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Fuller Icosahedron Model

Fuller Icosahedron Model
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2023-03-14 01:21
VectorSolid GeometryGeometric Construction
In collections geometriadinamica.es
This example demonstrates a Fuller Icosahedron model, involving the construction of polyhedra in solid geometry. It uses commands such as Ellipse, Point, Intersect, Angle, Vector, Translate, Circle, Line, Rotate, and Segment in GeoGebra. Suitable for high school or university solid geometry courses.

GeoGebra Commands & Parameters

  1. Ellipse(O_r - (0.95, 0), O_r + (0.95, 0), 1) → mira1
  2. Point(mira1) → A
  3. Ellipse(O_r - (0, 0.95), O_r + (0, 0.95), 1) → mira2
  4. Point(mira2) → B
  5. Intersect(mira1, mira2) → Mira1, Mira2, Mira3, Mira4
  6. Angle(M, O_r, B) → θ
  7. Angle(U, O_r, A) → φ
  8. Vector(O_r, O_0) → u
  9. Translate(Xr, u) → X0
  10. Translate(Zr, u) → Z0
  11. Translate(Yr, u) → Y0
  12. Vector(O_0, Z0) → v
  13. Vector(O_0, Y0) → w
  14. Vector(O_0, X0) → z
  15. Circle(O_0, L) → c
  16. Line(O_0, Y0) → a
  17. Line(O_0, yAxis) → b
  18. Line(O_0, X0) → g
  19. Line(Z0, O_0) → j
  20. Translate(P1r, u) → P1
  21. Rotate(A, botonpaso, O_r) → botonA
  22. Rotate(B, botonpaso, O_r) → botonB
  23. Segment(Mira3, Mira2) → k
  24. Segment((-1, 0), U) → l
  25. Segment((0, -1), M) → m
  26. punto3d(A, B, M, O_0, O_r, 0, 1, fi, U, L) → icoV1
  27. punto3d(A, B, M, O_0, O_r, 0, 1, (-fi), U, L) → icoV2
  28. punto3d(A, B, M, O_0, O_r, 0, -1, fi, U, L) → icoV3
  29. punto3d(A, B, M, O_0, O_r, 0, -1, (-fi), U, L) → icoV4
  30. punto3d(A, B, M, O_0, O_r, 1, fi, 0, U, L) → icoV5
  31. punto3d(A, B, M, O_0, O_r, 1, (-fi), 0, U, L) → icoV6
  32. punto3d(A, B, M, O_0, O_r, -1, fi, 0, U, L) → icoV7
  33. punto3d(A, B, M, O_0, O_r, -1, (-fi), 0, U, L) → icoV8
  34. punto3d(A, B, M, O_0, O_r, fi, 0, 1, U, L) → icoV9
  35. punto3d(A, B, M, O_0, O_r, fi, 0, -1, U, L) → icoV10
  36. punto3d(A, B, M, O_0, O_r, (-fi), 0, 1, U, L) → icoV11
  37. punto3d(A, B, M, O_0, O_r, (-fi), 0, -1, U, L) → icoV12
  38. Segment(icoV7, icoV11) → icoA04
  39. Segment(icoV11, icoV12) → icoA06
  40. Segment(icoV7, icoV12) → icoA08
  41. Segment(icoV11, icoV8) → icoA11
  42. Segment(icoV8, icoV12) → icoA13
  43. Segment(icoV7, icoV2) → icoA19
  44. Segment(icoV2, icoV12) → icoA21
  45. Segment(icoV4, icoV12) → icoA23
  46. Segment(icoV4, icoV2) → icoA25
  47. Segment(icoV4, icoV8) → icoA27
  48. Segment(icoV5, icoV2) → icoA29
  49. Segment(icoV5, icoV7) → icoA01
  50. Segment(icoV5, icoV1) → icoA02
  51. Segment(icoV1, icoV7) → icoA03
  52. Segment(icoV9, icoV5) → icoA05
  53. Segment(icoV5, icoV10) → icoA09
  54. Segment(icoV9, icoV10) → icoA10
  55. Segment(icoV2, icoV10) → icoA12
  56. Segment(icoV9, icoV1) → icoA07
  57. Segment(icoV4, icoV10) → icoA14
  58. Segment(icoV1, icoV11) → icoA15
  59. Segment(icoV3, icoV1) → icoA16
  60. Segment(icoV3, icoV11) → icoA17
  61. Segment(icoV3, icoV8) → icoA18
  62. Segment(icoV6, icoV8) → icoA20
  63. Segment(icoV6, icoV3) → icoA22
  64. Segment(icoV9, icoV3) → icoA24
