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Rhombicosidodecahedron 3D Geometric Construction

Rhombicosidodecahedron 3D Geometric Construction
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2017-01-19 13:06
PolygonVectorSolid GeometryTransformationGeometric Construction
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This example demonstrates how to construct a Rhombicosidodecahedron in GeoGebra's 3D view, an Archimedean solid derived from truncating both a regular dodecahedron and icosahedron, featuring 20 equilateral triangular faces, 30 square faces, and 12 regular pentagonal faces. The core mathematical concepts include polyhedron vertex-edge-face relationships, spatial transformations such as rotation, translation, and vectors. Construction highlights: based on the summary, commands like Point, Dodecahedron, Icosahedron create base solids; Centroid finds centers; Angle, OrthogonalLine, Intersect determine geometric relations; Vector, Translate, Polygon, Sequence, Rotate generate and arrange faces, finally assembling the complete rhombicosidodecahedron. This example suits high school or college solid geometry courses, helping students intuitively understand Archimedean solids and serving as a teaching demonstration for 3D modeling and geometric transformations.

GeoGebra Commands & Parameters

  1. Point(Circle[((dodeA * (1 - sqrt(5))) + (dodeB * (3 + sqrt(5)))) / 4, (Distance[dodeA, dodeB] * sqrt(10 + (2 * sqrt(5))) / 4), Segment[dodeA, dodeB]]) → dodeC
  2. Dodecahedron(dodeA, dodeB, dodeC) → a, dodeD, dodeM, dodeN, dodeO, dodeP, dodeQ, dodeR, dodeS, dodeT, dodeface1, dodeface3, dodeE, dodeface2, dodeface4, dodeface5, dodeface6, dodeface10, dodeface11, dodeface7, dodeface8, dodeface9, dodeface12, dodeF, edgeAE_1, edgeAB, edgeBC, edgeCD_1, edgeDE, edgeAJ, edgeEI, edgeIO, edgeJO, edgeJK, dodeG, edgeFK, edgeBF_1, edgeFL, edgeGL, edgeCG, edgeGM, edgeHM, edgeDH, edgeHN, edgeIN, dodeH, edgeNS, edgeST, edgeOT, edgePT, edgeKP, edgePQ, edgeLQ, edgeQR, edgeMR, edgeRS, dodeI, dodeJ, dodeK, dodeL
  3. Centroid(dodeface12) → centrod12
  4. Angle(dodeP, centrod12, dodeQ) → α
  5. Centroid(dodeface11) → centrod11
  6. Centroid(dodeface10) → centrod10
  7. OrthogonalLine(centrod10, dodeface10) → centrodode2
  8. Centroid(dodeface7) → centrod7
  9. OrthogonalLine(centrod7, dodeface7) → centrodode1
  10. Intersect(centrodode1, centrodode2) → centrodode
  11. Vector(centrodode, centrod11) → dodeu11
  12. Translate(dodeP, Vector[(t * dodeu11)]) → dodeP'
  13. Vector(centrodode, centrod7) → dodeu7
  14. Translate(dodeP, Vector[(t * dodeu7)]) → dodeP'_2
  15. Vector(centrodode, centrod12) → dodeu12
  16. Translate(dodeP, Vector[(t * dodeu12)]) → dodeP'_1
  17. Polygon(dodeP', dodeP'_2, dodeP'_1) → poly1, dodep'_1, dodep', dodep'_2
  18. Centroid(dodeface1) → centrod1
  19. Centroid(dodeface2) → centrod2
  20. Centroid(dodeface3) → centrod3
  21. Centroid(dodeface4) → centrodi4
  22. Centroid(dodeface5) → centrodi5
  23. Centroid(dodeface6) → centrod6
  24. Centroid(dodeface8) → centrodi8
  25. Centroid(dodeface9) → centrod9
  26. Vector(centrodode, centrod10) → dodeu10
  27. Vector(centrodode, centrod9) → dodeu9
