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Rhombicosidodecahedron

Rhombicosidodecahedron
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2022-04-26 22:50
PolygonSolid GeometryGeometric Construction
In collections Archimedean Solids
This example demonstrates the geometric construction and properties of the Rhombicosidodecahedron. Key math concepts include solid geometry, polygons, rotation, symmetry, etc. The construction uses GeoGebra commands and objects such as Polygon, Line, Rotate, Centroid, OrthogonalLine, Plane, Circle, Midpoint, Mirror, Intersect, and OrthogonalPlane. It is suitable for high school and above learning solid geometry, geometric construction, and spatial visualization skills.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 5, xOyPlane) → poly1, f, g, h, i, j, C, D, E
  2. Polygon(A, B, 4, xOyPlane) → poly2, k, l, m, n, F, G
  3. Line(A, B) → p
  4. Rotate(poly2, 148.28°, p) → poly2'
  5. Rotate(G, 148.28°, p) → G'
  6. Rotate(F, 148.28°, p) → F'
  7. Centroid(poly1) → H
  8. OrthogonalLine(H, poly1) → q
  9. Rotate(poly2', 72°, q) → poly2''
  10. Rotate(G', 72°, q) → G''
  11. Rotate(F', 72°, q) → F''
  12. Rotate(poly2', 144°, q) → poly2''_{1}
  13. Rotate(G'', 72°, q) → G'''
  14. Rotate(F'', 72°, q) → F'''
  15. Rotate(poly2''_{1}, 72°, q) → q1
  16. Rotate(G''', 72°, q) → I
  17. Rotate(F''', 72°, q) → J
  18. Rotate(q1, 72°, q) → q1'
  19. Rotate(J, 72°, q) → J'
  20. Rotate(I, 72°, q) → I'
  21. Polygon(I, F''', D) → t1, d, i_1, f'''
  22. Rotate(t1, 72°, q) → t1'
  23. Rotate(t1', 72°, q) → t1''
  24. Rotate(t1'', 72°, q) → t1'''
  25. Rotate(t1''', 72°, q) → t2
  26. Line(G', J') → r
  27. Rotate(A, -159.09°, r) → A'
  28. Plane(G', J', A') → p_1
  29. OrthogonalLine(J', p_1) → s
  30. OrthogonalLine(G', p_1) → t
  31. Circle(s, J') → c
  32. Circle(s, G') → e
  33. Circle(t, J') → c_1
  34. Rotate(J', 90°, t) → J''
  35. Rotate(G', -90°, s) → G''_{1}
  36. Polygon(J'', G', J', G''_{1}) → q2, j'', g', j', g''_{1}
  37. Rotate(q2, 72°, q) → q2'
  38. Rotate(q2, 144°, q) → q2'_{1}
  39. Rotate(q2, -72°, q) → q2'_{2}
  40. Rotate(q2'_{2}, -72°, q) → q3
  41. Midpoint(F', A) → K
  42. Plane(G'', K, J') → q_1
  43. Mirror(poly1, q_1) → poly1'
  44. Rotate(poly1', 72°, q) → poly1''
  45. Rotate(poly1'', 72°, q) → poly1'''
  46. Rotate(poly1''', 72°, q) → poly3
  47. Rotate(poly3, 72°, q) → poly3'
  48. Rotate(J'', 72°, q) → J'''
  49. Rotate(G''_{1}, 72°, q) → L
  50. Rotate(J''', 72°, q) → M
  51. Rotate(L, 72°, q) → L'
  52. Rotate(L', 72°, q) → L''
  53. Rotate(M, 72°, q) → M'
  54. Rotate(M', 72°, q) → M''
  55. Rotate(L'', 72°, q) → L'''
  56. Centroid(poly1') → N
  57. OrthogonalLine(N, poly1') → a
  58. Centroid(q2) → O
  59. OrthogonalLine(O, q2) → b
  60. Intersect(a, q) → P
  61. Rotate(J'', 72°, a) → J'''_{1}
  62. Rotate(J'''_{1}, 72°, q) → Q
  63. Rotate(Q, 72°, q) → Q'
  64. Rotate(Q', 72°, q) → Q''
  65. Rotate(Q'', 72°, q) → Q'''
  66. Rotate(q2', -72°, a) → q2''
  67. Rotate(q2'', -72°, a) → q2'''
  68. Rotate(q2'', 72°, q) → q2'''_{1}
  69. Rotate(q2''', 72°, q) → q4
  70. Rotate(q2'''_{1}, 72°, q) → q5
