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Icosahedron Net

Icosahedron Net
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2014-11-12 23:35
PolygonSolid Geometry
In collections 3D Geometry & Cross Sections Surface Area and Volume Nets of 3D Figures 立體圖形的摺紙圖樣
This example demonstrates the net of an icosahedron, a polyhedron composed of 20 equilateral triangles. Using GeoGebra commands such as Point, Icosahedron, Segment, Rotate, etc., the net of the icosahedron can be constructed. Suitable for students at the junior high school level and above to learn solid geometry.

GeoGebra Commands & Parameters

  1. Point(Circle[Midpoint[A, B], (Distance[A, B] * sqrt(3) / 2), Segment[A, B]]) → C
  2. Icosahedron(A, B, C) → a, D, faceABC, faceACF, faceAFG, faceADG, faceABD, faceBDH, faceBEH, faceBCE, faceCEI, faceCFI, E, faceEHK, faceEIK, faceIKL, faceFIL, faceHJK, faceJKL, faceGJL, faceFGL, faceDHJ, faceDGJ, F, edgeAC, edgeAB, edgeBC, edgeAF, edgeCF, edgeAG, edgeFG, edgeAD, edgeDG, edgeBD, G, edgeBH, edgeDH, edgeBE, edgeEH, edgeCE, edgeCI, edgeEI, edgeFI, edgeEK, edgeHK, H, edgeIK, edgeIL, edgeKL, edgeFL, edgeJK, edgeHJ, edgeJL, edgeGL, edgeGJ, edgeDJ, I, J, K, L
  3. Segment(M, M + (0, 0, 2)) → b
  4. Point(b) → N
  5. Rotate(Polygon[A, B, D], (α * t), Segment[A, B]) → poly1
  6. Rotate(Polygon[A, D, G], (α * t), Segment[A, D]) → poly2
  7. Rotate(Polygon[B, D, H], (α * t), Segment[D, B]) → poly3
  8. Rotate(Polygon[G, D, J], (α * t), Segment[G, D]) → poly4
  9. Rotate(Polygon[D, H, J], (α * t), Segment[D, H]) → poly5
  10. Rotate(Polygon[G, J, L], (α * t), Segment[G, J]) → poly6
  11. Rotate(poly2, (α * t), Segment[A, B]) → poly2'
  12. Rotate(poly3, (α * t), Segment[A, B]) → poly3'
  13. Rotate(poly4, (α * t), Segment[A, D]) → poly4'
  14. Rotate(poly4', (α * t), Segment[A, B]) → poly4''
  15. Rotate(poly5, (α * t), Segment[D, B]) → poly5'
  16. Rotate(poly5', (α * t), Segment[A, B]) → poly5''
  17. Rotate(poly6, (α * t), Segment[G, D]) → poly6'
  18. Rotate(poly6', (α * t), Segment[A, D]) → poly6''
  19. Rotate(poly6'', (α * t), Segment[A, B]) → poly6'''
  20. Rotate(Polygon[J, K, L], (α * t), Segment[L, J]) → poly7
  21. Rotate(poly7, (α * t), Segment[G, J]) → poly7'
  22. Rotate(poly7', (α * t), Segment[G, D]) → poly7''
  23. Rotate(poly7'', (α * t), Segment[A, D]) → poly7'''
  24. Rotate(poly7''', (α * t), Segment[A, B]) → poly8
  25. Circle(A, B, C) → c
  26. Center(c) → O
  27. OrthogonalLine(O, Plane[A, B, C]) → d
  28. Rotate(poly1, 120°, d) → poly1'
  29. Rotate(poly2', 120°, d) → poly2''
  30. Rotate(poly3', 120°, d) → poly3''
  31. Rotate(poly4'', 120°, d) → poly4'''
  32. Rotate(poly5'', 120°, d) → poly5'''
  33. Rotate(poly6''', 120°, d) → poly9
  34. Rotate(poly1', 120°, d) → poly1''
  35. Rotate(poly2'', 120°, d) → poly2'''
  36. Rotate(poly3'', 120°, d) → poly3'''
  37. Rotate(poly4''', 120°, d) → poly10
  38. Rotate(poly5''', 120°, d) → poly11
  39. Rotate(poly9, 120°, d) → poly9'
  40. Polygon(A, B, C) → poly12, c_1, a_1, b_1
  41. Polygon(A, B, C) → poly13, c_2, a_2, b_2
  42. Rotate(poly1', 120°, d) → poly1''_1
  43. Rotate(Polygon[A, B, D], (α * t), Segment[A, B]) → poly14
  44. Rotate(poly1, 120°, d) → poly1'_1
  45. Rotate(poly3', 120°, d) → poly3''_1
  46. Rotate(poly2'', 120°, d) → poly2'''_1
  47. Rotate(poly2', 120°, d) → poly2''_1
  48. Rotate(poly2, (α * t), Segment[A, B]) → poly2'_1
  49. Rotate(poly3, (α * t), Segment[A, B]) → poly3'_1
  50. Rotate(poly5', (α * t), Segment[A, B]) → poly5''_1
  51. Rotate(poly4', (α * t), Segment[A, B]) → poly4''_1
  52. Rotate(poly6'', (α * t), Segment[A, B]) → poly6'''_1
  53. Rotate(poly7''', (α * t), Segment[A, B]) → poly15
  54. Rotate(poly3'', 120°, d) → poly3'''_1
  55. Rotate(poly5''', 120°, d) → poly16
  56. Rotate(poly4''', 120°, d) → poly17
  57. Rotate(poly9, 120°, d) → poly9'_1
  58. Rotate(poly5'', 120°, d) → poly5'''_1
  59. Rotate(poly4'', 120°, d) → poly4'''_1
  60. Rotate(poly6''', 120°, d) → poly18