  28. Vector(centrodode, centrodi8) → dodeu8
  29. Vector(centrodode, centrodi4) → dodeu4
  30. Vector(centrodode, centrodi5) → dodeu5
  31. Vector(centrodode, centrod6) → dodeu6
  32. Vector(centrodode, centrod1) → dodeu1
  33. Vector(centrodode, centrod2) → dodeu2
  34. Vector(centrodode, centrod3) → dodeu3
  35. Icosahedron(centrodi5, centrodi4, centrodi8) → c, icoA, icoface20, icoface14, icoface13, icoface5, icoface4, icoface3, icoface8, icoface9, icoface10, icoface15, icoB, icoface6, icoface7, icoface18, icoface12, icoface17, icoface19, icoface16, icoface11, icoface2, icoface1, icoC, edgecentrod5centrod8, edgecentrod4centrod5, edgecentrod4centrod8, edgeCcentrod5, edgeCcentrod8, edgecentrod5D, edgeCD, edgeAcentrod5, edgeAD, edgeAcentrod4, icoD, edgecentrod4E, edgeAE, edgeBcentrod4, edgeBE, edgeBcentrod8, edgecentrod8F, edgeBF, edgeCF, edgeBH, edgeEH, icoE, edgeFH, edgeFI, edgeHI, edgeCI, edgeGH, edgeEG, edgeGI, edgeDI, edgeDG, edgeAG, icoF, icoG, icoH, icoI
  36. Translate(dodeface11, Vector[(t * dodeu11)]) → dodeface11'
  37. Translate(dodeface1, Vector[(t * dodeu1)]) → dodeface1'
  38. Translate(dodeface2, Vector[(t * dodeu2)]) → dodeface2'
  39. Translate(dodeface3, Vector[(t * dodeu3)]) → dodeface3'
  40. Translate(dodeface4, Vector[(t * dodeu4)]) → dodeface4'
  41. Translate(dodeface5, Vector[(t * dodeu5)]) → dodeface5'
  42. Translate(dodeface6, Vector[(t * dodeu6)]) → dodeface6'
  43. Translate(dodeface7, Vector[(t * dodeu7)]) → dodeface7'
  44. Translate(dodeface8, Vector[(t * dodeu8)]) → dodeface8'
  45. Translate(dodeface9, Vector[(t * dodeu9)]) → dodeface9'
  46. Translate(dodeface10, Vector[(t * dodeu10)]) → dodeface10'
  47. Translate(dodeface12, Vector[(t * dodeu12)]) → dodeface12'
  48. Centroid(icoface1) → centroi1
  49. Centroid(icoface2) → centroi2
  50. Centroid(icoface3) → centroi3
  51. Centroid(icoface4) → centroi4
  52. Centroid(icoface5) → centroi5
  53. Centroid(icoface6) → centroi6
  54. Centroid(icoface7) → centroi7
  55. Centroid(icoface8) → centroi8
  56. Centroid(icoface9) → centroi9
  57. Centroid(icoface10) → centroi10
  58. Centroid(icoface11) → centroi11
  59. Centroid(icoface12) → centroi12
  60. Centroid(icoface13) → centroi13
  61. Centroid(icoface14) → centroi14
  62. Centroid(icoface15) → centroi15
  63. Centroid(icoface16) → centroi16
  64. Centroid(icoface17) → centroi17
  65. Centroid(icoface18) → centroi18
  66. Centroid(icoface19) → centroi19
  67. Centroid(icoface20) → centroi20
  68. Vector(centrodode, dodeO) → icou1
  69. Translate(icoface19, icou1) → icoface19'
  70. Vector(centrodode, dodeA) → icou2
  71. Vector(centrodode, dodeB) → icou3
  72. Vector(centrodode, dodeC) → icou4
  73. Vector(centrodode, dodeD) → icou5
  74. Vector(centrodode, dodeG) → icou8
  75. Vector(centrodode, dodeE) → icou6
  76. Vector(centrodode, dodeF) → icou7
  77. Vector(centrodode, dodeH) → icou9
  78. Vector(centrodode, dodeI) → icou10
  79. Vector(centrodode, dodeJ) → icou11
  80. Vector(centrodode, dodeK) → icou12
  81. Vector(centrodode, dodeL) → icou13
  82. Vector(centrodode, dodeM) → icou14
  83. Vector(centrodode, dodeN) → icou15
  84. Vector(centrodode, dodeP) → icou16
  85. Vector(centrodode, dodeQ) → icou17
