843), (-2.12132, 2.12132)) → E_{6-10-S-1}
  54. Segment((-2.12132, 2.82843), (-2.12132, 2.12132)) → E_{6-10-S-2}
  55. Segment((-2.82843, 2.82843), (-2.12132, 2.12132)) → E_{6-10-S-3}
  56. Segment((-1.41421, 2.82843), (-2.12132, 2.82843)) → E_{6-10-W-1}
  57. Segment((-2.82843, 2.82843), (-2.12132, 2.82843)) → E_{6-10-W-3}
  58. Polygon({(-1.41421, 2.82843, 0), (-2.12132, 2.82843, 0), (-2.12132, 2.82843, 0.35), (-1.41421, 2.82843, 0.35)}) → E_{6-10-F-1}
  59. Polygon({(-2.12132, 2.82843, 0), (-2.82843, 2.82843, 0), (-2.82843, 2.82843, 0.35), (-2.12132, 2.82843, 0.35)}) → E_{6-10-F-2}
  60. Polygon({(-2.12132, 2.12132, 1.4), (-1.41421, 2.82843, 0.35), (-2.12132, 2.82843, 0.35)}) → E_{6-10-R-1}
  61. Polygon({(-2.12132, 2.12132, 1.4), (-2.82843, 2.82843, 0.35), (-2.12132, 2.82843, 0.35)}) → E_{6-10-R-3}
  62. Polygon({(-2.19203, 2.12132), (-2.75772, 2.68701), (-2.75772, 2.12132), (-2.75772, 1.55563)}) → E_{6-11-P}
  63. Segment((-2.82843, 2.82843), (-2.12132, 2.12132)) → E_{6-11-S-1}
  64. Segment((-2.82843, 2.12132), (-2.12132, 2.12132)) → E_{6-11-S-2}
  65. Segment((-2.82843, 1.41421), (-2.12132, 2.12132)) → E_{6-11-S-3}
  66. Segment((-2.82843, 2.82843), (-2.82843, 2.12132)) → E_{6-11-W-1}
  67. Segment((-2.82843, 1.41421), (-2.82843, 2.12132)) → E_{6-11-W-3}
  68. Polygon({(-2.82843, 2.82843, 0), (-2.82843, 2.12132, 0), (-2.82843, 2.12132, 0.35), (-2.82843, 2.82843, 0.35)}) → E_{6-11-F-1}
  69. Polygon({(-2.82843, 2.12132, 0), (-2.82843, 1.41421, 0), (-2.82843, 1.41421, 0.35), (-2.82843, 2.12132, 0.35)}) → E_{6-11-F-2}
  70. Polygon({(-2.12132, 2.12132, 1.4), (-2.82843, 2.82843, 0.35), (-2.82843, 2.12132, 0.35)}) → E_{6-11-R-1}
  71. Polygon({(-2.12132, 2.12132, 1.4), (-2.82843, 1.41421, 0.35), (-2.82843, 2.12132, 0.35)}) → E_{6-11-R-3}
  72. Polygon({(-2.19203, 0.70711), (-2.75772, 1.27279), (-2.75772, 0.70711), (-2.75772, 0.14142)}) → E_{6-13-P}
  73. Segment((-2.82843, 1.41421), (-2.12132, 0.70711)) → E_{6-13-S-1}
  74. Segment((-2.82843, 0.70711), (-2.12132, 0.70711)) → E_{6-13-S-2}
  75. Segment((-2.82843, 0), (-2.12132, 0.70711)) → E_{6-13-S-3}
  76. Segment((-2.82843, 1.41421), (-2.82843, 0.70711)) → E_{6-13-W-1}
  77. Segment((-2.82843, 0), (-2.82843, 0.70711)) → E_{6-13-W-3}
  78. Polygon({(-2.82843, 1.41421, 0), (-2.82843, 0.70711, 0), (-2.82843, 0.70711, 0.35), (-2.82843, 1.41421, 0.35)}) → E_{6-13-F-1}
  79. Polygon({(-2.82843, 0.70711, 0), (-2.82843, 0, 0), (-2.82843, 0, 0.35), (-2.82843, 0.70711, 0.35)}) → E_{6-13-F-2}
  80. Polygon({(-2.12132, 0.70711, 1.4), (-2.82843, 1.41421, 0.35), (-2.82843, 0.70711, 0.35)}) → E_{6-13-R-1}
  81. Polygon({(-2.12132, 0.70711, 1.4), (-2.82843, 0, 0.35), (-2.82843, 0.70711, 0.35)}) → E_{6-13-R-3}
  82. Polygon({(1.51421, 0.04142), (2.64558, 0.04142), (2.31421, 0.37279), (2.0799, 0.60711)}) → A1_{5-0-P}
  83. Segment((2.82843, 0), (1.41421, 0)) → A1_{5-0-S-1}
  84. Segment((2.41421, 0.41421), (1.41421, 0)) → A1_{5-0-S-2}
  85. Segment((2.12132, 0.70711), (1.41421, 0)) → A1_{5-0-S-3}
