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Regular Tetrahedron by jgrzyw

Regular Tetrahedron by jgrzyw
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2016-10-28 16:37
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates a regular tetrahedron. Key mathematical concepts include polyhedra in solid geometry, vertices, edges, and faces. Using GeoGebra commands such as Invert, Element, Circle, etc., a geometric model of the regular tetrahedron can be constructed. Suitable for high school or university-level solid geometry studies.

GeoGebra Commands & Parameters

  1. Invert(T) → T'
  2. Element(Join[B1], 3) → E1
  3. Element(Join[B1], 2) → D1
  4. Element(Join[B1], 1) → C1
  5. Circle(C, D) → d
  6. Point(d) → F
  7. Angle(D, C, F) → β
  8. Circle(A, B) → c
  9. Point(c) → E
  10. Angle(B, A, E) → α
  11. Segment(A, B) → a
  12. Segment(A, E) → b
  13. Segment(C, D) → e
  14. Segment(C, F) → f
  15. Element(Join[B2], 1) → C2
  16. Element(Join[B2], 2) → D2
  17. Element(Join[B2], 3) → E2
  18. Element(Join[B3], 1) → C3
  19. Element(Join[B3], 2) → D3
  20. Element(Join[B3], 3) → E3
  21. Element(Join[B4], 1) → C4
  22. Element(Join[B4], 2) → D4
  23. Element(Join[B4], 3) → E4
  24. Element(Join[B5], 1) → C5
  25. Element(Join[B5], 2) → D5
  26. Element(Join[B5], 3) → E5
  27. If(m ≟ 0, G + C1 * u + D1 * v + E1 * w) → F1
  28. Segment(F4, F5) → g
  29. Segment(F5, F2) → h
  30. Segment(F2, F3) → i
  31. Segment(F3, F4) → j
  32. Segment(F4, F1) → k
  33. Segment(F1, F5) → l
  34. Segment(F1, F2) → n
  35. Segment(F1, F3) → p
  36. Element(Join[B6], 1) → C6
  37. Element(Join[B6], 2) → D6
  38. Element(Join[B6], 3) → E6
  39. If(m > 0, G + C6 * u + D6 * v + E6 * w) → F6
  40. Segment(F2, F6) → q
  41. Segment(F5, F6) → r
  42. Invert(M_1) → M'_1
  43. Invert(M_2) → M'_2
  44. Invert(M_3) → M'_3
  45. Element(Join[B7], 1) → C7
  46. Element(Join[B7], 2) → D7
  47. Element(Join[B7], 3) → E7
  48. If(m > 0, G + C7 * u + D7 * v + E7 * w) → F7
  49. Segment(F2, F7) → s
  50. Segment(F7, F6) → t
  51. Invert(N_3) → N'_3
  52. Element(Join[B8], 1) → C8
  53. Element(Join[B8], 2) → D8
  54. Element(Join[B8], 3) → E8
  55. If(m > 0, G + C8 * u + D8 * v + E8 * w) → F8
  56. Segment(F7, F8) → a_1
  57. Segment(F6, F8) → b_1
  58. Invert(O_3) → O'_3
  59. Element(Join[B9], 1) → C9
  60. Element(Join[B9], 2) → D9
  61. Element(Join[B9], 3) → E9
  62. If(m > 0, G + C9 * u + D9 * v + E9 * w) → F9
  63. Segment(F9, F5) → c_1
  64. Segment(F9, F6) → d_1
  65. Segment(F5, F3) → e_1
  66. Segment(F4, F2) → f_1
  67. Intersect(e_1, f_1) → H
  68. Segment(F1, H) → g_1

AI Drawing Prompt Reference

Draw a regular tetrahedron with four vertices A, B, C, and D, six edges AB, AC, AD, BC, BD, and CD, and four faces ABC, ABD, ACD, and BCD. Start by positioning the vertices, then connect them to form the edges and faces.
The prompt above was compiled from the original drawing commands and is for reference only.