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Net of Triangular Prism by Ogechi

Net of Triangular Prism by Ogechi
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2018-10-25 17:25
PolygonSolid GeometryTransformationGeometric ConstructionSlider Animation
① This example demonstrates the net of a triangular prism, showing how a 3D solid can be unfolded into a 2D plane through rotation and folding. ② Core mathematical concepts include solid geometry of prisms, unfolding of faces and edges, spatial rotation and projection, and composition of polygonal faces. ③ Construction highlights: using GeoGebra commands such as Segment, Point, Polygon, Prism to build the prism, Centroid for centroid calculation, Rotate and Line for rotating faces, involving objects like vertices A, B, C, D, E, F, faces faceABED, faceBCFE, faceACFD, faceDEF, and edges edgeAD, edgeBE, etc., with copies like faceACFD' and faceDEF' for the unfolded state. ④ Suitable for middle school geometry teaching, helping students intuitively understand the unfolding and folding of solids, enhancing spatial visualization, and useful for dynamic demonstrations or math experiments.

GeoGebra Commands & Parameters

  1. Segment(I, I + (0, 0, 2)) → g
  2. Point(g) → K
  3. Polygon(A, B, C) → t1, c, a, b
  4. Prism(t1, 4) → d, D, edgeCF, edgeDE, edgeEF, edgeDF, E, F, faceABED, faceBCFE, faceACFD, faceDEF, edgeAD, edgeBE
  5. Polygon(B, C, F, E) → q2, b_2, c_1, f_1, e_1
  6. Centroid(t1) → G
  7. Centroid(faceDEF) → H
  8. Rotate(q2, (120° * k), Segment[B, E]) → q'2
  9. Line(G, H) → f
  10. Rotate(t1, (90° * k), Segment[A, B]) → t1'
  11. Rotate(faceACFD, (120° * k), Segment[D, A]) → faceACFD'
  12. Rotate(faceDEF, (90° * k), Segment[E, D]) → faceDEF'
  13. Polygon(A, B, E, D) → q1, a_1, b_1, e, d_1
  14. Rotate(B, (120° * k), Segment[B, E]) → B'
  15. Rotate(C, (120° * k), Segment[B, E]) → C'
  16. Segment(B', C') → a'
  17. Rotate(C, (120° * k), Segment[B, E]) → C'_1
  18. Rotate(F, (120° * k), Segment[B, E]) → F'
  19. Segment(C'_1, F') → edgeCF'
  20. Rotate(F, (120° * k), Segment[B, E]) → F'_1
  21. Rotate(E, (120° * k), Segment[B, E]) → E'
  22. Segment(F'_1, E') → edgeEF'
  23. Rotate(B, (90° * k), Segment[A, B]) → B'_1
  24. Rotate(C, (90° * k), Segment[A, B]) → C'_2
  25. Segment(B'_1, C'_2) → a'_1
  26. Rotate(C, (90° * k), Segment[A, B]) → C'_3
  27. Rotate(A, (90° * k), Segment[A, B]) → A'
  28. Segment(C'_3, A') → b'
  29. Rotate(C, (120° * k), Segment[D, A]) → C'_4
  30. Rotate(A, (120° * k), Segment[D, A]) → A'_1
  31. Segment(C'_4, A'_1) → b'_1
  32. Rotate(C, (120° * k), Segment[D, A]) → C'_5
  33. Rotate(F, (120° * k), Segment[D, A]) → F'_2
  34. Segment(C'_5, F'_2) → edgeCF'_1
  35. Rotate(D, (120° * k), Segment[D, A]) → D'
  36. Rotate(F, (120° * k), Segment[D, A]) → F'_3
  37. Segment(D', F'_3) → edgeDF'
  38. Segment(A, D) → h