  65. Segment(icoV9, icoV6) → icoA26
  66. Segment(icoV6, icoV10) → icoA28
  67. Segment(icoV6, icoV4) → icoA30
  68. Angle(icoV3, icoV9, icoV6) → ico01Ang
  69. If(ico01Ang < 180°, icoV9, icoV6) → icoV9b
  70. Angle(icoV3, icoV6, icoV8) → ico02Ang
  71. If(ico02Ang < 180°, icoV6, icoV8) → icoV6b
  72. Angle(icoV3, icoV8, icoV11) → ico03Ang
  73. If(ico03Ang < 180°, icoV8, icoV11) → icoV8b
  74. Angle(icoV3, icoV11, icoV1) → ico4Ang
  75. If(ico4Ang < 180°, icoV11, icoV1) → icoV11b
  76. Angle(icoV3, icoV1, icoV9) → ico5Ang
  77. If(ico5Ang < 180°, icoV1, icoV9) → icoV1b
  78. Angle(icoV9, icoV10, icoV6) → ico6Ang
  79. If(ico6Ang < 180°, icoV10, icoV6) → icoV10b
  80. Angle(icoV6, icoV10, icoV4) → ico7Ang
  81. If(ico7Ang < 180°, icoV10, icoV4) → icoV10c
  82. Angle(icoV6, icoV4, icoV8) → ico8Ang
  83. If(ico8Ang < 180°, icoV4, icoV8) → icoV4b
  84. Angle(icoV8, icoV4, icoV12) → ico9Ang
  85. If(ico9Ang < 180°, icoV4, icoV12) → icoV4c
  86. Angle(icoV8, icoV12, icoV11) → ico10Ang
  87. If(ico10Ang < 180°, icoV12, icoV11) → icoV12b
  88. Angle(icoV11, icoV12, icoV7) → ico11Ang
  89. If(ico11Ang < 180°, icoV12, icoV11) → icoV12c
  90. Angle(icoV11, icoV7, icoV1) → ico12Ang
  91. If(ico12Ang < 180°, icoV7, icoV11) → icoV7b
  92. Angle(icoV1, icoV7, icoV5) → ico13Ang
  93. If(ico13Ang < 180°, icoV7, icoV1) → icoV7c
  94. Angle(icoV1, icoV5, icoV9) → ico14Ang
  95. If(ico14Ang < 180°, icoV5, icoV1) → icoV5b
  96. Angle(icoV9, icoV5, icoV10) → ico15Ang
  97. If(ico15Ang < 180°, icoV5, icoV9) → icoV5c
  98. Angle(icoV10, icoV2, icoV4) → ico16Ang
  99. If(ico16Ang < 180°, icoV2, icoV4) → icoV2b
  100. Angle(icoV4, icoV2, icoV12) → ico17Ang
  101. If(ico17Ang < 180°, icoV2, icoV4) → icoV2c
  102. Angle(icoV2, icoV7, icoV12) → ico18Ang
  103. If(ico18Ang < 180°, icoV7, icoV12) → icoV7d
  104. Angle(icoV5, icoV7, icoV2) → ico19Ang
  105. If(ico19Ang < 180°, icoV7, icoV5) → icoV7e
  106. Angle(icoV5, icoV2, icoV10) → ico20Ang
  107. If(ico20Ang < 180°, icoV2, icoV5) → icoV2d
  108. Polygon(icoV6, icoV3, icoV9b) → ico01, ico01v9, ico01v6, ico01v3
  109. Polygon(icoV8, icoV3, icoV6b) → ico02, ico02v6, ico02v8, ico02v3
  110. Polygon(icoV11, icoV3, icoV8b) → ico03, ico03v8, ico03v11, ico03v3
  111. Polygon(icoV1, icoV3, icoV11b) → ico4, ico4v11, ico4v1, ico4v3
  112. Polygon(icoV9, icoV3, icoV1b) → ico5, ico5v1, ico5v9, ico5v3
  113. Polygon(icoV6, icoV9, icoV10b) → ico6, ico6v10, ico6v6, ico6v9
  114. Polygon(icoV4, icoV6, icoV10c) → ico7, ico7v10, ico7v4, ico7v6
  115. Polygon(icoV8, icoV6, icoV4b) → ico8, ico8v4, ico8v8, ico8v6
  116. Polygon(icoV8, icoV12, icoV4c) → ico9, ico9v4, ico9v8, ico9v12
  117. Polygon(icoV8, icoV11, icoV12b) → ico10, ico10v12, ico10v8, ico10v11
  118. Polygon(icoV7, icoV11, icoV12c) → ico11, ico11v12, ico11v7, ico11v11
  119. Polygon(icoV1, icoV11, icoV7b) → ico12, ico12v7, ico12v1, ico12v11
  120. Polygon(icoV1, icoV5, icoV7c) → ico13, ico13v7, ico13v1, ico13v5
  121. Polygon(icoV1, icoV9, icoV5b) → ico14, ico14v5, ico14v1, ico14v9
  122. Polygon(icoV10, icoV9, icoV5c) → ico15, ico15v5, ico15v10, ico15v9
  123. Polygon(icoV10, icoV4, icoV2b) → ico16, ico16v2, ico16v10, ico16v4