  86. Vector(centrodode, dodeR) → icou18
  87. Vector(centrodode, dodeS) → icou19
  88. Vector(centrodode, dodeT) → icou20
  89. Translate(icoface1, icou6) → icoface1'
  90. Translate(icoface10, icou17) → icoface10'
  91. Translate(icoface11, icou15) → icoface11'
  92. Translate(icoface12, icou19) → icoface12'
  93. Translate(icoface13, icou9) → icoface13'
  94. Translate(icoface14, icou14) → icoface14'
  95. Translate(icoface15, icou18) → icoface15'
  96. Translate(icoface16, icou10) → icoface16'
  97. Translate(icoface17, icou11) → icoface17'
  98. Translate(icoface18, icou20) → icoface18'
  99. Translate(icoface2, icou2) → icoface2'
  100. Translate(icoface20, icou8) → icoface20'
  101. Translate(icoface3, icou3) → icoface3'
  102. Translate(icoface4, icou4) → icoface4'
  103. Translate(icoface5, icou5) → icoface5'
  104. Translate(icoface7, icou16) → icoface7'
  105. Translate(icoface8, icou7) → icoface8'
  106. Translate(icoface9, icou13) → icoface9'
  107. Translate(icoface6, icou12) → icoface6'
  108. Sequence(Centroid[Element[list1, i]], i, 1, 20) → list2
  109. Sequence(Vector[Element[list2, i], Element[list3, i]], i, 1, 20) → list4
  110. Rotate(poly1, α) → poly1'
  111. Sequence(Translate[Element[list1, i], Vector[((t - 1) * Element[list4, i])]], i, 1, 20) → list5
  112. Rotate(poly1', α) → poly1''
  113. Rotate(poly1'', α) → poly1'''
  114. Rotate(poly1''', α) → poly1_4
  115. Translate(dodeQ, Vector[(t * dodeu7)]) → dodeQ'
  116. Translate(dodeQ, Vector[(t * dodeu12)]) → dodeQ'_1
  117. Polygon(dodeP'_1, dodeQ'_1, dodeQ', dodeP'_2) → poly2, dodep'_3, dodeq'_1, dodeq', dodep'_4
  118. Translate(dodeQ, Vector[(t * dodeu8)]) → dodeQ'_2
  119. Translate(dodeR, Vector[(t * dodeu8)]) → dodeR'
  120. Translate(dodeR, Vector[(t * dodeu12)]) → dodeR'_1
  121. Translate(dodeR, Vector[(t * dodeu9)]) → dodeR'_2
  122. Translate(dodeS, Vector[(t * dodeu9)]) → dodeS'
  123. Translate(dodeS, Vector[(t * dodeu12)]) → dodeS'_1
  124. Translate(dodeS, Vector[(t * dodeu10)]) → dodeS'_2
  125. Translate(dodeT, Vector[(t * dodeu10)]) → dodeT'
  126. Translate(dodeT, Vector[(t * dodeu12)]) → dodeT'_1
  127. Translate(dodeT, Vector[(t * dodeu11)]) → dodeT'_2
  128. Polygon(dodeQ', dodeQ'_2, dodeQ'_1) → poly3, dodeq'_2, dodeq'_3, dodeq'_4
  129. Polygon(dodeQ'_2, dodeR', dodeR'_1, dodeQ'_1) → poly4, dodeq'_5, doder', doder'_1, dodeq'_6
  130. Polygon(dodeR', dodeR'_2, dodeR'_1) → poly5, doder'_2, doder'_3, doder'_4
  131. Polygon(dodeR'_1, dodeR'_2, dodeS', dodeS'_1) → poly6, doder'_5, doder'_6, dodes', dodes'_1
  132. Polygon(dodeS'_1, dodeS'_2, dodeS') → poly7, dodes'_2, dodes'_3, dodes'_4
  133. Polygon(dodeT', dodeS'_2, dodeS'_1, dodeT'_1) → poly8, dodet', dodes'_5, dodes'_6, dodet'_1
  134. Polygon(dodeT'_2, dodeT', dodeT'_1) → poly9, dodet'_2, dodet'_3, dodet'_4
  135. Polygon(dodeP', dodeT'_2, dodeT'_1, dodeP'_1) → poly10, dodep'_5, dodet'_5, dodet'_6, dodep'_6
  136. Translate(dodeO, Vector[(t * dodeu10)]) → dodeO'
  137. Translate(dodeO, Vector[(t * dodeu11)]) → dodeO'_1
  138. Translate(dodeO, Vector[(t * dodeu3)]) → dodeO'_2
  139. Polygon(dodeT', dodeT'_2, dodeO'_1, dodeO') → poly11, dodet'_7, dodet'_8, dodeo'_1, dodeo'
