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Nets of a Tetrahedron by Dr. Dunphy

Nets of a Tetrahedron by Dr. Dunphy
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2018-04-09 21:52
PolygonAngleSolid GeometryGeometric Construction
This example demonstrates the net of a tetrahedron and its fundamental properties. It involves core mathematical concepts such as solid geometry, polygons, angles, and transformations. The construction utilizes GeoGebra commands and objects like Tetrahedron, OrthogonalPlane, IntersectPath, Intersect, Angle, Rotate, OrthogonalLine, Polygon, and Segment. It is suitable for high school students and teachers studying solid geometry, aiding in understanding the unfolding and reconstruction of polyhedra.

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) → , 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