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Spherical Model of Tetrahedron

Spherical Model of Tetrahedron
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2015-01-16 23:19
Coordinate GeometrySolid GeometryGeometric Construction
In collections My 3D Collection
This example demonstrates the projection of a tetrahedron on a sphere. Key mathematical concepts include solid geometry and spherical geometry. Using commands like Plane, UnitOrthogonalVector, Element, Surface, Circle, Segment, and Midpoint, the spherical model of a tetrahedron is constructed. Suitable for high school or university solid geometry courses.

GeoGebra Commands & Parameters

  1. Plane(A, B, E) → B1
  2. UnitOrthogonalVector(B1) → B2
  3. Element(B12, 1, 2) → B13
  4. Element(B12, 1, 3) → B14
  5. Element(B12, 2, 2) → B15
  6. Element(B12, 2, 3) → B16
  7. Element(B12, 3, 2) → B17
  8. Element(B12, 3, 3) → B18
  9. Surface(((B$13 * (4 + t)) * cos(k)) + ((B$14 * (4 + t)) * sin(k)), ((B$15 * (4 + t)) * cos(k)) + ((B$16 * (4 + t)) * sin(k)), ((B$17 * (4 + t)) * cos(k)) + ((B$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A19, $A19 + pi / 12) → B19
  10. Surface(((B$13 * (4 + t)) * cos(k)) + ((B$14 * (4 + t)) * sin(k)), ((B$15 * (4 + t)) * cos(k)) + ((B$16 * (4 + t)) * sin(k)), ((B$17 * (4 + t)) * cos(k)) + ((B$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A20, $A20 + pi / 12) → B20
  11. Surface(((B$13 * (4 + t)) * cos(k)) + ((B$14 * (4 + t)) * sin(k)), ((B$15 * (4 + t)) * cos(k)) + ((B$16 * (4 + t)) * sin(k)), ((B$17 * (4 + t)) * cos(k)) + ((B$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A21, $A21 + pi / 12) → B21
  12. Surface(((B$13 * (4 + t)) * cos(k)) + ((B$14 * (4 + t)) * sin(k)), ((B$15 * (4 + t)) * cos(k)) + ((B$16 * (4 + t)) * sin(k)), ((B$17 * (4 + t)) * cos(k)) + ((B$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A22, $A22 + pi / 12) → B22
  13. Surface(((B$13 * (4 + t)) * cos(k)) + ((B$14 * (4 + t)) * sin(k)), ((B$15 * (4 + t)) * cos(k)) + ((B$16 * (4 + t)) * sin(k)), ((B$17 * (4 + t)) * cos(k)) + ((B$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A23, $A23 + pi / 12) → B23
  14. Surface(((B$13 * (4 + t)) * cos(k)) + ((B$14 * (4 + t)) * sin(k)), ((B$15 * (4 + t)) * cos(k)) + ((B$16 * (4 + t)) * sin(k)), ((B$17 * (4 + t)) * cos(k)) + ((B$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A24, $A24 + pi / 12) → B24
  15. Surface(((B$13 * (4 + t)) * cos(k)) + ((B$14 * (4 + t)) * sin(k)), ((B$15 * (4 + t)) * cos(k)) + ((B$16 * (4 + t)) * sin(k)), ((B$17 * (4 + t)) * cos(k)) + ((B$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A25, $A25 + pi / 12) → B25
  16. Surface(((B$13 * (4 + t)) * cos(k)) + ((B$14 * (4 + t)) * sin(k)), ((B$15 * (4 + t)) * cos(k)) + ((B$16 * (4 + t)) * sin(k)), ((B$17 * (4 + t)) * cos(k)) + ((B$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A26, $A26 + pi / 12) → B26
  17. Surface(((B$13 * (4 + t)) * cos(k)) + ((B$14 * (4 + t)) * sin(k)), ((B$15 * (4 + t)) * cos(k)) + ((B$16 * (4 + t)) * sin(k)), ((B$17 * (4 + t)) * cos(k)) + ((B$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A27, $A27 + pi / 12) → B27
  18. Surface(((B$13 * (4 + t)) * cos(k)) + ((B$14 * (4 + t)) * sin(k)), ((B$15 * (4 + t)) * cos(k)) + ((B$16 * (4 + t)) * sin(k)), ((B$17 * (4 + t)) * cos(k)) + ((B$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A28, $A28 + pi / 12) → B28
  19. Surface(((B$13 * (4 + t)) * cos(k)) + ((B$14 * (4 + t)) * sin(k)), ((B$15 * (4 + t)) * cos(k)) + ((B$16 * (4 + t)) * sin(k)), ((B$17 * (4 + t)) * cos(k)) + ((B$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A29, $A29 + pi / 12) → B29
  20. Surface(((B$13 * (4 + t)) * cos(k)) + ((B$14 * (4 + t)) * sin(k)), ((B$15 * (4 + t)) * cos(k)) + ((B$16 * (4 + t)) * sin(k)), ((B$17 * (4 + t)) * cos(k)) + ((B$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A30, $A30 + pi / 12) → B30
  21. Surface(((B$13 * (4 + t)) * cos(k)) + ((B$14 * (4 + t)) * sin(k)), ((B$15 * (4 + t)) * cos(k)) + ((B$16 * (4 + t)) * sin(k)), ((B$17 * (4 + t)) * cos(k)) + ((B$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A31, $A31 + pi / 12) → B31
  22. Surface(((B$13 * (4 + t)) * cos(k)) + ((B$14 * (4 + t)) * sin(k)), ((B$15 * (4 + t)) * cos(k)) + ((B$16 * (4 + t)) * sin(k)), ((B$17 * (4 + t)) * cos(k)) + ((B$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A32, $A32 + pi / 12) → B32
  23. Surface(((B$13 * (4 + t)) * cos(k)) + ((B$14 * (4 + t)) * sin(k)), ((B$15 * (4 + t)) * cos(k)) + ((B$16 * (4 + t)) * sin(k)), ((B$17 * (4 + t)) * cos(k)) + ((B$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A33, $A33 + pi / 12) → B33
  24. Surface(((B$13 * (4 + t)) * cos(k)) + ((B$14 * (4 + t)) * sin(k)), ((B$15 * (4 + t)) * cos(k)) + ((B$16 * (4 + t)) * sin(k)), ((B$17 * (4 + t)) * cos(k)) + ((B$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A34, $A34 + pi / 12) → B34