  140. Polygon(dodeO'_2, dodeO'_1, dodeO') → poly12, dodeo'_2, dodeo'_3, dodeo'_4
  141. Translate(dodeK, Vector[(t * dodeu11)]) → dodeK'
  142. Translate(dodeK, Vector[(t * dodeu2)]) → dodeK'_1
  143. Translate(dodeK, Vector[(t * dodeu7)]) → dodeK'_2
  144. Translate(dodeL, Vector[(t * dodeu7)]) → dodeL'
  145. Translate(dodeL, Vector[(t * dodeu4)]) → dodeL'_1
  146. Translate(dodeL, Vector[(t * dodeu8)]) → dodeL'_2
  147. Translate(dodeM, Vector[(t * dodeu8)]) → dodeM'
  148. Translate(dodeM, Vector[(t * dodeu5)]) → dodeM'_1
  149. Translate(dodeM, Vector[(t * dodeu9)]) → dodeM'_2
  150. Translate(dodeN, Vector[(t * dodeu9)]) → dodeN'
  151. Translate(dodeN, Vector[(t * dodeu6)]) → dodeN'_1
  152. Translate(dodeN, Vector[(t * dodeu10)]) → dodeN'_2
  153. Polygon(dodeN', dodeN'_2, dodeS'_2, dodeS') → poly13, doden', doden'_2, dodes'_7, dodes'_8
  154. Polygon(dodeN', dodeN'_2, dodeN'_1) → poly14, doden'_1, doden'_3, doden'_4
  155. Polygon(dodeM'_1, dodeM'_2, dodeM') → poly15, dodem', dodem'_1, dodem'_2
  156. Polygon(dodeM', dodeM'_2, dodeR'_2, dodeR') → poly16, dodem'_3, dodem'_4, doder'_7, doder'_8
  157. Polygon(dodeL'_1, dodeL'_2, dodeL') → poly17, dodel', dodel'_1, dodel'_2
  158. Polygon(dodeL', dodeL'_2, dodeQ'_2, dodeQ') → poly18, dodel'_3, dodel'_4, dodeq'_7, dodeq'_8
  159. Polygon(dodeK'_1, dodeK'_2, dodeK') → poly19, dodek', dodek'_1, dodek'_2
  160. Polygon(dodeK', dodeK'_2, dodeP'_2, dodeP') → poly20, dodek'_3, dodek'_4, dodep'_7, dodep'_8
  161. Translate(dodeI, Vector[(t * dodeu6)]) → dodeI'
  162. Translate(dodeI, Vector[(t * dodeu3)]) → dodeI'_1
  163. Translate(dodeJ, Vector[(t * dodeu3)]) → dodeJ'
  164. Translate(dodeJ, Vector[(t * dodeu2)]) → dodeJ'_1
  165. Translate(dodeF, Vector[(t * dodeu2)]) → dodeF'
  166. Translate(dodeF, Vector[(t * dodeu4)]) → dodeF'_1
  167. Translate(dodeG, Vector[(t * dodeu4)]) → dodeG'
  168. Translate(dodeG, Vector[(t * dodeu5)]) → dodeG'_1
  169. Translate(dodeH, Vector[(t * dodeu5)]) → dodeH'
  170. Translate(dodeH, Vector[(t * dodeu6)]) → dodeH'_1
  171. Translate(dodeF, Vector[(t * dodeu7)]) → dodeF'_2
  172. Translate(dodeG, Vector[(t * dodeu8)]) → dodeG'_2
  173. Translate(dodeH, Vector[(t * dodeu9)]) → dodeH'_2
  174. Translate(dodeI, Vector[(t * dodeu10)]) → dodeI'_2
  175. Translate(dodeJ, Vector[(t * dodeu11)]) → dodeJ'_2
  176. Polygon(dodeO'_2, dodeJ', dodeJ'_2, dodeO'_1) → poly21, dodeo'_5, dodej', dodej'_2, dodeo'_6
  177. Polygon(dodeJ', dodeJ'_1, dodeJ'_2) → poly22, dodej'_1, dodej'_3, dodej'_4
  178. Polygon(dodeJ'_2, dodeJ'_1, dodeK'_1, dodeK') → poly23, dodej'_5, dodej'_6, dodek'_5, dodek'_6
  179. Polygon(dodeK'_1, dodeK'_2, dodeF'_2, dodeF') → poly24, dodek'_7, dodek'_8, dodef'_2, dodef'
  180. Polygon(dodeL', dodeL'_1, dodeF'_1, dodeF'_2) → poly25, dodel'_5, dodel'_6, dodef'_1, dodef'_3
  181. Polygon(dodeF'_1, dodeF'_2, dodeF') → poly26, dodef'_4, dodef'_5, dodef'_6
  182. Polygon(dodeL'_1, dodeG', dodeG'_2, dodeL'_2) → poly27, dodel'_7, dodeg', dodeg'_2, dodel'_8
  183. Polygon(dodeG', dodeG'_1, dodeG'_2) → poly28, dodeg'_1, dodeg'_3, dodeg'_4
  184. Polygon(dodeG'_2, dodeG'_1, dodeM'_1, dodeM') → poly29, dodeg'_5, dodeg'_6, dodem'_5, dodem'_6
