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Truncated Great Icosahedron

Truncated Great Icosahedron
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2014-10-09 02:44
PolygonSolid GeometryGeometric Construction
In collections surface 3D /3D-Oberflächen 1 surface 3D /3D-Oberflächen 1
This example demonstrates the geometric construction and properties of a truncated great icosahedron. Key math concepts include polygons, solid geometry, symmetry, and geometric transformations. The construction uses the Polygon command with vertices V0-V34 and circles C0-C4. Suitable for high school and above students learning polyhedron construction and geometric visualization.

GeoGebra Commands & Parameters

  1. Polygon(V0, V48, V13, V59, V19, V38) → poly1, v0, v48, v13, v59, v19, v38
  2. Polygon(V3, V51, V14, V56, V16, V37) → poly2, v3, v51, v14, v56, v16, v37
  3. Polygon(V6, V46, V11, V53, V21, V40) → poly3, v6, v46, v11, v53, v21, v40
  4. Polygon(V33, V35, V15, V57, V53, V11) → poly4, v33, v35, v15, v57, v53_1, v11_1
  5. Polygon(V35, V33, V10, V52, V56, V14) → poly5, v35_1, v33_1, v10, v52, v56_1, v14_1
  6. Polygon(V37, V16, V24, V26, V18, V39) → poly6, v37_1, v16_1, v24, v26, v18, v39
  7. Polygon(V38, V19, V27, V25, V17, V36) → poly7, v38_1, v19_1, v27, v25, v17, v36
  8. Polygon(V40, V21, V25, V27, V23, V42) → poly8, v40_1, v21_1, v25_1, v27_1, v23, v42
  9. Polygon(V43, V22, V26, V24, V20, V41) → poly9, v43, v22, v26_1, v24_1, v20, v41
  10. Polygon(V24, V16, V56, V52, V20) → poly10, v24_2, v16_2, v56_2, v52_1, v20_1
  11. Polygon(V25, V21, V53, V57, V17) → poly11, v25_2, v21_2, v53_2, v57_1, v17_1
  12. Polygon(V26, V22, V54, V58, V18) → poly12, v26_2, v22_1, v54, v58, v18_1
  13. Polygon(V27, V19, V59, V55, V23) → poly13, v27_2, v19_2, v59_1, v55, v23_1
  14. Polygon(V33, V11, V46, V47, V10) → poly14, v33_2, v11_2, v46_1, v47, v10_1
  15. Polygon(V34, V13, V48, V49, V12) → poly15, v34, v13_1, v48_1, v49, v12
  16. Polygon(V35, V14, V51, V50, V15) → poly16, v35_2, v14_2, v51_1, v50, v15_1
  17. Polygon(V0, V48, V13, V59, V19, V38) → poly17, v0_1, v48_2, v13_2, v59_2, v19_3, v38_2
  18. Polygon(V1, V49, V48, V0, V28, V29) → poly18, v1, v49_1, v48_3, v0_2, v28, v29
  19. Polygon(V2, V50, V51, V3, V29, V28) → poly19, v2, v50_1, v51_2, v3_1, v29_1, v28_1
  20. Polygon(V3, V51, V14, V56, V16, V37) → poly20, v3_2, v51_3, v14_3, v56_3, v16_3, v37_2
  21. Polygon(V4, V44, V45, V5, V31, V30) → poly21, v4, v44, v45, v5, v31, v30
  22. Polygon(V5, V45, V8, V54, V22, V43) → poly22, v5_1, v45_1, v8, v54_1, v22_2, v43_1