  86. Segment((2.82843, 0), (2.41421, 0.41421)) → A1_{5-0-W-1}
  87. Segment((2.12132, 0.70711), (2.41421, 0.41421)) → A1_{5-0-W-3}
  88. Polygon({(2.82843, 0, 1.4), (2.41421, 0.41421, 1.4), (2.41421, 0.41421, 1.75), (2.82843, 0, 1.75)}) → A1_{5-0-F-1}
  89. Polygon({(2.41421, 0.41421, 1.4), (2.12132, 0.70711, 1.4), (2.12132, 0.70711, 1.75), (2.41421, 0.41421, 1.75)}) → A1_{5-0-F-2}
  90. Polygon({(1.41421, 0, 2.8), (2.82843, 0, 1.75), (2.41421, 0.41421, 1.75)}) → A1_{5-0-R-1}
  91. Polygon({(1.41421, 0, 2.8), (2.12132, 0.70711, 1.75), (2.41421, 0.41421, 1.75)}) → A1_{5-0-R-3}
  92. Polygon({(2.82843, 0, 1.4), (2.12132, 0.70711, 1.4), (2.82843, 0, 0.35)}) → A1_{5-0-B-E}
  93. Polygon({(2.0799, 0.70711), (1.51421, 1.27279), (1.74853, 0.70711), (1.51421, 0.14142)}) → J_{5-1-P}
  94. Segment((2.12132, 0.70711), (1.41421, 1.41421)) → J_{5-1-S-1}
  95. Segment((2.12132, 0.70711), (1.70711, 0.70711)) → J_{5-1-S-2}
  96. Segment((2.12132, 0.70711), (1.41421, 0)) → J_{5-1-S-3}
  97. Segment((1.41421, 1.41421), (1.70711, 0.70711)) → J_{5-1-W-1}
  98. Segment((1.41421, 0), (1.70711, 0.70711)) → J_{5-1-W-3}
  99. Polygon({(2.12132, 0.70711, 1.75), (1.41421, 1.41421, 2.8), (1.70711, 0.70711, 2.8)}) → J_{5-1-R-1}
  100. Polygon({(2.12132, 0.70711, 1.75), (1.41421, 0, 2.8), (1.70711, 0.70711, 2.8)}) → J_{5-1-R-3}
  101. Polygon({(1.55563, 1.41421), (2.12132, 0.84853), (2.68701, 1.41421), (2.12132, 1.9799)}) → A_{5-2-P}
  102. Segment((2.12132, 0.70711), (1.41421, 1.41421)) → A_{5-2-S-1}
  103. Segment((2.82843, 1.41421), (1.41421, 1.41421)) → A_{5-2-S-2}
  104. Segment((2.12132, 2.12132), (1.41421, 1.41421)) → A_{5-2-S-3}
  105. Segment((2.12132, 0.70711), (2.82843, 1.41421)) → A_{5-2-W-1}
  106. Segment((2.12132, 2.12132), (2.82843, 1.41421)) → A_{5-2-W-3}
  107. Polygon({(2.12132, 0.70711, 1.4), (2.82843, 1.41421, 1.4), (2.82843, 1.41421, 1.75), (2.12132, 0.70711, 1.75)}) → A_{5-2-F-1}
  108. Polygon({(2.82843, 1.41421, 1.4), (2.12132, 2.12132, 1.4), (2.12132, 2.12132, 1.75), (2.82843, 1.41421, 1.75)}) → A_{5-2-F-2}
  109. Polygon({(1.41421, 1.41421, 2.8), (2.12132, 0.70711, 1.75), (2.82843, 1.41421, 1.75)}) → A_{5-2-R-1}
  110. Polygon({(1.41421, 1.41421, 2.8), (2.12132, 2.12132, 1.75), (2.82843, 1.41421, 1.75)}) → A_{5-2-R-3}
  111. Polygon({(2.82843, 1.41421, 1.4), (2.12132, 0.70711, 1.4), (2.82843, 1.41421, 0.35)}) → A_{5-2-B-R}
  112. Polygon({(2.82843, 1.41421, 1.4), (2.12132, 2.12132, 1.4), (2.82843, 1.41421, 0.35)}) → A_{5-2-B-L}
  113. Polygon({(1.41421, 1.55563), (1.9799, 2.12132), (1.41421, 2.68701), (0.84853, 2.12132)}) → A_{5-3-P}
  114. Segment((2.12132, 2.12132), (1.41421, 1.41421)) → A_{5-3-S-1}
  115. Segment((1.41421, 2.82843), (1.41421, 1.41421)) → A_{5-3-S-2}
  116. Segment((0.70711, 2.12132), (1.41421, 1.41421)) → A_{5-3-S-3}
  117. Segment((2.12132, 2.12132), (1.41421, 2.82843)) → A_{5-3-W-1}
  118. Segment((0.70711, 2.12132), (1.41421, 2.82843)) → A_{5-3-W-3}