  185. Polygon(dodeH', dodeH'_2, dodeM'_2, dodeM'_1) → poly30, dodeh', dodeh'_2, dodem'_7, dodem'_8
  186. Polygon(dodeH', dodeH'_1, dodeH'_2) → poly31, dodeh'_1, dodeh'_3, dodeh'_4
  187. Polygon(dodeH'_1, dodeN'_1, dodeN', dodeH'_2) → poly32, dodeh'_5, doden'_5, doden'_6, dodeh'_6
  188. Polygon(dodeN'_1, dodeI', dodeI'_2, dodeN'_2) → poly33, doden'_7, dodei', dodei'_2, doden'_8
  189. Polygon(dodeI'_1, dodeI'_2, dodeI') → poly34, dodei'_1, dodei'_3, dodei'_4
  190. Polygon(dodeI'_1, dodeO'_2, dodeO', dodeI'_2) → poly35, dodei'_5, dodeo'_7, dodeo'_8, dodei'_6
  191. Translate(dodeA, Vector[(t * dodeu3)]) → dodeA'
  192. Translate(dodeA, Vector[(t * dodeu2)]) → dodeA'_1
  193. Translate(dodeA, Vector[(t * dodeu1)]) → dodeA'_2
  194. Translate(dodeB, Vector[(t * dodeu2)]) → dodeB'
  195. Translate(dodeB, Vector[(t * dodeu4)]) → dodeB'_1
  196. Translate(dodeB, Vector[(t * dodeu1)]) → dodeB'_2
  197. Translate(dodeC, Vector[(t * dodeu4)]) → dodeC'
  198. Translate(dodeC, Vector[(t * dodeu5)]) → dodeC'_1
  199. Translate(dodeC, Vector[(t * dodeu1)]) → dodeC'_2
  200. Translate(dodeD, Vector[(t * dodeu5)]) → dodeD'
  201. Translate(dodeD, Vector[(t * dodeu6)]) → dodeD'_1
  202. Translate(dodeD, Vector[(t * dodeu1)]) → dodeD'_2
  203. Translate(dodeE, Vector[(t * dodeu6)]) → dodeE'
  204. Translate(dodeE, Vector[(t * dodeu3)]) → dodeE'_1
  205. Translate(dodeE, Vector[(t * dodeu1)]) → dodeE'_2
  206. Polygon(dodeE', dodeE'_1, dodeI'_1, dodeI') → poly36, dodee', dodee'_1, dodei'_7, dodei'_8
  207. Polygon(dodeE', dodeE'_2, dodeE'_1) → poly37, dodee'_2, dodee'_3, dodee'_4
  208. Polygon(dodeE'_2, dodeE', dodeD'_1, dodeD'_2) → poly38, dodee'_5, dodee'_6, doded'_1, doded'_2
  209. Polygon(dodeE'_2, dodeE'_1, dodeA', dodeA'_2) → poly39, dodee'_7, dodee'_8, dodea', dodea'_2
  210. Polygon(dodeA', dodeJ', dodeJ'_1, dodeA'_1) → poly40, dodea'_1, dodej'_7, dodej'_8, dodea'_3
  211. Polygon(dodeA'_2, dodeA'_1, dodeA') → poly41, dodea'_4, dodea'_5, dodea'_6
  212. Polygon(dodeA'_2, dodeB'_2, dodeB', dodeA'_1) → poly42, dodea'_7, dodeb'_2, dodeb', dodea'_8
  213. Polygon(dodeB', dodeB'_1, dodeF'_1, dodeF') → poly43, dodeb'_1, dodeb'_3, dodef'_7, dodef'_8
  214. Polygon(dodeB'_2, dodeB'_1, dodeB') → poly44, dodeb'_4, dodeb'_5, dodeb'_6
  215. Polygon(dodeB'_2, dodeC'_2, dodeC', dodeB'_1) → poly45, dodeb'_7, dodec'_2, dodec', dodeb'_8
  216. Polygon(dodeG', dodeG'_1, dodeC'_1, dodeC') → poly46, dodeg'_7, dodeg'_8, dodec'_1, dodec'_3
  217. Polygon(dodeC'_2, dodeC'_1, dodeC') → poly47, dodec'_4, dodec'_5, dodec'_6
  218. Polygon(dodeC'_2, dodeD'_2, dodeD', dodeC'_1) → poly48, dodec'_7, doded'_3, doded', dodec'_8
  219. Polygon(dodeD'_2, dodeD'_1, dodeD') → poly49, doded'_4, doded'_5, doded'_6
  220. Polygon(dodeD', dodeD'_1, dodeH'_1, dodeH') → poly50, doded'_7, doded'_8, dodeh'_7, dodeh'_8
  221. Translate(icoF, icou17) → icoF'
  222. Translate(icoF, icou16) → icoF'_1
  223. Translate(icoF, icou18) → icoF'_2
  224. Translate(icoF, icou19) → icoF'_3
  225. Translate(icoF, icou20) → icoF'_4
  226. Translate(icoH, icou16) → icoH'
  227. Translate(icoB, icou16) → icoB'
  228. Translate(icoB, icou17) → icoB'_1
  229. Translate(centrodi8, icou17) → centrodi8'