  23. Polygon(V6, V46, V11, V53, V21, V40) → poly23, v6_1, v46_2, v11_3, v53_3, v21_3, v40_2
  24. Polygon(V7, V47, V46, V6, V30, V31) → poly24, v7, v47_1, v46_3, v6_2, v30_1, v31_1
  25. Polygon(V32, V34, V12, V58, V54, V8) → poly25, v32, v34_1, v12_1, v58_1, v54_2, v8_1
  26. Polygon(V33, V35, V15, V57, V53, V11) → poly26, v33_3, v35_3, v15_2, v57_2, v53_4, v11_4
  27. Polygon(V34, V32, V9, V55, V59, V13) → poly27, v34_2, v32_1, v9, v55_1, v59_3, v13_3
  28. Polygon(V35, V33, V10, V52, V56, V14) → poly28, v35_4, v33_4, v10_2, v52_2, v56_4, v14_4
  29. Polygon(V36, V17, V57, V15, V50, V2) → poly29, v36_1, v17_2, v57_3, v15_3, v50_2, v2_1
  30. Polygon(V37, V16, V24, V26, V18, V39) → poly30, v37_3, v16_4, v24_3, v26_3, v18_2, v39_1
  31. Polygon(V38, V19, V27, V25, V17, V36) → poly31, v38_3, v19_4, v27_3, v25_3, v17_3, v36_2
  32. Polygon(V39, V18, V58, V12, V49, V1) → poly32, v39_2, v18_3, v58_2, v12_2, v49_2, v1_1
  33. Polygon(V40, V21, V25, V27, V23, V42) → poly33, v40_3, v21_4, v25_4, v27_4, v23_2, v42_1
  34. Polygon(V41, V20, V52, V10, V47, V7) → poly34, v41_1, v20_2, v52_3, v10_3, v47_2, v7_1
  35. Polygon(V42, V23, V55, V9, V44, V4) → poly35, v42_2, v23_3, v55_2, v9_1, v44_1, v4_1
  36. Polygon(V43, V22, V26, V24, V20, V41) → poly36, v43_2, v22_3, v26_4, v24_4, v20_3, v41_2
  37. Polygon(V24, V16, V56, V52, V20) → poly37, v24_5, v16_5, v56_5, v52_4, v20_4
  38. Polygon(V25, V21, V53, V57, V17) → poly38, v25_5, v21_5, v53_5, v57_4, v17_4
  39. Polygon(V26, V22, V54, V58, V18) → poly39, v26_5, v22_4, v54_3, v58_3, v18_4
  40. Polygon(V27, V19, V59, V55, V23) → poly40, v27_5, v19_5, v59_4, v55_3, v23_4
  41. Polygon(V28, V0, V38, V36, V2) → poly41, v28_2, v0_3, v38_4, v36_3, v2_2
  42. Polygon(V29, V3, V37, V39, V1) → poly42, v29_2, v3_3, v37_4, v39_3, v1_2
  43. Polygon(V30, V6, V40, V42, V4) → poly43, v30_2, v6_3, v40_4, v42_3, v4_2
  44. Polygon(V31, V5, V43, V41, V7) → poly44, v31_2, v5_2, v43_3, v41_3, v7_2
  45. Polygon(V32, V8, V45, V44, V9) → poly45, v32_2, v8_2, v45_2, v44_2, v9_2
  46. Polygon(V33, V11, V46, V47, V10) → poly46, v33_5, v11_5, v46_4, v47_3, v10_4
  47. Polygon(V34, V13, V48, V49, V12) → poly47, v34_3, v13_4, v48_4, v49_3, v12_3
  48. Polygon(V35, V14, V51, V50, V15) → poly48, v35_5, v14_5, v51_4, v50_3, v15_4
  49. Polygon(V0, V48, V13, V59, V19, V38) → poly49, v0_4, v48_5, v13_5, v59_5, v19_6, v38_5
  50. Polygon(V1, V49, V48, V0, V28, V29) → poly50, v1_3, v49_4, v48_6, v0_5, v28_3, v29_3
  51. Polygon(V2, V50, V51, V3, V29, V28) → poly51, v2_3, v50_4, v51_5, v3_4, v29_4, v28_4