  25. Surface(((B$13 * (4 + t)) * cos(k)) + ((B$14 * (4 + t)) * sin(k)), ((B$15 * (4 + t)) * cos(k)) + ((B$16 * (4 + t)) * sin(k)), ((B$17 * (4 + t)) * cos(k)) + ((B$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A35, $A35 + pi / 12) → B35
  26. Surface(((B$13 * (4 + t)) * cos(k)) + ((B$14 * (4 + t)) * sin(k)), ((B$15 * (4 + t)) * cos(k)) + ((B$16 * (4 + t)) * sin(k)), ((B$17 * (4 + t)) * cos(k)) + ((B$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A36, $A36 + pi / 12) → B36
  27. Surface(((B$13 * (4 + t)) * cos(k)) + ((B$14 * (4 + t)) * sin(k)), ((B$15 * (4 + t)) * cos(k)) + ((B$16 * (4 + t)) * sin(k)), ((B$17 * (4 + t)) * cos(k)) + ((B$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A37, $A37 + pi / 12) → B37
  28. Surface(((B$13 * (4 + t)) * cos(k)) + ((B$14 * (4 + t)) * sin(k)), ((B$15 * (4 + t)) * cos(k)) + ((B$16 * (4 + t)) * sin(k)), ((B$17 * (4 + t)) * cos(k)) + ((B$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A38, $A38 + pi / 12) → B38
  29. Surface(((B$13 * (4 + t)) * cos(k)) + ((B$14 * (4 + t)) * sin(k)), ((B$15 * (4 + t)) * cos(k)) + ((B$16 * (4 + t)) * sin(k)), ((B$17 * (4 + t)) * cos(k)) + ((B$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A39, $A39 + pi / 12) → B39
  30. Surface(((B$13 * (4 + t)) * cos(k)) + ((B$14 * (4 + t)) * sin(k)), ((B$15 * (4 + t)) * cos(k)) + ((B$16 * (4 + t)) * sin(k)), ((B$17 * (4 + t)) * cos(k)) + ((B$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A40, $A40 + pi / 12) → B40
  31. Surface(((B$13 * (4 + t)) * cos(k)) + ((B$14 * (4 + t)) * sin(k)), ((B$15 * (4 + t)) * cos(k)) + ((B$16 * (4 + t)) * sin(k)), ((B$17 * (4 + t)) * cos(k)) + ((B$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A41, $A41 + pi / 12) → B41
  32. Surface(((B$13 * (4 + t)) * cos(k)) + ((B$14 * (4 + t)) * sin(k)), ((B$15 * (4 + t)) * cos(k)) + ((B$16 * (4 + t)) * sin(k)), ((B$17 * (4 + t)) * cos(k)) + ((B$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A42, $A42 + pi / 12) → B42
  33. Circle((0, 0, 0), 4, Line[(0, 0, 0), B2]) → B43
  34. Circle((0, 0, 0), 5, Line[(0, 0, 0), B2]) → B44
  35. Plane(C, A, E) → C1
  36. UnitOrthogonalVector(C1) → C2
  37. Element(C12, 1, 2) → C13
  38. Element(C12, 1, 3) → C14
  39. Element(C12, 2, 2) → C15
  40. Element(C12, 2, 3) → C16
  41. Element(C12, 3, 2) → C17
  42. Element(C12, 3, 3) → C18
  43. Surface(((C$13 * (4 + t)) * cos(k)) + ((C$14 * (4 + t)) * sin(k)), ((C$15 * (4 + t)) * cos(k)) + ((C$16 * (4 + t)) * sin(k)), ((C$17 * (4 + t)) * cos(k)) + ((C$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A19, $A19 + pi / 12) → C19
  44. Surface(((C$13 * (4 + t)) * cos(k)) + ((C$14 * (4 + t)) * sin(k)), ((C$15 * (4 + t)) * cos(k)) + ((C$16 * (4 + t)) * sin(k)), ((C$17 * (4 + t)) * cos(k)) + ((C$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A20, $A20 + pi / 12) → C20
  45. Surface(((C$13 * (4 + t)) * cos(k)) + ((C$14 * (4 + t)) * sin(k)), ((C$15 * (4 + t)) * cos(k)) + ((C$16 * (4 + t)) * sin(k)), ((C$17 * (4 + t)) * cos(k)) + ((C$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A21, $A21 + pi / 12) → C21
  46. Surface(((C$13 * (4 + t)) * cos(k)) + ((C$14 * (4 + t)) * sin(k)), ((C$15 * (4 + t)) * cos(k)) + ((C$16 * (4 + t)) * sin(k)), ((C$17 * (4 + t)) * cos(k)) + ((C$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A22, $A22 + pi / 12) → C22
  47. Surface(((C$13 * (4 + t)) * cos(k)) + ((C$14 * (4 + t)) * sin(k)), ((C$15 * (4 + t)) * cos(k)) + ((C$16 * (4 + t)) * sin(k)), ((C$17 * (4 + t)) * cos(k)) + ((C$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A23, $A23 + pi / 12) → C23
  48. Surface(((C$13 * (4 + t)) * cos(k)) + ((C$14 * (4 + t)) * sin(k)), ((C$15 * (4 + t)) * cos(k)) + ((C$16 * (4 + t)) * sin(k)), ((C$17 * (4 + t)) * cos(k)) + ((C$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A24, $A24 + pi / 12) → C24
  49. Surface(((C$13 * (4 + t)) * cos(k)) + ((C$14 * (4 + t)) * sin(k)), ((C$15 * (4 + t)) * cos(k)) + ((C$16 * (4 + t)) * sin(k)), ((C$17 * (4 + t)) * cos(k)) + ((C$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A25, $A25 + pi / 12) → C25
  50. Surface(((C$13 * (4 + t)) * cos(k)) + ((C$14 * (4 + t)) * sin(k)), ((C$15 * (4 + t)) * cos(k)) + ((C$16 * (4 + t)) * sin(k)), ((C$17 * (4 + t)) * cos(k)) + ((C$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A26, $A26 + pi / 12) → C26
  51. Surface(((C$13 * (4 + t)) * cos(k)) + ((C$14 * (4 + t)) * sin(k)), ((C$15 * (4 + t)) * cos(k)) + ((C$16 * (4 + t)) * sin(k)), ((C$17 * (4 + t)) * cos(k)) + ((C$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A27, $A27 + pi / 12) → C27
  52. Surface(((C$13 * (4 + t)) * cos(k)) + ((C$14 * (4 + t)) * sin(k)), ((C$15 * (4 + t)) * cos(k)) + ((C$16 * (4 + t)) * sin(k)), ((C$17 * (4 + t)) * cos(k)) + ((C$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A28, $A28 + pi / 12) → C28
  53. Surface(((C$13 * (4 + t)) * cos(k)) + ((C$14 * (4 + t)) * sin(k)), ((C$15 * (4 + t)) * cos(k)) + ((C$16 * (4 + t)) * sin(k)), ((C$17 * (4 + t)) * cos(k)) + ((C$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A29, $A29 + pi / 12) → C29