  230. Translate(centrodi8, icou18) → centrodi8'_1
  231. Translate(icoC, icou18) → icoC'
  232. Translate(icoC, icou19) → icoC'_1
  233. Translate(icoI, icou19) → icoI'
  234. Translate(icoI, icou20) → icoI'_1
  235. Translate(icoH, icou20) → icoH'_1
  236. Translate(icoF'_2, Vector[((t - 1) * Element[list4, 15])]) → A
  237. Translate(icoC', Vector[((t - 1) * Element[list4, 15])]) → icoC''
  238. Translate(centrodi8'_1, Vector[((t - 1) * Element[list4, 15])]) → B
  239. Translate(icoF'_3, Vector[((t - 1) * Element[list4, 12])]) → C
  240. Translate(icoI', Vector[((t - 1) * Element[list4, 12])]) → icoI''
  241. Translate(icoC'_1, Vector[((t - 1) * Element[list4, 12])]) → D
  242. Translate(icoF'_4, Vector[((t - 1) * Element[list4, 18])]) → E
  243. Translate(icoI'_1, Vector[((t - 1) * Element[list4, 18])]) → F
  244. Translate(icoH'_1, Vector[((t - 1) * Element[list4, 18])]) → G
  245. Translate(icoH', Vector[((t - 1) * Element[list4, 7])]) → icoH''
  246. Translate(icoF'_1, Vector[((t - 1) * Element[list4, 7])]) → H
  247. Translate(icoB', Vector[((t - 1) * Element[list4, 7])]) → icoB''
  248. Translate(icoB'_1, Vector[((t - 1) * Element[list4, 10])]) → I
  249. Translate(icoF', Vector[((t - 1) * Element[list4, 10])]) → icoF''
  250. Translate(centrodi8', Vector[((t - 1) * Element[list4, 10])]) → centrodi8''
  251. Polygon(icoB'', I, icoF'', H) → poly51, icob'', i, icof'', h
  252. Polygon(E, H, icoH'', G) → poly52, e, h_1, icoh'', g
  253. Polygon(icoI'', F, E, C) → poly53, icoi'', f, e_1, c_1
  254. Polygon(icoC'', D, C, A) → poly54, icoc'', d, c_2, a_1
  255. Polygon(centrodi8'', B, A, icoF'') → poly55, centrodi8''_1, b_1, a_2, icof''_1
  256. Polygon(icoF'', A, C, E, H) → poly56, icof''_2, a_3, c_3, e_2, h_2
  257. Translate(icoH, icou12) → icoH'_2
  258. Translate(icoB, icou12) → icoB'_2
  259. Translate(icoB, icou13) → icoB'_3
  260. Translate(centrodi8, icou13) → centrodi8'_2
  261. Translate(centrodi8, icou14) → centrodi8'_3
  262. Translate(icoC, icou14) → icoC'_2
  263. Translate(icoC, icou15) → icoC'_3
  264. Translate(icoI, icou15) → icoI'_2
  265. Translate(icoI, icou1) → icoI'_3
  266. Translate(icoH, icou1) → icoH'_3
  267. Translate(icoG, icou1) → icoG'
  268. Translate(icoH, icou11) → icoH'_4
  269. Translate(icoE, icou12) → icoE'
  270. Translate(icoB, icou7) → icoB'_4
  271. Translate(centrodi4, icou13) → centrodi4'
  272. Translate(centrodi8, icou8) → centrodi8'_4
  273. Translate(centrodi5, icou14) → centrodi5'
  274. Translate(icoC, icou9) → icoC'_4
  275. Translate(icoD, icou15) → icoD'
  276. Translate(icoI, icou10) → icoI'_4
  277. Translate(icoE, icou7) → icoE'_1
  278. Translate(centrodi4, icou7) → centrodi4'_1
  279. Translate(centrodi4, icou8) → centrodi4'_2
  280. Translate(centrodi5, icou8) → centrodi5'_1
  281. Translate(centrodi5, icou9) → centrodi5'_2
  282. Translate(icoD, icou9) → icoD'_1
  283. Translate(icoD, icou10) → icoD'_2
  284. Translate(icoG, icou10) → icoG'_1
  285. Translate(icoG, icou11) → icoG'_2
  286. Translate(icoE, icou11) → icoE'_2
  287. Translate(icoC'_4, Vector[((t - 1) * Element[list4, 13])]) → J
  288. Translate(icoD'_1, Vector[((t - 1) * Element[list4, 13])]) → K