  119. Polygon({(2.12132, 2.12132, 1.4), (1.41421, 2.82843, 1.4), (1.41421, 2.82843, 1.75), (2.12132, 2.12132, 1.75)}) → A_{5-3-F-1}
  120. Polygon({(1.41421, 2.82843, 1.4), (0.70711, 2.12132, 1.4), (0.70711, 2.12132, 1.75), (1.41421, 2.82843, 1.75)}) → A_{5-3-F-2}
  121. Polygon({(1.41421, 1.41421, 2.8), (2.12132, 2.12132, 1.75), (1.41421, 2.82843, 1.75)}) → A_{5-3-R-1}
  122. Polygon({(1.41421, 1.41421, 2.8), (0.70711, 2.12132, 1.75), (1.41421, 2.82843, 1.75)}) → A_{5-3-R-3}
  123. Polygon({(1.41421, 2.82843, 1.4), (2.12132, 2.12132, 1.4), (1.41421, 2.82843, 0.35)}) → A_{5-3-B-R}
  124. Polygon({(1.41421, 2.82843, 1.4), (0.70711, 2.12132, 1.4), (1.41421, 2.82843, 0.35)}) → A_{5-3-B-L}
  125. Polygon({(0.70711, 2.0799), (0.14142, 1.51421), (0.70711, 1.74853), (1.27279, 1.51421)}) → J_{5-4-P}
  126. Segment((0.70711, 2.12132), (0, 1.41421)) → J_{5-4-S-1}
  127. Segment((0.70711, 2.12132), (0.70711, 1.70711)) → J_{5-4-S-2}
  128. Segment((0.70711, 2.12132), (1.41421, 1.41421)) → J_{5-4-S-3}
  129. Segment((0, 1.41421), (0.70711, 1.70711)) → J_{5-4-W-1}
  130. Segment((1.41421, 1.41421), (0.70711, 1.70711)) → J_{5-4-W-3}
  131. Polygon({(0.70711, 2.12132, 1.75), (0, 1.41421, 2.8), (0.70711, 1.70711, 2.8)}) → J_{5-4-R-1}
  132. Polygon({(0.70711, 2.12132, 1.75), (1.41421, 1.41421, 2.8), (0.70711, 1.70711, 2.8)}) → J_{5-4-R-3}
  133. Polygon({(0.04142, 1.51421), (0.60711, 2.0799), (0.37279, 2.31421), (0.04142, 2.64558)}) → A2_{5-5-P}
  134. Segment((0.70711, 2.12132), (0, 1.41421)) → A2_{5-5-S-1}
  135. Segment((0.41421, 2.41421), (0, 1.41421)) → A2_{5-5-S-2}
  136. Segment((0, 2.82843), (0, 1.41421)) → A2_{5-5-S-3}
  137. Segment((0.70711, 2.12132), (0.41421, 2.41421)) → A2_{5-5-W-1}
  138. Segment((0, 2.82843), (0.41421, 2.41421)) → A2_{5-5-W-3}
  139. Polygon({(0.70711, 2.12132, 1.4), (0.41421, 2.41421, 1.4), (0.41421, 2.41421, 1.75), (0.70711, 2.12132, 1.75)}) → A2_{5-5-F-1}
  140. Polygon({(0.41421, 2.41421, 1.4), (0, 2.82843, 1.4), (0, 2.82843, 1.75), (0.41421, 2.41421, 1.75)}) → A2_{5-5-F-2}
  141. Polygon({(0, 1.41421, 2.8), (0.70711, 2.12132, 1.75), (0.41421, 2.41421, 1.75)}) → A2_{5-5-R-1}
  142. Polygon({(0, 1.41421, 2.8), (0, 2.82843, 1.75), (0.41421, 2.41421, 1.75)}) → A2_{5-5-R-3}
  143. Polygon({(0, 2.82843, 1.4), (0.70711, 2.12132, 1.4), (0, 2.82843, 0.35)}) → A2_{5-5-B-E}
  144. Polygon({(-0.04142, 1.51421), (-0.04142, 2.64558), (-0.37279, 2.31421), (-0.60711, 2.0799)}) → A1_{5-6-P}
  145. Segment((0, 2.82843), (0, 1.41421)) → A1_{5-6-S-1}
  146. Segment((-0.41421, 2.41421), (0, 1.41421)) → A1_{5-6-S-2}
  147. Segment((-0.70711, 2.12132), (0, 1.41421)) → A1_{5-6-S-3}
  148. Segment((0, 2.82843), (-0.41421, 2.41421)) → A1_{5-6-W-1}
  149. Segment((-0.70711, 2.12132), (-0.41421, 2.41421)) → A1_{5-6-W-3}
  150. Polygon({(0, 2.82843, 1.4), (-0.41421, 2.41421, 1.4), (-0.41421, 2.41421, 1.75), (0, 2.82843, 1.75)}) → A1_{5-6-F-1}
  151. Polygon({(-0.41421, 2.41421, 1.4), (-0.70711, 2.12132, 1.4), (-0.70711, 2.12132, 1.75), (-0.41421, 2.41421, 1.75)}) → A1_{5-6-F-2}