  54. Surface(((C$13 * (4 + t)) * cos(k)) + ((C$14 * (4 + t)) * sin(k)), ((C$15 * (4 + t)) * cos(k)) + ((C$16 * (4 + t)) * sin(k)), ((C$17 * (4 + t)) * cos(k)) + ((C$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A30, $A30 + pi / 12) → C30
  55. Surface(((C$13 * (4 + t)) * cos(k)) + ((C$14 * (4 + t)) * sin(k)), ((C$15 * (4 + t)) * cos(k)) + ((C$16 * (4 + t)) * sin(k)), ((C$17 * (4 + t)) * cos(k)) + ((C$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A31, $A31 + pi / 12) → C31
  56. Surface(((C$13 * (4 + t)) * cos(k)) + ((C$14 * (4 + t)) * sin(k)), ((C$15 * (4 + t)) * cos(k)) + ((C$16 * (4 + t)) * sin(k)), ((C$17 * (4 + t)) * cos(k)) + ((C$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A32, $A32 + pi / 12) → C32
  57. Surface(((C$13 * (4 + t)) * cos(k)) + ((C$14 * (4 + t)) * sin(k)), ((C$15 * (4 + t)) * cos(k)) + ((C$16 * (4 + t)) * sin(k)), ((C$17 * (4 + t)) * cos(k)) + ((C$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A33, $A33 + pi / 12) → C33
  58. Surface(((C$13 * (4 + t)) * cos(k)) + ((C$14 * (4 + t)) * sin(k)), ((C$15 * (4 + t)) * cos(k)) + ((C$16 * (4 + t)) * sin(k)), ((C$17 * (4 + t)) * cos(k)) + ((C$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A34, $A34 + pi / 12) → C34
  59. Surface(((C$13 * (4 + t)) * cos(k)) + ((C$14 * (4 + t)) * sin(k)), ((C$15 * (4 + t)) * cos(k)) + ((C$16 * (4 + t)) * sin(k)), ((C$17 * (4 + t)) * cos(k)) + ((C$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A35, $A35 + pi / 12) → C35
  60. Surface(((C$13 * (4 + t)) * cos(k)) + ((C$14 * (4 + t)) * sin(k)), ((C$15 * (4 + t)) * cos(k)) + ((C$16 * (4 + t)) * sin(k)), ((C$17 * (4 + t)) * cos(k)) + ((C$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A36, $A36 + pi / 12) → C36
  61. Surface(((C$13 * (4 + t)) * cos(k)) + ((C$14 * (4 + t)) * sin(k)), ((C$15 * (4 + t)) * cos(k)) + ((C$16 * (4 + t)) * sin(k)), ((C$17 * (4 + t)) * cos(k)) + ((C$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A37, $A37 + pi / 12) → C37
  62. Surface(((C$13 * (4 + t)) * cos(k)) + ((C$14 * (4 + t)) * sin(k)), ((C$15 * (4 + t)) * cos(k)) + ((C$16 * (4 + t)) * sin(k)), ((C$17 * (4 + t)) * cos(k)) + ((C$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A38, $A38 + pi / 12) → C38
  63. Surface(((C$13 * (4 + t)) * cos(k)) + ((C$14 * (4 + t)) * sin(k)), ((C$15 * (4 + t)) * cos(k)) + ((C$16 * (4 + t)) * sin(k)), ((C$17 * (4 + t)) * cos(k)) + ((C$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A39, $A39 + pi / 12) → C39
  64. Surface(((C$13 * (4 + t)) * cos(k)) + ((C$14 * (4 + t)) * sin(k)), ((C$15 * (4 + t)) * cos(k)) + ((C$16 * (4 + t)) * sin(k)), ((C$17 * (4 + t)) * cos(k)) + ((C$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A40, $A40 + pi / 12) → C40
  65. Surface(((C$13 * (4 + t)) * cos(k)) + ((C$14 * (4 + t)) * sin(k)), ((C$15 * (4 + t)) * cos(k)) + ((C$16 * (4 + t)) * sin(k)), ((C$17 * (4 + t)) * cos(k)) + ((C$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A41, $A41 + pi / 12) → C41
  66. Surface(((C$13 * (4 + t)) * cos(k)) + ((C$14 * (4 + t)) * sin(k)), ((C$15 * (4 + t)) * cos(k)) + ((C$16 * (4 + t)) * sin(k)), ((C$17 * (4 + t)) * cos(k)) + ((C$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A42, $A42 + pi / 12) → C42
  67. Circle((0, 0, 0), 4, Line[(0, 0, 0), C2]) → C43
  68. Circle((0, 0, 0), 5, Line[(0, 0, 0), C2]) → C44
  69. Plane(A, D, E) → D1
  70. UnitOrthogonalVector(D1) → D2
  71. Element(D12, 1, 2) → D13
  72. Element(D12, 1, 3) → D14
  73. Element(D12, 2, 2) → D15
  74. Element(D12, 2, 3) → D16
  75. Element(D12, 3, 2) → D17
  76. Element(D12, 3, 3) → D18
  77. Surface(((D$13 * (4 + t)) * cos(k)) + ((D$14 * (4 + t)) * sin(k)), ((D$15 * (4 + t)) * cos(k)) + ((D$16 * (4 + t)) * sin(k)), ((D$17 * (4 + t)) * cos(k)) + ((D$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A19, $A19 + pi / 12) → D19
  78. Surface(((D$13 * (4 + t)) * cos(k)) + ((D$14 * (4 + t)) * sin(k)), ((D$15 * (4 + t)) * cos(k)) + ((D$16 * (4 + t)) * sin(k)), ((D$17 * (4 + t)) * cos(k)) + ((D$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A20, $A20 + pi / 12) → D20
  79. Surface(((D$13 * (4 + t)) * cos(k)) + ((D$14 * (4 + t)) * sin(k)), ((D$15 * (4 + t)) * cos(k)) + ((D$16 * (4 + t)) * sin(k)), ((D$17 * (4 + t)) * cos(k)) + ((D$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A21, $A21 + pi / 12) → D21
  80. Surface(((D$13 * (4 + t)) * cos(k)) + ((D$14 * (4 + t)) * sin(k)), ((D$15 * (4 + t)) * cos(k)) + ((D$16 * (4 + t)) * sin(k)), ((D$17 * (4 + t)) * cos(k)) + ((D$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A22, $A22 + pi / 12) → D22
  81. Surface(((D$13 * (4 + t)) * cos(k)) + ((D$14 * (4 + t)) * sin(k)), ((D$15 * (4 + t)) * cos(k)) + ((D$16 * (4 + t)) * sin(k)), ((D$17 * (4 + t)) * cos(k)) + ((D$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A23, $A23 + pi / 12) → D23