  52. Polygon(V3, V51, V14, V56, V16, V37) → poly52, v3_5, v51_6, v14_6, v56_6, v16_6, v37_5
  53. Polygon(V4, V44, V45, V5, V31, V30) → poly53, v4_3, v44_3, v45_3, v5_3, v31_3, v30_3
  54. Polygon(V5, V45, V8, V54, V22, V43) → poly54, v5_4, v45_4, v8_3, v54_4, v22_5, v43_4
  55. Polygon(V6, V46, V11, V53, V21, V40) → poly55, v6_4, v46_5, v11_6, v53_6, v21_6, v40_5
  56. Polygon(V7, V47, V46, V6, V30, V31) → poly56, v7_3, v47_4, v46_6, v6_5, v30_4, v31_4
  57. Polygon(V32, V34, V12, V58, V54, V8) → poly57, v32_3, v34_4, v12_4, v58_4, v54_5, v8_4
  58. Polygon(V33, V35, V15, V57, V53, V11) → poly58, v33_6, v35_6, v15_5, v57_5, v53_7, v11_7
  59. Polygon(V34, V32, V9, V55, V59, V13) → poly59, v34_5, v32_4, v9_3, v55_4, v59_6, v13_6
  60. Polygon(V35, V33, V10, V52, V56, V14) → poly60, v35_7, v33_7, v10_5, v52_5, v56_7, v14_7
  61. Polygon(V36, V17, V57, V15, V50, V2) → poly61, v36_4, v17_5, v57_6, v15_6, v50_5, v2_4
  62. Polygon(V37, V16, V24, V26, V18, V39) → poly62, v37_6, v16_7, v24_6, v26_6, v18_5, v39_4
  63. Polygon(V38, V19, V27, V25, V17, V36) → poly63, v38_6, v19_7, v27_6, v25_6, v17_6, v36_5
  64. Polygon(V39, V18, V58, V12, V49, V1) → poly64, v39_5, v18_6, v58_5, v12_5, v49_5, v1_4
  65. Polygon(V40, V21, V25, V27, V23, V42) → poly65, v40_6, v21_7, v25_7, v27_7, v23_5, v42_4
  66. Polygon(V41, V20, V52, V10, V47, V7) → poly66, v41_4, v20_5, v52_6, v10_6, v47_5, v7_4
  67. Polygon(V42, V23, V55, V9, V44, V4) → poly67, v42_5, v23_6, v55_5, v9_4, v44_4, v4_4
  68. Polygon(V43, V22, V26, V24, V20, V41) → poly68, v43_5, v22_6, v26_7, v24_7, v20_6, v41_5
  69. Polygon(V24, V16, V56, V52, V20) → poly69, v24_8, v16_8, v56_8, v52_7, v20_7
  70. Polygon(V25, V21, V53, V57, V17) → poly70, v25_8, v21_8, v53_8, v57_7, v17_7
  71. Polygon(V26, V22, V54, V58, V18) → poly71, v26_8, v22_7, v54_6, v58_6, v18_7
  72. Polygon(V27, V19, V59, V55, V23) → poly72, v27_8, v19_8, v59_7, v55_6, v23_7
  73. Polygon(V28, V0, V38, V36, V2) → poly73, v28_5, v0_6, v38_7, v36_6, v2_5
  74. Polygon(V29, V3, V37, V39, V1) → poly74, v29_5, v3_6, v37_7, v39_6, v1_5
  75. Polygon(V30, V6, V40, V42, V4) → poly75, v30_5, v6_6, v40_7, v42_6, v4_5
  76. Polygon(V31, V5, V43, V41, V7) → poly76, v31_5, v5_5, v43_6, v41_6, v7_5
  77. Polygon(V32, V8, V45, V44, V9) → poly77, v32_5, v8_5, v45_5, v44_5, v9_5
  78. Polygon(V33, V11, V46, V47, V10) → poly78, v33_8, v11_8, v46_7, v47_6, v10_7
  79. Polygon(V34, V13, V48, V49, V12) → poly79, v34_6, v13_7, v48_7, v49_6, v12_6
  80. Polygon(V35, V14, V51, V50, V15) → poly80, v35_8, v14_8, v51_7, v50_6, v15_7