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Net of Hexagonal Prism by Anthony OR 柯志明

Net of Hexagonal Prism by Anthony OR 柯志明
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2014-11-10 22:32
PolygonSolid Geometry
In collections 3D Geometry & Cross Sections Surface Area & Volume Surface Area & Volume Surface Area and Volume Nets of Solid Figures (Primary 6) Nets of 3D Figures 立體圖形的摺紙圖樣 Nets of Solids
This example demonstrates the net of a hexagonal prism, visually showing its surface composed of various polygonal faces. Core math concepts include polygons, solid geometry, volume calculation, and geometric transformations. Construction highlights involve GeoGebra commands like Polygon, Prism, Segment, Point, Rotate, and Mirror to build both the prism and its net. Suitable for high school students learning about the unfolding and reconstruction of solid geometric figures, as well as teaching volume calculations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 6, xOyPlane) → poly1, a, F, b, c, d, e, f, C, D, E
  2. Prism(poly1, A + (0, 0, 4)) → g, G, faceEFKJ, face2, face3, edge1, edgeBG, edgeCH, edgeDI, edgeEJ, edgeFK, edge2, H, edgeGH, edgeHI, edgeIJ, edgeJK, edge3, I, J, K, face1, faceBCHG, faceCDIH, faceDEJI
  3. Segment(M, M + (0, 0, 2)) → h
  4. Point(h) → N
  5. Rotate(Polygon[E, D, I, J], (90° * t), Segment[D, E]) → poly2
  6. Rotate(Polygon[G, H, I, J, K, L], (90° * t), Segment[I, J]) → poly3
  7. Rotate(poly3, (90° * t), Segment[D, E]) → poly3'
  8. Rotate(Polygon[C, D, I, H], (60° * t), Segment[D, I]) → poly4
  9. Rotate(poly4, (90° * t), Segment[D, E]) → poly4'
  10. Mirror(poly4, OrthogonalPlane[Midpoint[D, E], Segment[D, E]]) → poly4'_1
  11. Rotate(poly4'_1, (90° * t), Segment[D, E]) → poly5
  12. Rotate(C, (60° * t), Segment[D, I]) → C'
  13. Mirror(Polygon[D, E, J, I], OrthogonalPlane[Midpoint[D, C'], Segment[D, C']]) → poly6
  14. Mirror(poly6, OrthogonalPlane[Midpoint[D, E], Segment[D, E]]) → poly6'
  15. Rotate(poly6, (90° * t), Segment[D, E]) → poly6'_1
  16. Rotate(poly6', (90° * t), Segment[D, E]) → poly6''
  17. Mirror(E, OrthogonalPlane[Midpoint[D, C'], Segment[D, C']]) → E'
  18. Mirror(poly4, OrthogonalPlane[Midpoint[E', C'], Segment[E', C']]) → poly4'_2
  19. Rotate(poly4'_2, (90° * t), Segment[D, E]) → poly7
  20. Rotate(poly3, (90° * t), Segment[D, E]) → poly3'_1
  21. Polygon(A, B, 6, xOyPlane) → poly8, i, R, j, k, l, m, n, O, P, Q
  22. Rotate(poly6', (90° * t), Segment[D, E]) → poly6''_1
  23. Rotate(poly4'_1, (90° * t), Segment[D, E]) → poly9
  24. Rotate(Polygon[E, D, I, J], (90° * t), Segment[D, E]) → poly10
  25. Rotate(poly4, (90° * t), Segment[D, E]) → poly4'_3
  26. Rotate(poly6, (90° * t), Segment[D, E]) → poly6'_2
  27. Rotate(poly4'_2, (90° * t), Segment[D, E]) → poly11

AI Drawing Prompt Reference

Draw the net of a hexagonal prism, showing its base and lateral faces. The base is a regular hexagon, and the lateral faces are six rectangles. Start by drawing the base hexagon, then extend six rectangular faces upward to connect it with an upper hexagonal base. The upper base is parallel to the lower one. Unfold the lateral faces to lay them flat on a plane, forming the net. Pay attention to the connections and proportions between the parts.
The prompt above was compiled from the original drawing commands and is for reference only.