  82. Surface(((D$13 * (4 + t)) * cos(k)) + ((D$14 * (4 + t)) * sin(k)), ((D$15 * (4 + t)) * cos(k)) + ((D$16 * (4 + t)) * sin(k)), ((D$17 * (4 + t)) * cos(k)) + ((D$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A24, $A24 + pi / 12) → D24
  83. Surface(((D$13 * (4 + t)) * cos(k)) + ((D$14 * (4 + t)) * sin(k)), ((D$15 * (4 + t)) * cos(k)) + ((D$16 * (4 + t)) * sin(k)), ((D$17 * (4 + t)) * cos(k)) + ((D$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A25, $A25 + pi / 12) → D25
  84. Surface(((D$13 * (4 + t)) * cos(k)) + ((D$14 * (4 + t)) * sin(k)), ((D$15 * (4 + t)) * cos(k)) + ((D$16 * (4 + t)) * sin(k)), ((D$17 * (4 + t)) * cos(k)) + ((D$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A26, $A26 + pi / 12) → D26
  85. Surface(((D$13 * (4 + t)) * cos(k)) + ((D$14 * (4 + t)) * sin(k)), ((D$15 * (4 + t)) * cos(k)) + ((D$16 * (4 + t)) * sin(k)), ((D$17 * (4 + t)) * cos(k)) + ((D$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A27, $A27 + pi / 12) → D27
  86. Surface(((D$13 * (4 + t)) * cos(k)) + ((D$14 * (4 + t)) * sin(k)), ((D$15 * (4 + t)) * cos(k)) + ((D$16 * (4 + t)) * sin(k)), ((D$17 * (4 + t)) * cos(k)) + ((D$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A28, $A28 + pi / 12) → D28
  87. Surface(((D$13 * (4 + t)) * cos(k)) + ((D$14 * (4 + t)) * sin(k)), ((D$15 * (4 + t)) * cos(k)) + ((D$16 * (4 + t)) * sin(k)), ((D$17 * (4 + t)) * cos(k)) + ((D$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A29, $A29 + pi / 12) → D29
  88. Surface(((D$13 * (4 + t)) * cos(k)) + ((D$14 * (4 + t)) * sin(k)), ((D$15 * (4 + t)) * cos(k)) + ((D$16 * (4 + t)) * sin(k)), ((D$17 * (4 + t)) * cos(k)) + ((D$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A30, $A30 + pi / 12) → D30
  89. Surface(((D$13 * (4 + t)) * cos(k)) + ((D$14 * (4 + t)) * sin(k)), ((D$15 * (4 + t)) * cos(k)) + ((D$16 * (4 + t)) * sin(k)), ((D$17 * (4 + t)) * cos(k)) + ((D$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A31, $A31 + pi / 12) → D31
  90. Surface(((D$13 * (4 + t)) * cos(k)) + ((D$14 * (4 + t)) * sin(k)), ((D$15 * (4 + t)) * cos(k)) + ((D$16 * (4 + t)) * sin(k)), ((D$17 * (4 + t)) * cos(k)) + ((D$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A32, $A32 + pi / 12) → D32
  91. Surface(((D$13 * (4 + t)) * cos(k)) + ((D$14 * (4 + t)) * sin(k)), ((D$15 * (4 + t)) * cos(k)) + ((D$16 * (4 + t)) * sin(k)), ((D$17 * (4 + t)) * cos(k)) + ((D$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A33, $A33 + pi / 12) → D33
  92. Surface(((D$13 * (4 + t)) * cos(k)) + ((D$14 * (4 + t)) * sin(k)), ((D$15 * (4 + t)) * cos(k)) + ((D$16 * (4 + t)) * sin(k)), ((D$17 * (4 + t)) * cos(k)) + ((D$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A34, $A34 + pi / 12) → D34
  93. Surface(((D$13 * (4 + t)) * cos(k)) + ((D$14 * (4 + t)) * sin(k)), ((D$15 * (4 + t)) * cos(k)) + ((D$16 * (4 + t)) * sin(k)), ((D$17 * (4 + t)) * cos(k)) + ((D$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A35, $A35 + pi / 12) → D35
  94. Surface(((D$13 * (4 + t)) * cos(k)) + ((D$14 * (4 + t)) * sin(k)), ((D$15 * (4 + t)) * cos(k)) + ((D$16 * (4 + t)) * sin(k)), ((D$17 * (4 + t)) * cos(k)) + ((D$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A36, $A36 + pi / 12) → D36
  95. Surface(((D$13 * (4 + t)) * cos(k)) + ((D$14 * (4 + t)) * sin(k)), ((D$15 * (4 + t)) * cos(k)) + ((D$16 * (4 + t)) * sin(k)), ((D$17 * (4 + t)) * cos(k)) + ((D$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A37, $A37 + pi / 12) → D37
  96. Surface(((D$13 * (4 + t)) * cos(k)) + ((D$14 * (4 + t)) * sin(k)), ((D$15 * (4 + t)) * cos(k)) + ((D$16 * (4 + t)) * sin(k)), ((D$17 * (4 + t)) * cos(k)) + ((D$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A38, $A38 + pi / 12) → D38
  97. Surface(((D$13 * (4 + t)) * cos(k)) + ((D$14 * (4 + t)) * sin(k)), ((D$15 * (4 + t)) * cos(k)) + ((D$16 * (4 + t)) * sin(k)), ((D$17 * (4 + t)) * cos(k)) + ((D$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A39, $A39 + pi / 12) → D39
  98. Surface(((D$13 * (4 + t)) * cos(k)) + ((D$14 * (4 + t)) * sin(k)), ((D$15 * (4 + t)) * cos(k)) + ((D$16 * (4 + t)) * sin(k)), ((D$17 * (4 + t)) * cos(k)) + ((D$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A40, $A40 + pi / 12) → D40
  99. Surface(((D$13 * (4 + t)) * cos(k)) + ((D$14 * (4 + t)) * sin(k)), ((D$15 * (4 + t)) * cos(k)) + ((D$16 * (4 + t)) * sin(k)), ((D$17 * (4 + t)) * cos(k)) + ((D$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A41, $A41 + pi / 12) → D41
  100. Surface(((D$13 * (4 + t)) * cos(k)) + ((D$14 * (4 + t)) * sin(k)), ((D$15 * (4 + t)) * cos(k)) + ((D$16 * (4 + t)) * sin(k)), ((D$17 * (4 + t)) * cos(k)) + ((D$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A42, $A42 + pi / 12) → D42
  101. Circle((0, 0, 0), 4, Line[(0, 0, 0), D2]) → D43
  102. Circle((0, 0, 0), 5, Line[(0, 0, 0), D2]) → D44
  103. Plane(B, C, E) → E1
  104. UnitOrthogonalVector(E1) → E2
  105. Element(E12, 1, 2) → E13
  106. Element(E12, 1, 3) → E14
  107. Element(E12, 2, 2) → E15
  108. Element(E12, 2, 3) → E16
  109. Element(E12, 3, 2) → E17
