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Two Polyhedra

Two Polyhedra
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2013-07-06 21:50
PolygonSolid GeometryGeometric Construction
This GeoGebra example demonstrates the construction of two polyhedra. It covers key concepts in polyhedra, pyramids, and solid geometry. Using commands like If, Corner, and Polygon, users can dynamically explore the structure of polyhedra. Suitable for high school or university solid geometry courses.

GeoGebra Commands & Parameters

  1. If(Angle[A4, B4, B1] < 180°, Polygon[A4, B4, B1, A1]) → многоугольник15
  2. If((Angle[A2, B2, B3] < 180°) ∧ (Angle[D2, E2, E3] < 180°), Polygon[A2, B2, B3, A3]) → многоугольник2
  3. If((Angle[A4, B4, B1] < 180°) ∧ (Angle[D4, E4, E1] < 180°), Polygon[A4, B4, B1, A1]) → многоугольник4
  4. If((Angle[A1, B1, B2] < 180°) ∧ (Angle[D1, E1, E2] < 180°), Polygon[A1, B1, B2, A2]) → многоугольник1
  5. If((Angle[A3, B3, B4] < 180°) ∧ (Angle[D3, E3, E4] < 180°), Polygon[A3, B3, B4, A4]) → многоугольник3
  6. If(Angle[B4, B3, C3] < 180°, Polygon[F3, B3, B4, F4]) → многоугольник7
  7. If(Angle[B2, B1, C1] < 180°, Polygon[F1, B1, B2, F2]) → многоугольник5
  8. If(Angle[B3, B2, C2] < 180°, Polygon[F2, B2, B3, F3]) → многоугольник6
  9. If(Angle[B1, B4, C4] < 180°, Polygon[F4, B4, B1, F1]) → многоугольник8
  10. If(Angle[D2, E2, E3] < 180°, Polygon[D2, E2, E3, D3]) → многоугольник10
  11. If(Angle[D3, E3, E4] < 180°, Polygon[D3, E3, E4, D4]) → многоугольник11
  12. If(Angle[D4, E4, E1] < 180°, Polygon[D4, E4, E1, D1]) → многоугольник12
  13. If(Angle[D1, E1, E2] < 180°, Polygon[D1, E1, E2, D2]) → многоугольник13
  14. If(Angle[E1, E4, E3] < 180°, Polygon[E1, E2, E3, E4]) → многоугольник14
  15. If(Angle[D1, D2, D3] < 180°, Polygon[D1, D2, D3, D4]) → многоугольник16
  16. If(Angle[A2, B2, B3] < 180°, Polygon[A2, B2, B3, A3]) → многоугольник17
  17. If(Angle[A3, B3, B4] < 180°, Polygon[A3, B3, B4, A4]) → многоугольник18
  18. If(Angle[A1, B1, B2] < 180°, Polygon[A1, B1, B2, A2]) → многоугольник19
  19. If((Angle[A1, F1, F4] < 180°) ∧ (Angle[D4, E4, E1] < 180°), Polygon[A4, F4, F1, A1]) → многоугольник9
  20. If((Angle[A2, F2, F1] < 180°) ∧ (Angle[E2, D2, D1] < 180°), Polygon[A2, F2, F1, A1]) → многоугольник20
  21. If((Angle[A3, F3, F2] < 180°) ∧ (Angle[E3, D3, D2] < 180°), Polygon[A3, F3, F2, A2]) → многоугольник21
  22. If((Angle[A4, F4, F3] < 180°) ∧ (Angle[E4, D4, D3] < 180°), Polygon[A4, F4, F3, A3]) → многоугольник22
  23. If(Angle[F1, F4, A4] < 180°, Polygon[F1, F4, A4, A1]) → многоугольник23
  24. If(Angle[F4, F3, A3] < 180°, Polygon[F4, F3, A3, A4]) → многоугольник24
  25. If(Angle[F3, F2, A2] < 180°, Polygon[F3, F2, A2, A3]) → многоугольник25
  26. If(Angle[F2, F1, A1] < 180°, Polygon[F2, F1, A1, A2]) → многоугольник26
  27. Corner(1) → A
  28. Corner(2) → B
  29. Corner(3) → C
  30. Corner(4) → D
  31. Polygon(A, B, C, D) → многоугольник27, a_1, b_1, c_1, d
  32. Polygon(A, B, C, D) → многоугольник28, a_2, b_2, c_2, d_1

AI Drawing Prompt Reference

Draw two tetrahedra, each with four triangular faces. Start by drawing a tetrahedron with base ABCD, then draw another tetrahedron whose base is connected to the vertices of the first tetrahedron, forming two tetrahedra sharing a common base. Ensure each face is convex and use angle conditions to determine the existence of each face.
The prompt above was compiled from the original drawing commands and is for reference only.