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Nets of Tetrahedron

Nets of Tetrahedron
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2014-10-12 14:40
PolygonAngleSolid GeometryGeometric Construction
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This example demonstrates the net of a tetrahedron and its fundamental properties. Key math concepts include solid geometry, polygons, and angle calculations. The construction utilizes GeoGebra commands and objects such as Tetrahedron, OrthogonalPlane, IntersectPath, Intersect, Angle, Rotate, OrthogonalLine, Polygon, and Segment. It is suitable for high school students learning solid geometry or for educational demonstrations.

GeoGebra Commands & Parameters

  1. Tetrahedron(A, B, xOyPlane) → a, C, edgeAD_1, edgeCD, edgeBD_1, D, faceABC, faceACD, faceABD, faceBCD, edgeAC, edgeAB, edgeBC
  2. Tetrahedron(D, B, xOyPlane) → c, E, edgeDF, edgeEF, edgeBF, F, faceBDE, faceDEF, faceBDF, faceBEF, edgeDE, edgeBD_2, edgeBE
  3. OrthogonalPlane(D, edgeAB) → d
  4. IntersectPath(d, xOyPlane) → e
  5. IntersectPath(d, faceABD) → f
  6. Intersect(d, faceABD) → I, J
  7. Angle(f, e) → α
  8. Rotate(faceABD, (t * α), edgeAB) → faceABD'
  9. OrthogonalLine(D, xOyPlane) → g
  10. Rotate(faceABD', 120°, g) → faceABD''
  11. Rotate(faceABD'', 120°, g) → faceABD'''
  12. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  13. Rotate(D, (t * α), edgeAB) → D'
  14. Rotate(A, (t * α), edgeAB) → A'
  15. Segment(D', A') → h
  16. Rotate(Rotate[faceACD, (t * α), edgeAB], (-((t * α))), h) → faceACD''
  17. Rotate(Segment[Rotate[C, (t * α), edgeAB], Rotate[D, (t * α), edgeAB]], (-((t * α))), h) → i
  18. Rotate(Rotate[Rotate[faceBCD, (t * α), edgeAB], (-((t * α))), h], (t * α), i) → poly2
  19. Rotate(Rotate[Rotate[C, (t * α), edgeAB], (-((t * α))), h], (t * α), i) → K
  20. Rotate(Rotate[Rotate[B, (t * α), edgeAB], (-((t * α))), h], (t * α), i) → L
  21. Segment(K, A) → j
  22. Segment(K, D') → k
  23. Segment(D', L) → l
  24. Segment(L, K) → m
  25. Segment(D', B) → n
  26. Rotate(D', 120°, g) → D''
  27. Rotate(D', (-(120°)), g) → D''_1
  28. Segment(D', B) → p
  29. Segment(B, D'') → q
  30. Segment(D'', C) → r
  31. Segment(C, D''_1) → s
  32. Segment(D''_1, A) → d_1
  33. Segment(A', D') → e_1