  110. Element(E12, 3, 3) → E18
  111. Surface(((E$13 * (4 + t)) * cos(k)) + ((E$14 * (4 + t)) * sin(k)), ((E$15 * (4 + t)) * cos(k)) + ((E$16 * (4 + t)) * sin(k)), ((E$17 * (4 + t)) * cos(k)) + ((E$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A19, $A19 + pi / 12) → E19
  112. Surface(((E$13 * (4 + t)) * cos(k)) + ((E$14 * (4 + t)) * sin(k)), ((E$15 * (4 + t)) * cos(k)) + ((E$16 * (4 + t)) * sin(k)), ((E$17 * (4 + t)) * cos(k)) + ((E$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A20, $A20 + pi / 12) → E20
  113. Surface(((E$13 * (4 + t)) * cos(k)) + ((E$14 * (4 + t)) * sin(k)), ((E$15 * (4 + t)) * cos(k)) + ((E$16 * (4 + t)) * sin(k)), ((E$17 * (4 + t)) * cos(k)) + ((E$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A21, $A21 + pi / 12) → E21
  114. Surface(((E$13 * (4 + t)) * cos(k)) + ((E$14 * (4 + t)) * sin(k)), ((E$15 * (4 + t)) * cos(k)) + ((E$16 * (4 + t)) * sin(k)), ((E$17 * (4 + t)) * cos(k)) + ((E$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A22, $A22 + pi / 12) → E22
  115. Surface(((E$13 * (4 + t)) * cos(k)) + ((E$14 * (4 + t)) * sin(k)), ((E$15 * (4 + t)) * cos(k)) + ((E$16 * (4 + t)) * sin(k)), ((E$17 * (4 + t)) * cos(k)) + ((E$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A23, $A23 + pi / 12) → E23
  116. Surface(((E$13 * (4 + t)) * cos(k)) + ((E$14 * (4 + t)) * sin(k)), ((E$15 * (4 + t)) * cos(k)) + ((E$16 * (4 + t)) * sin(k)), ((E$17 * (4 + t)) * cos(k)) + ((E$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A24, $A24 + pi / 12) → E24
  117. Surface(((E$13 * (4 + t)) * cos(k)) + ((E$14 * (4 + t)) * sin(k)), ((E$15 * (4 + t)) * cos(k)) + ((E$16 * (4 + t)) * sin(k)), ((E$17 * (4 + t)) * cos(k)) + ((E$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A25, $A25 + pi / 12) → E25
  118. Surface(((E$13 * (4 + t)) * cos(k)) + ((E$14 * (4 + t)) * sin(k)), ((E$15 * (4 + t)) * cos(k)) + ((E$16 * (4 + t)) * sin(k)), ((E$17 * (4 + t)) * cos(k)) + ((E$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A26, $A26 + pi / 12) → E26
  119. Surface(((E$13 * (4 + t)) * cos(k)) + ((E$14 * (4 + t)) * sin(k)), ((E$15 * (4 + t)) * cos(k)) + ((E$16 * (4 + t)) * sin(k)), ((E$17 * (4 + t)) * cos(k)) + ((E$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A27, $A27 + pi / 12) → E27
  120. Surface(((E$13 * (4 + t)) * cos(k)) + ((E$14 * (4 + t)) * sin(k)), ((E$15 * (4 + t)) * cos(k)) + ((E$16 * (4 + t)) * sin(k)), ((E$17 * (4 + t)) * cos(k)) + ((E$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A28, $A28 + pi / 12) → E28
  121. Surface(((E$13 * (4 + t)) * cos(k)) + ((E$14 * (4 + t)) * sin(k)), ((E$15 * (4 + t)) * cos(k)) + ((E$16 * (4 + t)) * sin(k)), ((E$17 * (4 + t)) * cos(k)) + ((E$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A29, $A29 + pi / 12) → E29
  122. Surface(((E$13 * (4 + t)) * cos(k)) + ((E$14 * (4 + t)) * sin(k)), ((E$15 * (4 + t)) * cos(k)) + ((E$16 * (4 + t)) * sin(k)), ((E$17 * (4 + t)) * cos(k)) + ((E$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A30, $A30 + pi / 12) → E30
  123. Surface(((E$13 * (4 + t)) * cos(k)) + ((E$14 * (4 + t)) * sin(k)), ((E$15 * (4 + t)) * cos(k)) + ((E$16 * (4 + t)) * sin(k)), ((E$17 * (4 + t)) * cos(k)) + ((E$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A31, $A31 + pi / 12) → E31
  124. Surface(((E$13 * (4 + t)) * cos(k)) + ((E$14 * (4 + t)) * sin(k)), ((E$15 * (4 + t)) * cos(k)) + ((E$16 * (4 + t)) * sin(k)), ((E$17 * (4 + t)) * cos(k)) + ((E$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A32, $A32 + pi / 12) → E32
  125. Surface(((E$13 * (4 + t)) * cos(k)) + ((E$14 * (4 + t)) * sin(k)), ((E$15 * (4 + t)) * cos(k)) + ((E$16 * (4 + t)) * sin(k)), ((E$17 * (4 + t)) * cos(k)) + ((E$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A33, $A33 + pi / 12) → E33
  126. Surface(((E$13 * (4 + t)) * cos(k)) + ((E$14 * (4 + t)) * sin(k)), ((E$15 * (4 + t)) * cos(k)) + ((E$16 * (4 + t)) * sin(k)), ((E$17 * (4 + t)) * cos(k)) + ((E$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A34, $A34 + pi / 12) → E34
  127. Surface(((E$13 * (4 + t)) * cos(k)) + ((E$14 * (4 + t)) * sin(k)), ((E$15 * (4 + t)) * cos(k)) + ((E$16 * (4 + t)) * sin(k)), ((E$17 * (4 + t)) * cos(k)) + ((E$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A35, $A35 + pi / 12) → E35
  128. Surface(((E$13 * (4 + t)) * cos(k)) + ((E$14 * (4 + t)) * sin(k)), ((E$15 * (4 + t)) * cos(k)) + ((E$16 * (4 + t)) * sin(k)), ((E$17 * (4 + t)) * cos(k)) + ((E$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A36, $A36 + pi / 12) → E36
  129. Surface(((E$13 * (4 + t)) * cos(k)) + ((E$14 * (4 + t)) * sin(k)), ((E$15 * (4 + t)) * cos(k)) + ((E$16 * (4 + t)) * sin(k)), ((E$17 * (4 + t)) * cos(k)) + ((E$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A37, $A37 + pi / 12) → E37
  130. Surface(((E$13 * (4 + t)) * cos(k)) + ((E$14 * (4 + t)) * sin(k)), ((E$15 * (4 + t)) * cos(k)) + ((E$16 * (4 + t)) * sin(k)), ((E$17 * (4 + t)) * cos(k)) + ((E$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A38, $A38 + pi / 12) → E38