  71. Rotate(q4, 72°, q) → q4'
  72. Rotate(q5, 72°, q) → q5'
  73. Rotate(q4', 72°, q) → q4''
  74. Rotate(q5', 72°, q) → q5''
  75. Rotate(q4'', 72°, q) → q4'''
  76. Centroid(q2'') → R
  77. OrthogonalLine(R, q2'') → f_1
  78. Rotate(J'''_{1}, 90°, f_1) → S
  79. Rotate(J'''_{1}, 180°, f_1) → T
  80. Rotate(T, 72°, q) → T'
  81. Rotate(T, 144°, q) → T'_{1}
  82. Rotate(T, -72°, q) → T'_{2}
  83. Rotate(T, -144°, q) → T'_{3}
  84. Rotate(S, 72°, q) → S'
  85. Rotate(S', 72°, q) → S''
  86. Rotate(S, -72°, q) → S'_{1}
  87. Rotate(S, -144°, q) → S'_{2}
  88. Rotate(t1''', -72°, a) → t3
  89. Rotate(t3, -72°, a) → t3'
  90. Rotate(t3', -72°, a) → t3''
  91. Rotate(t3'', -72°, q) → t3'''
  92. Rotate(t3''', -72°, q) → t4
  93. Rotate(t4, -72°, q) → t4'
  94. Rotate(t4', -72°, q) → t4''
  95. Rotate(t3', 72°, q) → t3''_{1}
  96. Rotate(t3''_{1}, 72°, q) → t5
  97. Rotate(t5, 72°, q) → t5'
  98. Rotate(t5', 72°, q) → t5''
  99. OrthogonalPlane(P, q) → r_1
  100. Centroid(t4) → U
  101. OrthogonalLine(U, t4) → g_1
  102. Rotate(poly3, 120°, g_1) → poly3'_{1}
  103. Rotate(Q'', 120°, g_1) → Q'''_{1}
  104. Rotate(L''', 120°, g_1) → V
  105. Rotate(J, 120°, g_1) → J'_{1}
  106. Rotate(I, 120°, g_1) → I'_{1}
  107. Rotate(poly3'_{1}, -72°, q) → poly4
  108. Rotate(poly4, -72°, q) → poly4'
  109. Rotate(poly4', 72°, q) → poly4''
  110. Rotate(poly4', -72°, q) → poly4''_{1}
  111. Rotate(poly4''_{1}, -72°, q) → poly5
  112. Rotate(q6, 72°, q) → q6'
  113. Rotate(q6, -72°, q) → q6'_{1}
  114. Rotate(q5, -72°, a) → q5'_{1}
  115. Rotate(q5'_{1}, -72°, a) → q7
  116. Rotate(q7, -72°, a) → q7'
  117. Rotate(q7, 72°, q) → q7'_{1}
  118. Rotate(q7'_{1}, 72°, q) → q8
  119. Rotate(q7'_{1}, 144°, q) → q9
  120. Rotate(q7, -72°, q) → q7'_{2}
  121. Rotate(t5', 72°, a) → t5''_{1}
  122. Rotate(t5''_{1}, 72°, a) → t6
  123. Rotate(t6, -72°, q) → t6'
  124. Rotate(q5'_{1}, -72°, q) → q10
  125. Rotate(q10, -72°, q) → q10'
  126. Rotate(t6', -72°, q) → t6''
  127. Rotate(t6'', -72°, q) → t6'''
  128. Rotate(poly5, 72°, a) → poly5'
  129. Rotate(q10', -72°, q) → q10''

AI Drawing Prompt Reference

In a 2D plane view, start by drawing an initial polygon face using a set of points on the same plane, then connect corresponding vertices to form edges. Take an edge line as a rotation axis and replicate the polygon by rotating it by specified angles to create several surrounding, congruent faces and their vertices in a symmetric pattern. Compute the centroid of the first polygon, draw an orthogonal line from the centroid to that polygon to obtain a key axis, and use this axis for further 72°/144° rotations to generate additional neighboring faces. Build auxiliary directions from lines through rotated points, define relevant planes with three points, and use orthogonal lines and circles through key points to guide the construction. Finally mirror the original face across a constructed plane and continue rotating around the main axis to complete the solid’s overall shape.
The prompt above was compiled from the original drawing commands and is for reference only.