  152. Polygon({(0, 1.41421, 2.8), (0, 2.82843, 1.75), (-0.41421, 2.41421, 1.75)}) → A1_{5-6-R-1}
  153. Polygon({(0, 1.41421, 2.8), (-0.70711, 2.12132, 1.75), (-0.41421, 2.41421, 1.75)}) → A1_{5-6-R-3}
  154. Polygon({(0, 2.82843, 1.4), (-0.70711, 2.12132, 1.4), (0, 2.82843, 0.35)}) → A1_{5-6-B-E}
  155. Polygon({(-0.70711, 2.0799), (-1.27279, 1.51421), (-0.70711, 1.74853), (-0.14142, 1.51421)}) → J_{5-7-P}
  156. Segment((-0.70711, 2.12132), (-1.41421, 1.41421)) → J_{5-7-S-1}
  157. Segment((-0.70711, 2.12132), (-0.70711, 1.70711)) → J_{5-7-S-2}
  158. Segment((-0.70711, 2.12132), (0, 1.41421)) → J_{5-7-S-3}
  159. Segment((-1.41421, 1.41421), (-0.70711, 1.70711)) → J_{5-7-W-1}
  160. Segment((0, 1.41421), (-0.70711, 1.70711)) → J_{5-7-W-3}
  161. Polygon({(-0.70711, 2.12132, 1.75), (-1.41421, 1.41421, 2.8), (-0.70711, 1.70711, 2.8)}) → J_{5-7-R-1}
  162. Polygon({(-0.70711, 2.12132, 1.75), (0, 1.41421, 2.8), (-0.70711, 1.70711, 2.8)}) → J_{5-7-R-3}
  163. Polygon({(-1.41421, 1.55563), (-0.84853, 2.12132), (-1.41421, 2.68701), (-1.9799, 2.12132)}) → A_{5-8-P}
  164. Segment((-0.70711, 2.12132), (-1.41421, 1.41421)) → A_{5-8-S-1}
  165. Segment((-1.41421, 2.82843), (-1.41421, 1.41421)) → A_{5-8-S-2}
  166. Segment((-2.12132, 2.12132), (-1.41421, 1.41421)) → A_{5-8-S-3}
  167. Segment((-0.70711, 2.12132), (-1.41421, 2.82843)) → A_{5-8-W-1}
  168. Segment((-2.12132, 2.12132), (-1.41421, 2.82843)) → A_{5-8-W-3}
  169. Polygon({(-0.70711, 2.12132, 1.4), (-1.41421, 2.82843, 1.4), (-1.41421, 2.82843, 1.75), (-0.70711, 2.12132, 1.75)}) → A_{5-8-F-1}
  170. Polygon({(-1.41421, 2.82843, 1.4), (-2.12132, 2.12132, 1.4), (-2.12132, 2.12132, 1.75), (-1.41421, 2.82843, 1.75)}) → A_{5-8-F-2}
  171. Polygon({(-1.41421, 1.41421, 2.8), (-0.70711, 2.12132, 1.75), (-1.41421, 2.82843, 1.75)}) → A_{5-8-R-1}
  172. Polygon({(-1.41421, 1.41421, 2.8), (-2.12132, 2.12132, 1.75), (-1.41421, 2.82843, 1.75)}) → A_{5-8-R-3}
  173. Polygon({(-1.41421, 2.82843, 1.4), (-0.70711, 2.12132, 1.4), (-1.41421, 2.82843, 0.35)}) → A_{5-8-B-R}
  174. Polygon({(-1.41421, 2.82843, 1.4), (-2.12132, 2.12132, 1.4), (-1.41421, 2.82843, 0.35)}) → A_{5-8-B-L}
  175. Polygon({(-1.55563, 1.41421), (-2.12132, 1.9799), (-2.68701, 1.41421), (-2.12132, 0.84853)}) → A_{5-9-P}
  176. Segment((-2.12132, 2.12132), (-1.41421, 1.41421)) → A_{5-9-S-1}
  177. Segment((-2.82843, 1.41421), (-1.41421, 1.41421)) → A_{5-9-S-2}
  178. Segment((-2.12132, 0.70711), (-1.41421, 1.41421)) → A_{5-9-S-3}
  179. Segment((-2.12132, 2.12132), (-2.82843, 1.41421)) → A_{5-9-W-1}
  180. Segment((-2.12132, 0.70711), (-2.82843, 1.41421)) → A_{5-9-W-3}
  181. Polygon({(-2.12132, 2.12132, 1.4), (-2.82843, 1.41421, 1.4), (-2.82843, 1.41421, 1.75), (-2.12132, 2.12132, 1.75)}) → A_{5-9-F-1}
  182. Polygon({(-2.82843, 1.41421, 1.4), (-2.12132, 0.70711, 1.4), (-2.12132, 0.70711, 1.75), (-2.82843, 1.41421, 1.75)}) → A_{5-9-F-2}
  183. Polygon({(-1.41421, 1.41421, 2.8), (-2.12132, 2.12132, 1.75), (-2.82843, 1.41421, 1.75)}) → A_{5-9-R-1}