  131. Surface(((E$13 * (4 + t)) * cos(k)) + ((E$14 * (4 + t)) * sin(k)), ((E$15 * (4 + t)) * cos(k)) + ((E$16 * (4 + t)) * sin(k)), ((E$17 * (4 + t)) * cos(k)) + ((E$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A39, $A39 + pi / 12) → E39
  132. Surface(((E$13 * (4 + t)) * cos(k)) + ((E$14 * (4 + t)) * sin(k)), ((E$15 * (4 + t)) * cos(k)) + ((E$16 * (4 + t)) * sin(k)), ((E$17 * (4 + t)) * cos(k)) + ((E$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A40, $A40 + pi / 12) → E40
  133. Surface(((E$13 * (4 + t)) * cos(k)) + ((E$14 * (4 + t)) * sin(k)), ((E$15 * (4 + t)) * cos(k)) + ((E$16 * (4 + t)) * sin(k)), ((E$17 * (4 + t)) * cos(k)) + ((E$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A41, $A41 + pi / 12) → E41
  134. Surface(((E$13 * (4 + t)) * cos(k)) + ((E$14 * (4 + t)) * sin(k)), ((E$15 * (4 + t)) * cos(k)) + ((E$16 * (4 + t)) * sin(k)), ((E$17 * (4 + t)) * cos(k)) + ((E$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A42, $A42 + pi / 12) → E42
  135. Circle((0, 0, 0), 4, Line[(0, 0, 0), E2]) → E43
  136. Circle((0, 0, 0), 5, Line[(0, 0, 0), E2]) → E44
  137. Plane(B, D, E) → F1
  138. UnitOrthogonalVector(F1) → F2
  139. Element(F12, 1, 2) → F13
  140. Element(F12, 1, 3) → F14
  141. Element(F12, 2, 2) → F15
  142. Element(F12, 2, 3) → F16
  143. Element(F12, 3, 2) → F17
  144. Element(F12, 3, 3) → F18
  145. Surface(((F$13 * (4 + t)) * cos(k)) + ((F$14 * (4 + t)) * sin(k)), ((F$15 * (4 + t)) * cos(k)) + ((F$16 * (4 + t)) * sin(k)), ((F$17 * (4 + t)) * cos(k)) + ((F$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A19, $A19 + pi / 12) → F19
  146. Surface(((F$13 * (4 + t)) * cos(k)) + ((F$14 * (4 + t)) * sin(k)), ((F$15 * (4 + t)) * cos(k)) + ((F$16 * (4 + t)) * sin(k)), ((F$17 * (4 + t)) * cos(k)) + ((F$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A20, $A20 + pi / 12) → F20
  147. Surface(((F$13 * (4 + t)) * cos(k)) + ((F$14 * (4 + t)) * sin(k)), ((F$15 * (4 + t)) * cos(k)) + ((F$16 * (4 + t)) * sin(k)), ((F$17 * (4 + t)) * cos(k)) + ((F$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A21, $A21 + pi / 12) → F21
  148. Surface(((F$13 * (4 + t)) * cos(k)) + ((F$14 * (4 + t)) * sin(k)), ((F$15 * (4 + t)) * cos(k)) + ((F$16 * (4 + t)) * sin(k)), ((F$17 * (4 + t)) * cos(k)) + ((F$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A22, $A22 + pi / 12) → F22
  149. Surface(((F$13 * (4 + t)) * cos(k)) + ((F$14 * (4 + t)) * sin(k)), ((F$15 * (4 + t)) * cos(k)) + ((F$16 * (4 + t)) * sin(k)), ((F$17 * (4 + t)) * cos(k)) + ((F$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A23, $A23 + pi / 12) → F23
  150. Surface(((F$13 * (4 + t)) * cos(k)) + ((F$14 * (4 + t)) * sin(k)), ((F$15 * (4 + t)) * cos(k)) + ((F$16 * (4 + t)) * sin(k)), ((F$17 * (4 + t)) * cos(k)) + ((F$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A24, $A24 + pi / 12) → F24
  151. Surface(((F$13 * (4 + t)) * cos(k)) + ((F$14 * (4 + t)) * sin(k)), ((F$15 * (4 + t)) * cos(k)) + ((F$16 * (4 + t)) * sin(k)), ((F$17 * (4 + t)) * cos(k)) + ((F$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A25, $A25 + pi / 12) → F25
  152. Surface(((F$13 * (4 + t)) * cos(k)) + ((F$14 * (4 + t)) * sin(k)), ((F$15 * (4 + t)) * cos(k)) + ((F$16 * (4 + t)) * sin(k)), ((F$17 * (4 + t)) * cos(k)) + ((F$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A26, $A26 + pi / 12) → F26
  153. Surface(((F$13 * (4 + t)) * cos(k)) + ((F$14 * (4 + t)) * sin(k)), ((F$15 * (4 + t)) * cos(k)) + ((F$16 * (4 + t)) * sin(k)), ((F$17 * (4 + t)) * cos(k)) + ((F$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A27, $A27 + pi / 12) → F27
  154. Surface(((F$13 * (4 + t)) * cos(k)) + ((F$14 * (4 + t)) * sin(k)), ((F$15 * (4 + t)) * cos(k)) + ((F$16 * (4 + t)) * sin(k)), ((F$17 * (4 + t)) * cos(k)) + ((F$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A28, $A28 + pi / 12) → F28
  155. Surface(((F$13 * (4 + t)) * cos(k)) + ((F$14 * (4 + t)) * sin(k)), ((F$15 * (4 + t)) * cos(k)) + ((F$16 * (4 + t)) * sin(k)), ((F$17 * (4 + t)) * cos(k)) + ((F$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A29, $A29 + pi / 12) → F29
  156. Surface(((F$13 * (4 + t)) * cos(k)) + ((F$14 * (4 + t)) * sin(k)), ((F$15 * (4 + t)) * cos(k)) + ((F$16 * (4 + t)) * sin(k)), ((F$17 * (4 + t)) * cos(k)) + ((F$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A30, $A30 + pi / 12) → F30
  157. Surface(((F$13 * (4 + t)) * cos(k)) + ((F$14 * (4 + t)) * sin(k)), ((F$15 * (4 + t)) * cos(k)) + ((F$16 * (4 + t)) * sin(k)), ((F$17 * (4 + t)) * cos(k)) + ((F$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A31, $A31 + pi / 12) → F31
  158. Surface(((F$13 * (4 + t)) * cos(k)) + ((F$14 * (4 + t)) * sin(k)), ((F$15 * (4 + t)) * cos(k)) + ((F$16 * (4 + t)) * sin(k)), ((F$17 * (4 + t)) * cos(k)) + ((F$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A32, $A32 + pi / 12) → F32
