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Hexagonal Pyramid: Dynamic Construction and Rotation

Hexagonal Pyramid: Dynamic Construction and Rotation
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2020-12-07 17:51
PolygonSolid GeometryTransformationGeometric ConstructionSlider Animation
In collections P1 P2 立體圖形 / 3D Shapes
This GeoGebra example demonstrates a regular hexagonal pyramid (six-sided pyramid) in 3D, showing its base as a regular hexagon and an apex above the center, with interactive rotation for spatial exploration. Core mathematical concepts include solid geometry definitions of pyramids, properties of regular polygon bases, lateral edges, and rotational symmetry. The construction uses commands such as Polygon to create the hexagonal base, Pyramid to generate the solid, Rotate for axis rotation, and Line/If for dynamic control, with sliders (TextSlider1-6) adjusting parameters. Objects like ShapeBase, Shape, and face1 enable interactive manipulation. This is suitable for high school or early college students learning solid geometry, enhancing spatial visualization, and for teachers demonstrating 3D shapes dynamically.

GeoGebra Commands & Parameters

  1. Line((0, 1, 0), (0, 0, 0)) → RotateAxis
  2. If(ShowChi, "依據立體底的形狀命名", "Naming by the base of the shape") → TextShowName2
  3. If(ShowChi, "立體高度", "Height") → TextSlider1
  4. If(ShowChi, "立體大小", "Size") → TextSlider2
  5. If(ShowChi, "立體位置(高低)", "Vertical Position") → TextSlider3
  6. If(ShowChi, "立體位置(橫向)", "Horizontal Position") → TextSlider4
  7. If(ShowChi, "施轉立體", "Rotate the shape") → TextSlider5
  8. If(ShowChi, "透明度", "Transparency") → TextSlider6
  9. Polygon(ShapePt1, ShapePt2, ShapePt3, ShapePt4, ShapePt5, ShapePt6) → ShapeBase, shapept1, shapept2, shapept3, shapept4, shapept5, shapept6
  10. Rotate(ShapeBase, S5, ShapePtAxis, RotateAxis) → ShapeBaseR
  11. If(ShowChi, "六角錐體", "Hexagonal Pyramid") → TextName2
  12. Pyramid(ShapeBaseR, (S1 * S2)) → Shape, A, edge3, edge4, edge5, edge6, face1, face3, face4, face5, face6, face2, edge1, edge2
  13. If(ShowChi, "角錐", "Pyramid") → TextName1

AI Drawing Prompt Reference

Draw a hexagonal pyramid with a regular hexagon as its base. Use a slider to adjust the height, size, position, and transparency of the pyramid, and rotate it to view from different angles.
The prompt above was compiled from the original drawing commands and is for reference only.