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Cutting a Tetrahedron into a Net

Cutting a Tetrahedron into a Net
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2025-03-19 18:26
In collections La fábrica de teselados
This example shows how to cut a regular tetrahedron along a plane and unfold it into a flat net using GeoGebra. It introduces the geometry of a tetrahedron, the creation of cutting lines, and the formation of a net. Construction highlights: Vector for translation vectors, Circle for auxiliary circles, Mirror for reflections, PointIn to pick interior points, Spline to draw smooth curves, Point to m

GeoGebra Commands & Parameters

  1. Vector(D, D') → u1
  2. Circle((0, 0), 7) → c
  3. Mirror(A, B) → A'
  4. PointIn(t1(1)) → A3
  5. Spline(L4, 3) → a4
  6. PointIn(t4(1)) → A2
  7. PointIn(t3(1)) → A1
  8. Point(Segment[B, D']) → C1
  9. Spline(L1, 3) → a1
  10. PointIn(t2(1)) → A4
  11. Spline(L3, 3) → a3
  12. Spline(L2, 3) → a2
  13. Mirror(a4, B) → a4'
  14. Mirror(a1, C) → a1'
  15. Mirror(a2, C) → a2'
  16. Translate(a3, u1) → a3'
  17. Sequence(Point[a1, s], s, 0, 1, 0.05) → po1
  18. Sequence(Point[a2, s], s, 0, 1, 0.05) → po2
  19. Sequence(Point[a4', s], s, 0, 1, 0.05) → po4
  20. Sequence(Point[a4, s], s, 0, 1, 0.05) → po5
  21. Sequence(Point[a3, s], s, 0, 1, 0.05) → po6
  22. Reverse(Sequence[Point[a3', s], s, 0, 1, 0.05]) → po3
  23. Sequence(Point[a2', s], s, 0, 1, 0.05) → po7
  24. Reverse(Sequence[Point[a1', s], s, 0, 1, 0.05]) → po8
  25. Join({po1, po2, po3, po4, po5, po6, po7, po8}) → po
  26. Polygon(po) → pol1
  27. Translate(pol1, Vector[((aa - 3) * u1)]) → pol1'
  28. Rotate(pol1, If[2 < aa < 3, (pi * (aa - 2)), pi], C) → pol2
  29. Corner(1, 1) → Export_1
  30. Corner(1, 3) → Export_2
  31. Sequence({random(), random(), random()}, k, 1, númeroListas) → listaAzar
  32. Angle(F, Midpoint[A, C], D) → ang
  33. Rotate(a3, ((1 - a) * ang), Midpoint[A, C], Segment[A, C]) → b3
  34. Rotate(t3, ((1 - a) * ang), Midpoint[B, C], Segment[C, B]) → t3a
  35. Rotate(D', ((1 - a) * ang), Midpoint[B, C], Segment[C, B]) → DD
  36. Rotate(t4, ((1 - a) * ang), Midpoint[B, C], Segment[C, B]) → t4a
  37. Rotate(t4a, ((1 - a) * ang), Midpoint[B, DD], Segment[DD, B]) → t4b
  38. Rotate(a2, ((1 - a) * ang), Midpoint[B, C], Segment[C, B]) → b2a
  39. Rotate(b2a, ((1 - a) * ang), Midpoint[B, DD], Segment[DD, B]) → b2b
  40. Translate(pol2, Vector[((aa - 3) * u1)]) → pol2'
  41. Mirror(t3, C) → t3'
  42. Mirror(t1, B) → t1'
  43. Mirror(t4b, C) → t4b'
  44. Rotate(t2, ((1 - a) * ang), Midpoint[A, C], Segment[A, C]) → t2a
  45. Rotate(a1, ((1 - a) * ang), Midpoint[B, C], Segment[C, B]) → b1