  184. Polygon({(-1.41421, 1.41421, 2.8), (-2.12132, 0.70711, 1.75), (-2.82843, 1.41421, 1.75)}) → A_{5-9-R-3}
  185. Polygon({(-2.82843, 1.41421, 1.4), (-2.12132, 2.12132, 1.4), (-2.82843, 1.41421, 0.35)}) → A_{5-9-B-R}
  186. Polygon({(-2.82843, 1.41421, 1.4), (-2.12132, 0.70711, 1.4), (-2.82843, 1.41421, 0.35)}) → A_{5-9-B-L}
  187. Polygon({(-2.0799, 0.70711), (-1.51421, 0.14142), (-1.74853, 0.70711), (-1.51421, 1.27279)}) → J_{5-10-P}
  188. Segment((-2.12132, 0.70711), (-1.41421, 0)) → J_{5-10-S-1}
  189. Segment((-2.12132, 0.70711), (-1.70711, 0.70711)) → J_{5-10-S-2}
  190. Segment((-2.12132, 0.70711), (-1.41421, 1.41421)) → J_{5-10-S-3}
  191. Segment((-1.41421, 0), (-1.70711, 0.70711)) → J_{5-10-W-1}
  192. Segment((-1.41421, 1.41421), (-1.70711, 0.70711)) → J_{5-10-W-3}
  193. Polygon({(-2.12132, 0.70711, 1.75), (-1.41421, 0, 2.8), (-1.70711, 0.70711, 2.8)}) → J_{5-10-R-1}
  194. Polygon({(-2.12132, 0.70711, 1.75), (-1.41421, 1.41421, 2.8), (-1.70711, 0.70711, 2.8)}) → J_{5-10-R-3}
  195. Polygon({(-1.51421, 0.04142), (-2.0799, 0.60711), (-2.31421, 0.37279), (-2.64558, 0.04142)}) → A2_{5-11-P}
  196. Segment((-2.12132, 0.70711), (-1.41421, 0)) → A2_{5-11-S-1}
  197. Segment((-2.41421, 0.41421), (-1.41421, 0)) → A2_{5-11-S-2}
  198. Segment((-2.82843, 0), (-1.41421, 0)) → A2_{5-11-S-3}
  199. Segment((-2.12132, 0.70711), (-2.41421, 0.41421)) → A2_{5-11-W-1}
  200. Segment((-2.82843, 0), (-2.41421, 0.41421)) → A2_{5-11-W-3}
  201. Polygon({(-2.12132, 0.70711, 1.4), (-2.41421, 0.41421, 1.4), (-2.41421, 0.41421, 1.75), (-2.12132, 0.70711, 1.75)}) → A2_{5-11-F-1}
  202. Polygon({(-2.41421, 0.41421, 1.4), (-2.82843, 0, 1.4), (-2.82843, 0, 1.75), (-2.41421, 0.41421, 1.75)}) → A2_{5-11-F-2}
  203. Polygon({(-1.41421, 0, 2.8), (-2.12132, 0.70711, 1.75), (-2.41421, 0.41421, 1.75)}) → A2_{5-11-R-1}
  204. Polygon({(-1.41421, 0, 2.8), (-2.82843, 0, 1.75), (-2.41421, 0.41421, 1.75)}) → A2_{5-11-R-3}
  205. Polygon({(-2.82843, 0, 1.4), (-2.12132, 0.70711, 1.4), (-2.82843, 0, 0.35)}) → A2_{5-11-B-E}
  206. Polygon({(1.36421, 0.02071), (0.79853, 0.5864), (0.96421, 0.1864), (1.03284, 0.02071)}) → J1_{4-0-P}
  207. Segment((1.41421, 0), (0.70711, 0.70711)) → J1_{4-0-S-1}
  208. Segment((1.41421, 0), (0.91421, 0.20711)) → J1_{4-0-S-2}
  209. Segment((1.41421, 0), (1, 0)) → J1_{4-0-S-3}
  210. Segment((0.70711, 0.70711), (0.91421, 0.20711)) → J1_{4-0-W-1}
  211. Segment((1, 0), (0.91421, 0.20711)) → J1_{4-0-W-3}
  212. Polygon({(1.41421, 0, 3.15), (0.70711, 0.70711, 4.2), (0.91421, 0.20711, 4.2)}) → J1_{4-0-R-1}
  213. Polygon({(1.41421, 0, 3.15), (1, 0, 4.2), (0.91421, 0.20711, 4.2)}) → J1_{4-0-R-3}
  214. Polygon({(0.80711, 0.70711), (1.37279, 0.14142), (1.60711, 0.70711), (1.37279, 1.27279)}) → D_{4-1-P}
  215. Segment((1.41421, 0), (0.70711, 0.70711)) → D_{4-1-S-1}
  216. Segment((1.70711, 0.70711), (0.70711, 0.70711)) → D_{4-1-S-2}
  217. Segment((1.41421, 1.41421), (0.70711, 0.70711)) → D_{4-1-S-3}
  218. Segment((1.41421, 0), (1.70711, 0.70711)) → D_{4-1-W-1}
