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Pentagonal Prism: Dynamic Construction and Exploration

Pentagonal Prism: Dynamic Construction and Exploration
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2020-12-07 17:30
PolygonSolid GeometryTransformationGeometric ConstructionSlider Animation
In collections P1 P2 立體圖形 / 3D Shapes
① This example demonstrates a dynamically adjustable pentagonal prism (regular pentagonal prism) in 3D, with sliders controlling height and base rotation to visualize geometric properties. ② Core math concepts include solid geometry definitions of prisms, relationships between base and lateral faces, rotational symmetry, and observing volume/shape changes with parameters. ③ Construction highlights: uses GeoGebra commands Polygon to create the pentagonal base, Rotate to rotate the base around an axis, Prism to generate the solid, Line and If for auxiliary lines and conditional display, multiple sliders (TextSlider1-6) for parameter control, and text objects (TextShowChi, etc.) for labeling. ④ Suitable for high school or early college students, for teaching solid geometry, dynamic demonstration of prism properties, and as an introductory example of parametric 3D modeling.

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. If(ShowChi, "五角柱體", "Pentagonal Prism") → TextName2
  10. Polygon(ShapePt1, ShapePt2, ShapePt3, ShapePt4, ShapePt5) → ShapeBase, shapept1, shapept2, shapept3, shapept4, shapept5
  11. Rotate(ShapeBase, S5, ShapePtAxis, RotateAxis) → ShapeBaseR
  12. Prism(ShapeBaseR, (S1 * S2)) → Shape, A, face2, faceABCDE, edge1, edge2, edge3, edge4, edge5, edgeAB, edgeBC, edgeCD, B, edgeDE, edgeAE, C, D, E, face1, face3, face4, face5
  13. If(ShowChi, "角柱", "Prism") → TextName1

AI Drawing Prompt Reference

Draw a pentagonal prism with adjustable height and base rotation. First, create a regular pentagon as the base using the Polygon command, then rotate the base around an axis using the Rotate command. Generate the prism using the Prism command. Use multiple TextSlider controls to adjust the prism's height, size, position, and transparency, and display auxiliary lines and labels.
The prompt above was compiled from the original drawing commands and is for reference only.