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Hexagonal Prism Construction by CHAU CHUN SING

Hexagonal Prism Construction by CHAU CHUN SING
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2015-06-22 15:14
PolygonVectorSolid GeometryGeometric Construction
This example demonstrates the geometric construction of a hexagonal prism, involving core concepts in solid geometry, polygons, vectors, and transformations. Key GeoGebra commands used include Point, Circle, Intersect, Segment, OrthogonalLine, Prism, Vector, Dilate, and Distance to construct faces and edges. Suitable for high school geometry education, aiding in understanding polyhedra and surface area calculations.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(yAxis) → B
  3. Circle(A, B) → c
  4. Circle(B, C) → d
  5. Intersect(c, d, 1) → D
  6. Circle(D, B) → e
  7. Intersect(c, e, 2) → E
  8. Intersect(d, e, 2) → F
  9. Circle(E, D) → f
  10. Circle(F, D) → g
  11. Intersect(e, f, 2) → G
  12. Intersect(e, g, 1) → H
  13. Segment(A, B) → a
  14. Segment(B, F) → b
  15. Segment(F, H) → h
  16. Segment(H, G) → i
  17. Segment(G, E) → j
  18. Segment(E, A) → k
  19. OrthogonalLine(A, xOyPlane) → l
  20. Intersect(k, j) → I
  21. Point(l) → O
  22. Prism(A, B, F, H, G, E, O) → m, J, faceGHLM, faceEGMN, faceAENO, faceJKLMNO, edgeAB, edgeBF, edgeFH, edgeGH, edgeEG, edgeAE, K, edgeAO, edgeBJ, edgeFK, edgeHL, edgeGM, edgeEN, edgeJO, edgeJK, edgeKL, edgeLM, L, edgeMN, edgeNO, M, N, faceABFHGE, faceABJO, faceBFKJ, faceFHLK
  23. Vector(A, O) → u
  24. Vector(O, L) → v
  25. Dilate(B, 0.6666666666666666, J) → B'
  26. Dilate(F, 0.3333333333333333, K) → F'
  27. Vector(A, B') → w
  28. Vector(B', F') → n
  29. Vector(F', L) → p
  30. Distance(A, B') → distanceAB'
  31. Distance(B', F') → distanceB'F'
  32. Distance(F', L) → distanceF'L
  33. Distance(A, O) → distanceAO
  34. Distance(O, L) → distanceOL

AI Drawing Prompt Reference

Draw a hexagonal prism by first determining two points A and B on the coordinate axes, then drawing circles with these points as centers to find intersection points D, E, F, G, and H, which form the hexagon. Connect these points to form the hexagon's edges, then draw the base and sides of the hexagonal prism. Finally, use vectors from point A to O to scale and rotate the prism to adjust its size and position.
The prompt above was compiled from the original drawing commands and is for reference only.