  219. Segment((1.41421, 1.41421), (1.70711, 0.70711)) → D_{4-1-W-3}
  220. Polygon({(1.41421, 0, 2.8), (1.70711, 0.70711, 2.8), (1.70711, 0.70711, 3.15), (1.41421, 0, 3.15)}) → D_{4-1-F-1}
  221. Polygon({(1.70711, 0.70711, 2.8), (1.41421, 1.41421, 2.8), (1.41421, 1.41421, 3.15), (1.70711, 0.70711, 3.15)}) → D_{4-1-F-2}
  222. Polygon({(0.70711, 0.70711, 4.2), (1.41421, 0, 3.15), (1.70711, 0.70711, 3.15)}) → D_{4-1-R-1}
  223. Polygon({(0.70711, 0.70711, 4.2), (1.41421, 1.41421, 3.15), (1.70711, 0.70711, 3.15)}) → D_{4-1-R-3}
  224. Polygon({(0.70711, 0.80711), (1.27279, 1.37279), (0.70711, 1.60711), (0.14142, 1.37279)}) → D_{4-2-P}
  225. Segment((1.41421, 1.41421), (0.70711, 0.70711)) → D_{4-2-S-1}
  226. Segment((0.70711, 1.70711), (0.70711, 0.70711)) → D_{4-2-S-2}
  227. Segment((0, 1.41421), (0.70711, 0.70711)) → D_{4-2-S-3}
  228. Segment((1.41421, 1.41421), (0.70711, 1.70711)) → D_{4-2-W-1}
  229. Segment((0, 1.41421), (0.70711, 1.70711)) → D_{4-2-W-3}
  230. Polygon({(1.41421, 1.41421, 2.8), (0.70711, 1.70711, 2.8), (0.70711, 1.70711, 3.15), (1.41421, 1.41421, 3.15)}) → D_{4-2-F-1}
  231. Polygon({(0.70711, 1.70711, 2.8), (0, 1.41421, 2.8), (0, 1.41421, 3.15), (0.70711, 1.70711, 3.15)}) → D_{4-2-F-2}
  232. Polygon({(0.70711, 0.70711, 4.2), (1.41421, 1.41421, 3.15), (0.70711, 1.70711, 3.15)}) → D_{4-2-R-1}
  233. Polygon({(0.70711, 0.70711, 4.2), (0, 1.41421, 3.15), (0.70711, 1.70711, 3.15)}) → D_{4-2-R-3}
  234. Polygon({(0.02071, 1.36421), (0.02071, 1.03284), (0.1864, 0.96421), (0.5864, 0.79853)}) → J2_{4-3-P}
  235. Segment((0, 1.41421), (0, 1)) → J2_{4-3-S-1}
  236. Segment((0, 1.41421), (0.20711, 0.91421)) → J2_{4-3-S-2}
  237. Segment((0, 1.41421), (0.70711, 0.70711)) → J2_{4-3-S-3}
  238. Segment((0, 1), (0.20711, 0.91421)) → J2_{4-3-W-1}
  239. Segment((0.70711, 0.70711), (0.20711, 0.91421)) → J2_{4-3-W-3}
  240. Polygon({(0, 1.41421, 3.15), (0, 1, 4.2), (0.20711, 0.91421, 4.2)}) → J2_{4-3-R-1}
  241. Polygon({(0, 1.41421, 3.15), (0.70711, 0.70711, 4.2), (0.20711, 0.91421, 4.2)}) → J2_{4-3-R-3}
  242. Polygon({(-0.02071, 1.36421), (-0.5864, 0.79853), (-0.1864, 0.96421), (-0.02071, 1.03284)}) → J1_{4-4-P}
  243. Segment((0, 1.41421), (-0.70711, 0.70711)) → J1_{4-4-S-1}
  244. Segment((0, 1.41421), (-0.20711, 0.91421)) → J1_{4-4-S-2}
  245. Segment((0, 1.41421), (0, 1)) → J1_{4-4-S-3}
  246. Segment((-0.70711, 0.70711), (-0.20711, 0.91421)) → J1_{4-4-W-1}
  247. Segment((0, 1), (-0.20711, 0.91421)) → J1_{4-4-W-3}
  248. Polygon({(0, 1.41421, 3.15), (-0.70711, 0.70711, 4.2), (-0.20711, 0.91421, 4.2)}) → J1_{4-4-R-1}
  249. Polygon({(0, 1.41421, 3.15), (0, 1, 4.2), (-0.20711, 0.91421, 4.2)}) → J1_{4-4-R-3}
  250. Polygon({(-0.70711, 0.80711), (-0.14142, 1.37279), (-0.70711, 1.60711), (-1.27279, 1.37279)}) → D_{4-5-P}
  251. Segment((0, 1.41421), (-0.70711, 0.70711)) → D_{4-5-S-1}
  252. Segment((-0.70711, 1.70711), (-0.70711, 0.70711)) → D_{4-5-S-2}
  253. Segment((-1.41421, 1.41421), (-0.70711, 0.70711)) → D_{4-5-S-3}