  124. Polygon(icoV12, icoV4, icoV2c) → ico17, ico17v2, ico17v12, ico17v4
  125. Polygon(icoV12, icoV2, icoV7d) → ico18, ico18v7, ico18v12, ico18v2
  126. Polygon(icoV5, icoV2, icoV7e) → ico19, ico19v7, ico19v5, ico19v2
  127. Polygon(icoV5, icoV10, icoV2d) → ico20, ico20v2, ico20v5, ico20v10
  128. Segment(icoV5, icoV7) → icoA01'
  129. Segment(icoV5, icoV1) → icoA02'
  130. Segment(icoV1, icoV7) → icoA03'
  131. Segment(icoV7, icoV11) → icoA04'
  132. Segment(icoV9, icoV5) → icoA05'
  133. Segment(icoV11, icoV12) → icoA06'
  134. Segment(icoV9, icoV1) → icoA07'
  135. Segment(icoV7, icoV12) → icoA08'
  136. Segment(icoV5, icoV10) → icoA09'
  137. Segment(icoV9, icoV10) → icoA10'
  138. Segment(icoV11, icoV8) → icoA11'
  139. Segment(icoV2, icoV10) → icoA12'
  140. Segment(icoV8, icoV12) → icoA13'
  141. Segment(icoV4, icoV10) → icoA14'
  142. Segment(icoV1, icoV11) → icoA15'
  143. Segment(icoV3, icoV1) → icoA16'
  144. Segment(icoV3, icoV11) → icoA17'
  145. Segment(icoV3, icoV8) → icoA18'
  146. Segment(icoV7, icoV2) → icoA19'
  147. Segment(icoV6, icoV8) → icoA20'
  148. Segment(icoV2, icoV12) → icoA21'
  149. Segment(icoV6, icoV3) → icoA22'
  150. Segment(icoV4, icoV12) → icoA23'
  151. Segment(icoV9, icoV3) → icoA24'
  152. Segment(icoV4, icoV2) → icoA25'
  153. Segment(icoV9, icoV6) → icoA26'
  154. Segment(icoV4, icoV8) → icoA27'
  155. Segment(icoV6, icoV10) → icoA28'
  156. Segment(icoV5, icoV2) → icoA29'
  157. Segment(icoV6, icoV4) → icoA30'
  158. Midpoint(icoV1, icoV11) → icoA15M
  159. Midpoint(icoV1, icoV7) → icoA03M
  160. Midpoint(icoV9, icoV1) → icoA07M
  161. Midpoint(icoV9, icoV5) → icoA05M
  162. Midpoint(icoV5, icoV7) → icoA01M
  163. Midpoint(icoV9, icoV10) → icoA10M
  164. Midpoint(icoV4, icoV10) → icoA14M
  165. Midpoint(icoV2, icoV12) → icoA21M
  166. Midpoint(icoV4, icoV8) → icoA27M
  167. Midpoint(icoV12, icoV7) → icoA08M
  168. Midpoint(icoV8, icoV12) → icoA13M
  169. Midpoint(icoV8, icoV6) → icoA20M
  170. Midpoint(icoV3, icoV5) → C
  171. Midpoint(icoV8, icoV2) → D
  172. Polygon(icoV5, C, D, icoV2) → poly1, icov5, c_1, d, icov2
  173. Polygon(C, icoV3, icoV8, D) → poly4, c_2, icov3, icov8, d_1
  174. Midpoint(icoV6, icoV11) → E
  175. Midpoint(icoV10, icoV7) → F
  176. Polygon(icoV11, E, F, icoV7) → poly3, icov11, e, f, icov7
  177. Polygon(E, icoV6, icoV10, F) → poly5, e_1, icov6, icov10, f_1
  178. Midpoint(icoV9, icoV4) → G
  179. Midpoint(icoV1, icoV12) → H
  180. Polygon(icoV1, icoV9, G, H) → poly2, icov1, icov9, g_1, h
  181. Polygon(icoV4, G, H, icoV12) → poly6, icov4, g_2, h_1, icov12

AI Drawing Prompt Reference

Draw a Fuller icosahedron model by first creating two perpendicular ellipses and finding their intersection points. Then, draw coordinate axes and a unit circle centered at the ellipse's center. Use vector rotations and translations to construct the model's vertices and faces. Finally, connect these vertices to form the three-dimensional structure of the Fuller icosahedron.
The prompt above was compiled from the original drawing commands and is for reference only.