  159. Surface(((F$13 * (4 + t)) * cos(k)) + ((F$14 * (4 + t)) * sin(k)), ((F$15 * (4 + t)) * cos(k)) + ((F$16 * (4 + t)) * sin(k)), ((F$17 * (4 + t)) * cos(k)) + ((F$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A33, $A33 + pi / 12) → F33
  160. Surface(((F$13 * (4 + t)) * cos(k)) + ((F$14 * (4 + t)) * sin(k)), ((F$15 * (4 + t)) * cos(k)) + ((F$16 * (4 + t)) * sin(k)), ((F$17 * (4 + t)) * cos(k)) + ((F$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A34, $A34 + pi / 12) → F34
  161. Surface(((F$13 * (4 + t)) * cos(k)) + ((F$14 * (4 + t)) * sin(k)), ((F$15 * (4 + t)) * cos(k)) + ((F$16 * (4 + t)) * sin(k)), ((F$17 * (4 + t)) * cos(k)) + ((F$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A35, $A35 + pi / 12) → F35
  162. Surface(((F$13 * (4 + t)) * cos(k)) + ((F$14 * (4 + t)) * sin(k)), ((F$15 * (4 + t)) * cos(k)) + ((F$16 * (4 + t)) * sin(k)), ((F$17 * (4 + t)) * cos(k)) + ((F$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A36, $A36 + pi / 12) → F36
  163. Surface(((F$13 * (4 + t)) * cos(k)) + ((F$14 * (4 + t)) * sin(k)), ((F$15 * (4 + t)) * cos(k)) + ((F$16 * (4 + t)) * sin(k)), ((F$17 * (4 + t)) * cos(k)) + ((F$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A37, $A37 + pi / 12) → F37
  164. Surface(((F$13 * (4 + t)) * cos(k)) + ((F$14 * (4 + t)) * sin(k)), ((F$15 * (4 + t)) * cos(k)) + ((F$16 * (4 + t)) * sin(k)), ((F$17 * (4 + t)) * cos(k)) + ((F$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A38, $A38 + pi / 12) → F38
  165. Surface(((F$13 * (4 + t)) * cos(k)) + ((F$14 * (4 + t)) * sin(k)), ((F$15 * (4 + t)) * cos(k)) + ((F$16 * (4 + t)) * sin(k)), ((F$17 * (4 + t)) * cos(k)) + ((F$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A39, $A39 + pi / 12) → F39
  166. Surface(((F$13 * (4 + t)) * cos(k)) + ((F$14 * (4 + t)) * sin(k)), ((F$15 * (4 + t)) * cos(k)) + ((F$16 * (4 + t)) * sin(k)), ((F$17 * (4 + t)) * cos(k)) + ((F$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A40, $A40 + pi / 12) → F40
  167. Surface(((F$13 * (4 + t)) * cos(k)) + ((F$14 * (4 + t)) * sin(k)), ((F$15 * (4 + t)) * cos(k)) + ((F$16 * (4 + t)) * sin(k)), ((F$17 * (4 + t)) * cos(k)) + ((F$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A41, $A41 + pi / 12) → F41
  168. Surface(((F$13 * (4 + t)) * cos(k)) + ((F$14 * (4 + t)) * sin(k)), ((F$15 * (4 + t)) * cos(k)) + ((F$16 * (4 + t)) * sin(k)), ((F$17 * (4 + t)) * cos(k)) + ((F$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A42, $A42 + pi / 12) → F42
  169. Circle((0, 0, 0), 4, Line[(0, 0, 0), F2]) → F43
  170. Circle((0, 0, 0), 5, Line[(0, 0, 0), F2]) → F44
  171. Plane(C, D, E) → G1
  172. UnitOrthogonalVector(G1) → G2
  173. Element(G12, 1, 2) → G13
  174. Element(G12, 1, 3) → G14
  175. Element(G12, 2, 2) → G15
  176. Element(G12, 2, 3) → G16
  177. Element(G12, 3, 2) → G17
  178. Element(G12, 3, 3) → G18
  179. Surface(((G$13 * (4 + t)) * cos(k)) + ((G$14 * (4 + t)) * sin(k)), ((G$15 * (4 + t)) * cos(k)) + ((G$16 * (4 + t)) * sin(k)), ((G$17 * (4 + t)) * cos(k)) + ((G$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A19, $A19 + pi / 12) → G19
  180. Surface(((G$13 * (4 + t)) * cos(k)) + ((G$14 * (4 + t)) * sin(k)), ((G$15 * (4 + t)) * cos(k)) + ((G$16 * (4 + t)) * sin(k)), ((G$17 * (4 + t)) * cos(k)) + ((G$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A20, $A20 + pi / 12) → G20
  181. Surface(((G$13 * (4 + t)) * cos(k)) + ((G$14 * (4 + t)) * sin(k)), ((G$15 * (4 + t)) * cos(k)) + ((G$16 * (4 + t)) * sin(k)), ((G$17 * (4 + t)) * cos(k)) + ((G$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A21, $A21 + pi / 12) → G21
  182. Surface(((G$13 * (4 + t)) * cos(k)) + ((G$14 * (4 + t)) * sin(k)), ((G$15 * (4 + t)) * cos(k)) + ((G$16 * (4 + t)) * sin(k)), ((G$17 * (4 + t)) * cos(k)) + ((G$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A22, $A22 + pi / 12) → G22
  183. Surface(((G$13 * (4 + t)) * cos(k)) + ((G$14 * (4 + t)) * sin(k)), ((G$15 * (4 + t)) * cos(k)) + ((G$16 * (4 + t)) * sin(k)), ((G$17 * (4 + t)) * cos(k)) + ((G$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A23, $A23 + pi / 12) → G23
  184. Surface(((G$13 * (4 + t)) * cos(k)) + ((G$14 * (4 + t)) * sin(k)), ((G$15 * (4 + t)) * cos(k)) + ((G$16 * (4 + t)) * sin(k)), ((G$17 * (4 + t)) * cos(k)) + ((G$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A24, $A24 + pi / 12) → G24
  185. Surface(((G$13 * (4 + t)) * cos(k)) + ((G$14 * (4 + t)) * sin(k)), ((G$15 * (4 + t)) * cos(k)) + ((G$16 * (4 + t)) * sin(k)), ((G$17 * (4 + t)) * cos(k)) + ((G$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A25, $A25 + pi / 12) → G25
  186. Surface(((G$13 * (4 + t)) * cos(k)) + ((G$14 * (4 + t)) * sin(k)), ((G$15 * (4 + t)) * cos(k)) + ((G$16 * (4 + t)) * sin(k)), ((G$17 * (4 + t)) * cos(k)) + ((G$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A26, $A26 + pi / 12) → G26
  187. Surface(((G$13 * (4 + t)) * cos(k)) + ((G$14 * (4 + t)) * sin(k)), ((G$15 * (4 + t)) * cos(k)) + ((G$16 * (4 + t)) * sin(k)), ((G$17 * (4 + t)) * cos(k)) + ((G$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A27, $A27 + pi / 12) → G27