  254. Segment((0, 1.41421), (-0.70711, 1.70711)) → D_{4-5-W-1}
  255. Segment((-1.41421, 1.41421), (-0.70711, 1.70711)) → D_{4-5-W-3}
  256. Polygon({(0, 1.41421, 2.8), (-0.70711, 1.70711, 2.8), (-0.70711, 1.70711, 3.15), (0, 1.41421, 3.15)}) → D_{4-5-F-1}
  257. Polygon({(-0.70711, 1.70711, 2.8), (-1.41421, 1.41421, 2.8), (-1.41421, 1.41421, 3.15), (-0.70711, 1.70711, 3.15)}) → D_{4-5-F-2}
  258. Polygon({(-0.70711, 0.70711, 4.2), (0, 1.41421, 3.15), (-0.70711, 1.70711, 3.15)}) → D_{4-5-R-1}
  259. Polygon({(-0.70711, 0.70711, 4.2), (-1.41421, 1.41421, 3.15), (-0.70711, 1.70711, 3.15)}) → D_{4-5-R-3}
  260. Polygon({(-0.80711, 0.70711), (-1.37279, 1.27279), (-1.60711, 0.70711), (-1.37279, 0.14142)}) → D_{4-6-P}
  261. Segment((-1.41421, 1.41421), (-0.70711, 0.70711)) → D_{4-6-S-1}
  262. Segment((-1.70711, 0.70711), (-0.70711, 0.70711)) → D_{4-6-S-2}
  263. Segment((-1.41421, 0), (-0.70711, 0.70711)) → D_{4-6-S-3}
  264. Segment((-1.41421, 1.41421), (-1.70711, 0.70711)) → D_{4-6-W-1}
  265. Segment((-1.41421, 0), (-1.70711, 0.70711)) → D_{4-6-W-3}
  266. Polygon({(-1.41421, 1.41421, 2.8), (-1.70711, 0.70711, 2.8), (-1.70711, 0.70711, 3.15), (-1.41421, 1.41421, 3.15)}) → D_{4-6-F-1}
  267. Polygon({(-1.70711, 0.70711, 2.8), (-1.41421, 0, 2.8), (-1.41421, 0, 3.15), (-1.70711, 0.70711, 3.15)}) → D_{4-6-F-2}
  268. Polygon({(-0.70711, 0.70711, 4.2), (-1.41421, 1.41421, 3.15), (-1.70711, 0.70711, 3.15)}) → D_{4-6-R-1}
  269. Polygon({(-0.70711, 0.70711, 4.2), (-1.41421, 0, 3.15), (-1.70711, 0.70711, 3.15)}) → D_{4-6-R-3}
  270. Polygon({(-1.36421, 0.02071), (-1.03284, 0.02071), (-0.96421, 0.1864), (-0.79853, 0.5864)}) → J2_{4-7-P}
  271. Segment((-1.41421, 0), (-1, 0)) → J2_{4-7-S-1}
  272. Segment((-1.41421, 0), (-0.91421, 0.20711)) → J2_{4-7-S-2}
  273. Segment((-1.41421, 0), (-0.70711, 0.70711)) → J2_{4-7-S-3}
  274. Segment((-1, 0), (-0.91421, 0.20711)) → J2_{4-7-W-1}
  275. Segment((-0.70711, 0.70711), (-0.91421, 0.20711)) → J2_{4-7-W-3}
  276. Polygon({(-1.41421, 0, 3.15), (-1, 0, 4.2), (-0.91421, 0.20711, 4.2)}) → J2_{4-7-R-1}
  277. Polygon({(-1.41421, 0, 3.15), (-0.70711, 0.70711, 4.2), (-0.91421, 0.20711, 4.2)}) → J2_{4-7-R-3}
  278. Polygon({(0.08536, 0.03536), (0.88536, 0.03536), (0.7682, 0.3182), (0.65104, 0.60104)}) → F_{3-0-P}
  279. Segment((1, 0), (0, 0)) → F_{3-0-S-1}
  280. Segment((0.85355, 0.35355), (0, 0)) → F_{3-0-S-2}
  281. Segment((0.70711, 0.70711), (0, 0)) → F_{3-0-S-3}
  282. Segment((1, 0), (0.85355, 0.35355)) → F_{3-0-W-1}
  283. Segment((0.70711, 0.70711), (0.85355, 0.35355)) → F_{3-0-W-3}
  284. Polygon({(1, 0, 4.2), (0.85355, 0.35355, 4.2), (0.85355, 0.35355, 4.55), (1, 0, 4.55)}) → F_{3-0-F-1}
  285. Polygon({(0.85355, 0.35355, 4.2), (0.70711, 0.70711, 4.2), (0.70711, 0.70711, 4.55), (0.85355, 0.35355, 4.55)}) → F_{3-0-F-2}
  286. Polygon({(0, 0, 5.6), (1, 0, 4.55), (0.85355, 0.35355, 4.55)}) → F_{3-0-R-1}
  287. Polygon({(0, 0, 5.6), (0.70711, 0.70711, 4.55), (0.85355, 0.35355, 4.55)}) → F_{3-0-R-3}
