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Truncated Cube Net (Archimedean Solid)

Truncated Cube Net (Archimedean Solid)
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2015-05-10 03:26
PolygonSolid GeometryTransformationGeometric Construction
① This example demonstrates the planar net of a truncated cube, an Archimedean solid, by unfolding its faces onto a two-dimensional plane to visualize its structure and surface area. ② Core mathematical concepts include solid geometry, polyhedra, regular polygon faces, vertex truncation, and the correspondence between a 3D shape and its net. ③ Construction details: using GeoGebra commands Polygon to draw faces, Midpoint to determine truncation points, and Rotate to rotate face pieces for unfolding; objects include multiple vertices (A1-A8, B1-B16, C1-C15) and faces, arranged through rotation and positioning to form the complete net. ④ Suitable for high school or early college solid geometry lessons, as well as for 3D printing or paper model design, helping students intuitively understand properties of Archimedean solids.

GeoGebra Commands & Parameters

  1. Polygon(D16, D12, D6, D2, D11, D15, D4, D8) → wielokąt1, d16, d12, d6, d2, d11, d15, d4, d8
  2. Midpoint(D4, D15) → A
  3. Midpoint(D12, D6) → B
  4. Rotate(Polygon[D4, D22, D15], β, Line[D4, D15]) → wielokąt2
  5. Rotate(Polygon[D11, D21, D2], β, Line[D11, D2]) → wielokąt3
  6. Rotate(Polygon[D6, D23, D12], β, Line[D6, D12]) → wielokąt4
  7. Rotate(Polygon[D16, D24, D8], β, Line[D16, D8]) → wielokąt5
  8. Rotate(Polygon[D12, D23, D19, D10, D14, D20, D24, D16], α, Line[D12, D16]) → wielokąt6
  9. Rotate(Polygon[D8, D24, D20, D7, D3, D18, D22, D4], α, Line[D8, D4]) → wielokąt7
  10. Rotate(Polygon[D2, D21, D17, D1, D5, D19, D23, D6], α, Line[D2, D6]) → wielokąt8
  11. Rotate(Polygon[D15, D22, D18, D13, D9, D17, D21, D11], α, Line[D15, D11]) → wielokąt9
  12. Rotate(Rotate[Polygon[D1, D17, D9], β, Line[D17, D1]], α, Line[D2, D6]) → wielokąt10
  13. Rotate(Rotate[Polygon[D3, D13, D18], β, Line[D18, D13]], α, Line[D15, D11]) → wielokąt11
  14. Rotate(Rotate[Polygon[D20, D14, D7], β, Line[D20, D7]], α, Line[D8, D4]) → wielokąt12
  15. Rotate(Rotate[Polygon[D10, D19, D5], β, Line[D19, D10]], α, Line[D12, D16]) → wielokąt13
  16. Rotate(Rotate[Polygon[D1, D9, D13, D3, D7, D14, D10, D5], α, Line[D10, D14]], α, Line[D12, D16]) → wielokąt14

AI Drawing Prompt Reference

Draw the net of a truncated cube, which consists of 8 squares and 6 equilateral triangles. First, draw 8 squares and 6 equilateral triangles as the faces of the truncated cube. Then, rotate these faces to unfold them into a 2D plane. Finally, arrange them so that all faces are closely connected to form the complete net of the truncated cube.
The prompt above was compiled from the original drawing commands and is for reference only.