  289. Translate(centrodi5'_2, Vector[((t - 1) * Element[list4, 13])]) → L
  290. Translate(icoC'_3, Vector[((t - 1) * Element[list4, 11])]) → M
  291. Translate(icoI'_2, Vector[((t - 1) * Element[list4, 11])]) → N
  292. Translate(icoD', Vector[((t - 1) * Element[list4, 11])]) → icoD''
  293. Translate(icoI'_4, Vector[((t - 1) * Element[list4, 16])]) → O
  294. Translate(icoG'_1, Vector[((t - 1) * Element[list4, 16])]) → P
  295. Translate(icoD'_2, Vector[((t - 1) * Element[list4, 16])]) → Q
  296. Translate(icoI'_3, Vector[((t - 1) * Element[list4, 19])]) → R
  297. Translate(icoH'_3, Vector[((t - 1) * Element[list4, 19])]) → S
  298. Translate(icoG', Vector[((t - 1) * Element[list4, 19])]) → icoG''
  299. Translate(icoH'_4, Vector[((t - 1) * Element[list4, 17])]) → T
  300. Translate(icoG'_2, Vector[((t - 1) * Element[list4, 17])]) → U
  301. Translate(icoE'_2, Vector[((t - 1) * Element[list4, 17])]) → V
  302. Translate(icoH'_2, Vector[((t - 1) * Element[list4, 6])]) → W
  303. Translate(icoE', Vector[((t - 1) * Element[list4, 6])]) → icoE''
  304. Translate(icoB'_2, Vector[((t - 1) * Element[list4, 6])]) → Z
  305. Translate(icoB'_4, Vector[((t - 1) * Element[list4, 8])]) → A_1
  306. Translate(icoE'_1, Vector[((t - 1) * Element[list4, 8])]) → B_1
  307. Translate(centrodi4'_1, Vector[((t - 1) * Element[list4, 8])]) → C_1
  308. Translate(centrodi8'_2, Vector[((t - 1) * Element[list4, 9])]) → D_1
  309. Translate(centrodi4', Vector[((t - 1) * Element[list4, 9])]) → centrodi4''
  310. Translate(icoB'_3, Vector[((t - 1) * Element[list4, 9])]) → E_1
  311. Translate(centrodi8'_4, Vector[((t - 1) * Element[list4, 20])]) → F_1
  312. Translate(centrodi4'_2, Vector[((t - 1) * Element[list4, 20])]) → G_1
  313. Translate(centrodi5'_1, Vector[((t - 1) * Element[list4, 20])]) → H_1
  314. Translate(centrodi8'_3, Vector[((t - 1) * Element[list4, 14])]) → I_1
  315. Translate(centrodi5', Vector[((t - 1) * Element[list4, 14])]) → centrodi5''
  316. Translate(icoC'_2, Vector[((t - 1) * Element[list4, 14])]) → J_1
  317. Polygon(I_1, J_1, icoC'', B) → poly57, i_1, j_1, icoc''_1, b_2
  318. Polygon(J_1, J, M, D, icoC'') → poly58, j_2, j_3, m, d_1, icoc''_2
  319. Polygon(M, N, icoI'', D) → poly59, m_1, n, icoi''_1, d_2
  320. Polygon(N, O, R, F, icoI'') → poly60, n_1, o, r, f_1, icoi''_2
  321. Polygon(R, S, G, F) → poly61, r_1, s, g_1, f_2
  322. Polygon(S, T, W, icoH'', G) → poly62, s_1, t_1, w, icoh''_1, g_2
  323. Polygon(W, Z, icoB'', icoH'') → poly63, w_1, z_1, icob''_1, icoh''_2
  324. Polygon(Z, A_1, E_1, I, icoB'') → poly64, z_2, a_4, e_3, i_2, icob''_2
  325. Polygon(I, E_1, D_1, centrodi8'') → poly65, i_3, e_4, d_3, centrodi8''_2
  326. Polygon(D_1, F_1, I_1, B, centrodi8'') → poly66, d_4, f_3, i_4, b_3, centrodi8''_3
  327. Polygon(icoG'', U, T, S) → poly67, icog'', u, t_2, s_2
  328. Polygon(icoG'', R, O, P) → poly68, icog''_1, r_2, o_1, p
  329. Polygon(N, O, Q, icoD'') → poly69, n_2, o_2, q, icod''
  330. Polygon(K, icoD'', M, J) → poly70, k, icod''_1, m_2, j_4
  331. Polygon(centrodi5'', L, J, J_1) → poly71, centrodi5''_1, l, j_5, j_6
  332. Polygon(H_1, centrodi5'', I_1, F_1) → poly72, h_3, centrodi5''_2, i_5, f_4