  288. Polygon({(0.03536, 0.08536), (0.60104, 0.65104), (0.3182, 0.7682), (0.03536, 0.88536)}) → F_{3-1-P}
  289. Segment((0.70711, 0.70711), (0, 0)) → F_{3-1-S-1}
  290. Segment((0.35355, 0.85355), (0, 0)) → F_{3-1-S-2}
  291. Segment((0, 1), (0, 0)) → F_{3-1-S-3}
  292. Segment((0.70711, 0.70711), (0.35355, 0.85355)) → F_{3-1-W-1}
  293. Segment((0, 1), (0.35355, 0.85355)) → F_{3-1-W-3}
  294. Polygon({(0.70711, 0.70711, 4.2), (0.35355, 0.85355, 4.2), (0.35355, 0.85355, 4.55), (0.70711, 0.70711, 4.55)}) → F_{3-1-F-1}
  295. Polygon({(0.35355, 0.85355, 4.2), (0, 1, 4.2), (0, 1, 4.55), (0.35355, 0.85355, 4.55)}) → F_{3-1-F-2}
  296. Polygon({(0, 0, 5.6), (0.70711, 0.70711, 4.55), (0.35355, 0.85355, 4.55)}) → F_{3-1-R-1}
  297. Polygon({(0, 0, 5.6), (0, 1, 4.55), (0.35355, 0.85355, 4.55)}) → F_{3-1-R-3}
  298. Polygon({(-0.03536, 0.08536), (-0.03536, 0.88536), (-0.3182, 0.7682), (-0.60104, 0.65104)}) → F_{3-2-P}
  299. Segment((0, 1), (0, 0)) → F_{3-2-S-1}
  300. Segment((-0.35355, 0.85355), (0, 0)) → F_{3-2-S-2}
  301. Segment((-0.70711, 0.70711), (0, 0)) → F_{3-2-S-3}
  302. Segment((0, 1), (-0.35355, 0.85355)) → F_{3-2-W-1}
  303. Segment((-0.70711, 0.70711), (-0.35355, 0.85355)) → F_{3-2-W-3}
  304. Polygon({(0, 1, 4.2), (-0.35355, 0.85355, 4.2), (-0.35355, 0.85355, 4.55), (0, 1, 4.55)}) → F_{3-2-F-1}
  305. Polygon({(-0.35355, 0.85355, 4.2), (-0.70711, 0.70711, 4.2), (-0.70711, 0.70711, 4.55), (-0.35355, 0.85355, 4.55)}) → F_{3-2-F-2}
  306. Polygon({(0, 0, 5.6), (0, 1, 4.55), (-0.35355, 0.85355, 4.55)}) → F_{3-2-R-1}
  307. Polygon({(0, 0, 5.6), (-0.70711, 0.70711, 4.55), (-0.35355, 0.85355, 4.55)}) → F_{3-2-R-3}
  308. Polygon({(-0.08536, 0.03536), (-0.65104, 0.60104), (-0.7682, 0.3182), (-0.88536, 0.03536)}) → F_{3-3-P}
  309. Segment((-0.70711, 0.70711), (0, 0)) → F_{3-3-S-1}
  310. Segment((-0.85355, 0.35355), (0, 0)) → F_{3-3-S-2}
  311. Segment((-1, 0), (0, 0)) → F_{3-3-S-3}
  312. Segment((-0.70711, 0.70711), (-0.85355, 0.35355)) → F_{3-3-W-1}
  313. Segment((-1, 0), (-0.85355, 0.35355)) → F_{3-3-W-3}
  314. Polygon({(-0.70711, 0.70711, 4.2), (-0.85355, 0.35355, 4.2), (-0.85355, 0.35355, 4.55), (-0.70711, 0.70711, 4.55)}) → F_{3-3-F-1}
  315. Polygon({(-0.85355, 0.35355, 4.2), (-1, 0, 4.2), (-1, 0, 4.55), (-0.85355, 0.35355, 4.55)}) → F_{3-3-F-2}
  316. Polygon({(0, 0, 5.6), (-0.70711, 0.70711, 4.55), (-0.85355, 0.35355, 4.55)}) → F_{3-3-R-1}
  317. Polygon({(0, 0, 5.6), (-1, 0, 4.55), (-0.85355, 0.35355, 4.55)}) → F_{3-3-R-3}

AI Drawing Prompt Reference

Draw a complex Muqarnas geometric pattern composed of multiple polygons and segments. Start by drawing the bottom polygon, then add connecting segments to form a continuous boundary. Next, build the middle layer polygons and segments, and finally add the top polygons and segments, ensuring each part seamlessly connects to its adjacent parts.
The prompt above was compiled from the original drawing commands and is for reference only.