Truncated Cuboctahedron

Truncated Cuboctahedron
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2022-04-25 11:49
In collections Archimedean Solids
This example demonstrates the construction of a truncated cuboctahedron, a polyhedron formed by truncating the vertices of a cube. Key mathematical concepts include solid geometry and geometric construction. Commands used include Polygon, Line, Rotate, Ray, Sphere, Intersect, Centroid, OrthogonalLine, Plane, Midpoint, OrthogonalPlane, Mirror. Suitable for high school or university solid geometry courses.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 8, xOyPlane) → poly1, f, D, E, F, G, H, g, h, i, j, k, l, m, C
  2. Line(D, C) → n
  3. Rotate(H, -135°, n) → H'
  4. Rotate(G, -135°, n) → G'
  5. Ray(D, G') → p
  6. Ray(C, H') → q
  7. Sphere(D, C) → a
  8. Sphere(C, D) → b
  9. Intersect(p, a) → I,
  10. Intersect(q, b) → J,
  11. Polygon(I, J, C, D) → q1, i_1, j_1, c, d
  12. Centroid(poly1) → K
  13. OrthogonalLine(K, poly1) → r
  14. Rotate(q1, 90°, r) → q1'
  15. Rotate(q1, 180°, r) → q1'_{1}
  16. Rotate(q1, 270°, r) → q1'_{2}
  17. Rotate(I, 90°, r) → I'
  18. Rotate(I, 180°, r) → I'_{1}
  19. Rotate(I, 270°, r) → I'_{2}
  20. Rotate(J, 90°, r) → J'
  21. Rotate(J, 90°, r) → J'_{1}
  22. Rotate(J, 180°, r) → J'_{2}
  23. Rotate(J, 270°, r) → J'_{3}
  24. Plane(J'_{2}, G, F) → p_1
  25. Plane(J'_{2}, F, I') → q_1
  26. Midpoint(J'_{2}, I') → L
  27. OrthogonalLine(L, q_1) → s
  28. Rotate(J'_{2}, -60°, s) → M
  29. Rotate(J'_{2}, -120°, s) → N
  30. Polygon(J'_{2}, G, F, I', N, M) → poly2, j'_{2}, g_1, f_1, i', n_1, m_1
  31. Rotate(poly2, 90°, r) → poly2'
  32. Rotate(poly2, 180°, r) → poly2'_{1}
  33. Rotate(poly2, 270°, r) → poly2'_{2}
  34. Rotate(N, -90°, r) → N'
  35. Rotate(M, -90°, r) → M'
  36. Rotate(N', -90°, r) → N''
  37. Rotate(M', -90°, r) → M''
  38. Rotate(M'', -90°, r) → M'''
  39. Rotate(N'', -90°, r) → N'''
  40. Plane(N'', I'_{2}, J'_{3}) → r_1
  41. Centroid(poly2') → O
  42. OrthogonalLine(O, poly2') → t
  43. Intersect(t, r) → P
  44. OrthogonalLine(L, poly2) → e
  45. OrthogonalPlane(P, r) → p_2
  46. Mirror(poly1, p_2) → poly1'
  47. Mirror(poly2'_{2}, p_2) → poly3
  48. Mirror(poly2'_{1}, p_2) → poly4
  49. Mirror(q1', p_2) → q1''
  50. Mirror(q1, p_2) → q1'_{3}
  51. Mirror(poly2, p_2) → poly2'_{3}
  52. Mirror(q1'_{1}, p_2) → q2
  53. Mirror(poly2', p_2) → poly2''
  54. Mirror(q1'_{2}, p_2) → q3
  55. Mirror(M', p_2) → M''_{1}
  56. Mirror(N', p_2) → N''_{1}
  57. Mirror(I, p_2) → I'_{3}
  58. Mirror(J, p_2) → J'_{4}
  59. Mirror(N'', p_2) → N'''_{1}
  60. Mirror(M'', p_2) → M'''_{1}
  61. Mirror(J'_{3}, p_2) → Q
  62. Mirror(I'_{2}, p_2) → R
  63. Mirror(M''', p_2) → S
  64. Mirror(N''', p_2) → T
  65. Mirror(I'_{1}, p_2) → U
  66. Mirror(J'_{2}, p_2) → V
  67. Mirror(M, p_2) → M'_{1}
  68. Mirror(N, p_2) → N'_{1}
  69. Mirror(I', p_2) → I''
  70. Mirror(J'_{1}, p_2) → W
  71. Mirror(E, p_2) → E'
  72. Mirror(F, p_2) → F'
  73. Mirror(G, p_2) → G'_{1}
  74. Mirror(D, p_2) → D'
  75. Mirror(C, p_2) → C'
  76. Mirror(B, p_2) → B'
  77. Mirror(A, p_2) → A'
  78. Mirror(H, p_2) → H'_{1}
  79. Polygon(J'_{4}, M'''_{1}, M'', J, I, N', N''_{1}, I'_{3}) → poly5, j'_{4}, m'''_{1}, m'', j_2, i_2, n', n''_{1}, i'_{3}
  80. Rotate(poly5, 90°, r) → poly5'
  81. Rotate(poly5, 180°, r) → poly5'_{1}
  82. Rotate(poly5, 270°, r) → poly5'_{2}
  83. Polygon(T, N''', M''', S) → q4, t_1, n''', m''', s_1
  84. Rotate(q4, 90°, r) → q4'
  85. Rotate(q4, 180°, r) → q4'_{1}
  86. Rotate(q4, 270°, r) → q4'_{2}

AI Drawing Prompt Reference

Draw a truncated cuboctahedron by starting with a regular octagon in the xy-plane, connecting midpoints of opposite sides to form a cube, and truncating each vertex to create the polyhedron, focusing on symmetry and geometric construction.
The prompt above was compiled from the original drawing commands and is for reference only.