  333. Polygon(D_1, F_1, G_1, centrodi4'') → poly73, d_5, f_5, g_3, centrodi4''_1
  334. Polygon(A_1, C_1, centrodi4'', E_1) → poly74, a_5, c_4, centrodi4''_2, e_5
  335. Polygon(Z, A_1, B_1, icoE'') → poly75, z_3, a_6, b_4, icoe''
  336. Polygon(W, icoE'', V, T) → poly76, w_2, icoe''_1, v, t_3
  337. Translate(icoE, icou3) → icoE'_3
  338. Translate(centrodi4, icou3) → centrodi4'_3
  339. Translate(icoA, icou3) → icoA'
  340. Translate(centrodi4, icou4) → centrodi4'_4
  341. Translate(centrodi5, icou4) → centrodi5'_3
  342. Translate(icoA, icou4) → icoA'_1
  343. Translate(centrodi5, icou5) → centrodi5'_4
  344. Translate(icoD, icou5) → icoD'_3
  345. Translate(icoA, icou5) → icoA'_2
  346. Translate(icoD, icou6) → icoD'_4
  347. Translate(icoG, icou6) → icoG'_3
  348. Translate(icoA, icou6) → icoA'_3
  349. Translate(icoG, icou2) → icoG'_4
  350. Translate(icoE, icou2) → icoE'_4
  351. Translate(icoA, icou2) → icoA'_4
  352. Translate(icoG'_4, Vector[((t - 1) * Element[list4, 2])]) → K_1
  353. Translate(icoE'_4, Vector[((t - 1) * Element[list4, 2])]) → L_1
  354. Translate(icoA'_4, Vector[((t - 1) * Element[list4, 2])]) → M_1
  355. Translate(icoE'_3, Vector[((t - 1) * Element[list4, 3])]) → N_1
  356. Translate(centrodi4'_3, Vector[((t - 1) * Element[list4, 3])]) → O_1
  357. Translate(icoA', Vector[((t - 1) * Element[list4, 3])]) → icoA''
  358. Translate(centrodi4'_4, Vector[((t - 1) * Element[list4, 4])]) → P_1
  359. Translate(centrodi5'_3, Vector[((t - 1) * Element[list4, 4])]) → Q_1
  360. Translate(icoA'_1, Vector[((t - 1) * Element[list4, 4])]) → R_1
  361. Translate(centrodi5'_4, Vector[((t - 1) * Element[list4, 5])]) → S_1
  362. Translate(icoD'_3, Vector[((t - 1) * Element[list4, 5])]) → T_1
  363. Translate(icoA'_2, Vector[((t - 1) * Element[list4, 5])]) → U_1
  364. Translate(icoD'_4, Vector[((t - 1) * Element[list4, 1])]) → V_1
  365. Translate(icoA'_3, Vector[((t - 1) * Element[list4, 1])]) → W_1
  366. Translate(icoG'_3, Vector[((t - 1) * Element[list4, 1])]) → Z_1
  367. Polygon(Q_1, S_1, L, centrodi5'', H_1) → poly77, q_1, s_3, l_1, centrodi5''_3, h_4
  368. Polygon(S_1, T_1, K, L) → poly78, s_4, t_4, k_1, l_2
  369. Polygon(T_1, V_1, Q, icoD'', K) → poly79, t_5, v_1, q_2, icod''_2, k_2
  370. Polygon(V_1, Z_1, P, Q) → poly80, v_2, z_4, p_1, q_3
  371. Polygon(Z_1, K_1, U, icoG'', P) → poly81, z_5, k_3, u_1, icog''_2, p_2
  372. Polygon(K_1, L_1, V, U) → poly82, k_4, l_3, v_3, u_2
  373. Polygon(L_1, N_1, B_1, icoE'', V) → poly83, l_4, n_3, b_5, icoe''_2, v_4
  374. Intersect(n_3, l_4) → A_2
  375. Polygon(N_1, O_1, C_1, B_1) → poly84, n_4, o_3, c_5, b_6
  376. Polygon(O_1, P_1, G_1, centrodi4'', C_1) → poly85, o_4, p_3, g_4, centrodi4''_3, c_6
  377. Polygon(P_1, Q_1, H_1, G_1) → poly86, p_4, q_4, h_5, g_5
  378. Polygon(R_1, U_1, S_1, Q_1) → poly87, r_3, u_3, s_5, q_5
  379. Polygon(R_1, P_1, O_1, icoA'') → poly88, r_4, p_5, o_5, icoa''
  380. Polygon(N_1, L_1, M_1, icoA'') → poly89, n_5, l_5, m_3, icoa''_1
  381. Polygon(M_1, K_1, Z_1, W_1) → poly90, m_4, k_5, z_6, w_3
  382. Polygon(W_1, V_1, T_1, U_1) → poly91, w_4, v_5, t_6, u_4
  383. Polygon(W_1, M_1, icoA'', R_1, U_1) → poly92, w_5, m_5, icoa''_2, r_5, u_5