  188. Surface(((G$13 * (4 + t)) * cos(k)) + ((G$14 * (4 + t)) * sin(k)), ((G$15 * (4 + t)) * cos(k)) + ((G$16 * (4 + t)) * sin(k)), ((G$17 * (4 + t)) * cos(k)) + ((G$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A28, $A28 + pi / 12) → G28
  189. Surface(((G$13 * (4 + t)) * cos(k)) + ((G$14 * (4 + t)) * sin(k)), ((G$15 * (4 + t)) * cos(k)) + ((G$16 * (4 + t)) * sin(k)), ((G$17 * (4 + t)) * cos(k)) + ((G$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A29, $A29 + pi / 12) → G29
  190. Surface(((G$13 * (4 + t)) * cos(k)) + ((G$14 * (4 + t)) * sin(k)), ((G$15 * (4 + t)) * cos(k)) + ((G$16 * (4 + t)) * sin(k)), ((G$17 * (4 + t)) * cos(k)) + ((G$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A30, $A30 + pi / 12) → G30
  191. Surface(((G$13 * (4 + t)) * cos(k)) + ((G$14 * (4 + t)) * sin(k)), ((G$15 * (4 + t)) * cos(k)) + ((G$16 * (4 + t)) * sin(k)), ((G$17 * (4 + t)) * cos(k)) + ((G$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A31, $A31 + pi / 12) → G31
  192. Surface(((G$13 * (4 + t)) * cos(k)) + ((G$14 * (4 + t)) * sin(k)), ((G$15 * (4 + t)) * cos(k)) + ((G$16 * (4 + t)) * sin(k)), ((G$17 * (4 + t)) * cos(k)) + ((G$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A32, $A32 + pi / 12) → G32
  193. Surface(((G$13 * (4 + t)) * cos(k)) + ((G$14 * (4 + t)) * sin(k)), ((G$15 * (4 + t)) * cos(k)) + ((G$16 * (4 + t)) * sin(k)), ((G$17 * (4 + t)) * cos(k)) + ((G$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A33, $A33 + pi / 12) → G33
  194. Surface(((G$13 * (4 + t)) * cos(k)) + ((G$14 * (4 + t)) * sin(k)), ((G$15 * (4 + t)) * cos(k)) + ((G$16 * (4 + t)) * sin(k)), ((G$17 * (4 + t)) * cos(k)) + ((G$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A34, $A34 + pi / 12) → G34
  195. Surface(((G$13 * (4 + t)) * cos(k)) + ((G$14 * (4 + t)) * sin(k)), ((G$15 * (4 + t)) * cos(k)) + ((G$16 * (4 + t)) * sin(k)), ((G$17 * (4 + t)) * cos(k)) + ((G$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A35, $A35 + pi / 12) → G35
  196. Surface(((G$13 * (4 + t)) * cos(k)) + ((G$14 * (4 + t)) * sin(k)), ((G$15 * (4 + t)) * cos(k)) + ((G$16 * (4 + t)) * sin(k)), ((G$17 * (4 + t)) * cos(k)) + ((G$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A36, $A36 + pi / 12) → G36
  197. Surface(((G$13 * (4 + t)) * cos(k)) + ((G$14 * (4 + t)) * sin(k)), ((G$15 * (4 + t)) * cos(k)) + ((G$16 * (4 + t)) * sin(k)), ((G$17 * (4 + t)) * cos(k)) + ((G$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A37, $A37 + pi / 12) → G37
  198. Surface(((G$13 * (4 + t)) * cos(k)) + ((G$14 * (4 + t)) * sin(k)), ((G$15 * (4 + t)) * cos(k)) + ((G$16 * (4 + t)) * sin(k)), ((G$17 * (4 + t)) * cos(k)) + ((G$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A38, $A38 + pi / 12) → G38
  199. Surface(((G$13 * (4 + t)) * cos(k)) + ((G$14 * (4 + t)) * sin(k)), ((G$15 * (4 + t)) * cos(k)) + ((G$16 * (4 + t)) * sin(k)), ((G$17 * (4 + t)) * cos(k)) + ((G$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A39, $A39 + pi / 12) → G39
  200. Surface(((G$13 * (4 + t)) * cos(k)) + ((G$14 * (4 + t)) * sin(k)), ((G$15 * (4 + t)) * cos(k)) + ((G$16 * (4 + t)) * sin(k)), ((G$17 * (4 + t)) * cos(k)) + ((G$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A40, $A40 + pi / 12) → G40
  201. Surface(((G$13 * (4 + t)) * cos(k)) + ((G$14 * (4 + t)) * sin(k)), ((G$15 * (4 + t)) * cos(k)) + ((G$16 * (4 + t)) * sin(k)), ((G$17 * (4 + t)) * cos(k)) + ((G$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A41, $A41 + pi / 12) → G41
  202. Surface(((G$13 * (4 + t)) * cos(k)) + ((G$14 * (4 + t)) * sin(k)), ((G$15 * (4 + t)) * cos(k)) + ((G$16 * (4 + t)) * sin(k)), ((G$17 * (4 + t)) * cos(k)) + ((G$18 * (4 + t)) * sin(k)), t, 0, 1, k, $A42, $A42 + pi / 12) → G42
  203. Circle((0, 0, 0), 4, Line[(0, 0, 0), G2]) → G43
  204. Circle((0, 0, 0), 5, Line[(0, 0, 0), G2]) → G44
  205. Segment(E + (4 * I1), E + (5 * I1)) → J1
  206. Segment(E + (4 * I2), E + (5 * I2)) → J2
  207. Segment(E + (4 * I3), E + (5 * I3)) → J3
  208. Segment(E + (4 * I4), E + (5 * I4)) → J4
  209. Segment(E - (4 * I1), E - (5 * I1)) → K1
  210. Segment(E - (4 * I2), E - (5 * I2)) → K2
  211. Segment(E - (4 * I3), E - (5 * I3)) → K3
  212. Segment(E - (4 * I4), E - (5 * I4)) → K4
  213. Midpoint(A, B) → H5
  214. Midpoint(A, C) → H6
  215. Midpoint(A, D) → H7
  216. Midpoint(B, C) → H8
  217. Midpoint(B, D) → H9
  218. Midpoint(C, D) → H10

AI Drawing Prompt Reference

Draw a sphere and project a tetrahedron onto it. Start by creating a plane and a unit orthogonal vector, then use these vectors to generate multiple surfaces on the sphere, each representing a face of the tetrahedron. Finally, combine these surfaces to form a complete spherical tetrahedron model, showcasing the relationship between spherical and solid geometry.
The prompt above was compiled from the original drawing commands and is for reference only.