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CubeOctahedron and Prism

CubeOctahedron and Prism
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2013-07-19 03:10
Solid GeometryTransformationGeometric Construction
This example demonstrates the geometric construction and relationship between a cube and an octahedral prism. It involves core math concepts like solid geometry, rotation symmetry, volume calculation, and geometric distribution. The construction uses GeoGebra commands such as Midpoint, If, and Polygon. Suitable for high school and above students to learn 3D shape construction and spatial reasoning.

GeoGebra Commands & Parameters

  1. Midpoint(A3, A4) → D3
  2. Midpoint(R_1, A4) → B4
  3. Midpoint(R_1, A3) → B3
  4. Midpoint(A2, A3) → D2
  5. Midpoint(R_1, A2) → B2
  6. Midpoint(A2, A1) → D1
  7. Midpoint(R_1, A1) → B1
  8. Midpoint(A4, S_1) → C4
  9. Midpoint(A1, S_1) → C1
  10. Midpoint(A2, S_1) → C2
  11. Midpoint(A3, S_1) → C3
  12. Midpoint(A4, A1) → D4
  13. If((Angle[D1, B1, B2] < 180°) ∧ (Angle[E1, F1, F2] < 180°), Polygon[D1, B1, B2]) → многоугольник5
  14. If((Angle[D2, B2, B3] < 180°) ∧ (Angle[E2, F2, F3] < 180°), Polygon[D2, B2, B3]) → многоугольник6
  15. If((Angle[D3, B3, B4] < 180°) ∧ (Angle[E3, F3, F4] < 180°), Polygon[D3, B3, B4]) → многоугольник7
  16. If((Angle[D4, B4, B1] < 180°) ∧ (Angle[E4, F4, F1] < 180°), Polygon[D4, B4, B1]) → многоугольник8
  17. If((Angle[D1, C2, C1] < 180°) ∧ (Angle[F2, E2, E1] < 180°), Polygon[D1, C2, C1]) → многоугольник9
  18. If((Angle[D2, C3, C2] < 180°) ∧ (Angle[F3, E3, E2] < 180°), Polygon[D2, C3, C2]) → многоугольник10
  19. If((Angle[D3, C4, C3] < 180°) ∧ (Angle[F4, E4, E3] < 180°), Polygon[D3, C4, C3]) → многоугольник11
  20. If((Angle[D4, C1, C4] < 180°) ∧ (Angle[F1, E1, E4] < 180°), Polygon[D4, C1, C4]) → многоугольник12
  21. If(Angle[E1, F1, F2] < 180°, Polygon[E1, F1, F2, E2]) → многоугольник17
  22. If(Angle[E2, F2, F3] < 180°, Polygon[E2, F2, F3, E3]) → многоугольник18
  23. If(Angle[E3, F3, F4] < 180°, Polygon[E3, F3, F4, E4]) → многоугольник19
  24. If(Angle[E4, F4, F1] < 180°, Polygon[E4, F4, F1, E1]) → многоугольник20
  25. If(Angle[F1, F4, F3] < 180°, Polygon[F1, F4, F3, F2]) → многоугольник21
  26. If(Angle[E3, E4, E1] < 180°, Polygon[E3, E4, E1, E2]) → многоугольник22
  27. If((Angle[D1, B2, B1] < 180°) ∧ (Angle[F2, E2, E1] < 180°), Polygon[D1, B2, B1]) → многоугольник1
  28. If((Angle[D2, B3, B2] < 180°) ∧ (Angle[F3, E3, E2] < 180°), Polygon[D2, B3, B2]) → многоугольник2
  29. If((Angle[D3, B4, B3] < 180°) ∧ (Angle[F4, E4, E3] < 180°), Polygon[D3, B4, B3]) → многоугольник3
  30. If((Angle[D4, B1, B4] < 180°) ∧ (Angle[F1, E1, E4] < 180°), Polygon[D4, B1, B4]) → многоугольник4
  31. If(Angle[C2, D1, C1] < 180°, Polygon[C2, D1, C1]) → многоугольник13
  32. If(Angle[C3, D2, C2] < 180°, Polygon[C3, D2, C2]) → многоугольник14
  33. If(Angle[C4, D3, C3] < 180°, Polygon[C4, D3, C3]) → многоугольник15
  34. If(Angle[C1, D4, C4] < 180°, Polygon[C1, D4, C4]) → многоугольник16
  35. If(Angle[B1, B2, D1] < 180°, Polygon[B1, B2, D1]) → многоугольник23
  36. If(Angle[B2, B3, D2] < 180°, Polygon[B2, B3, D2]) → многоугольник24
  37. If(Angle[B3, B4, D3] < 180°, Polygon[B3, B4, D3]) → многоугольник25
  38. If(Angle[B4, B1, D4] < 180°, Polygon[B4, B1, D4]) → многоугольник26
  39. If(Angle[C2, C1, D1] < 180°, Polygon[C2, C1, D1]) → многоугольник27
  40. If(Angle[C3, C2, D2] < 180°, Polygon[C3, C2, D2]) → многоугольник28
  41. If(Angle[C4, C3, D3] < 180°, Polygon[C4, C3, D3]) → многоугольник29
  42. If(Angle[C1, C4, D4] < 180°, Polygon[C1, C4, D4]) → многоугольник30
  43. If(Angle[B3, B2, D2] < 180°, Polygon[B3, B2, D2]) → многоугольник32
  44. If(Angle[B4, B3, D3] < 180°, Polygon[B4, B3, D3]) → многоугольник33
  45. If(Angle[B1, B4, D4] < 180°, Polygon[B1, B4, D4]) → многоугольник34
  46. If((Angle[D3, C3, C4] < 180°) ∧ (Angle[E3, F3, F4] < 180°), Polygon[D3, C3, C4]) → многоугольник35
  47. If((Angle[D2, C2, C3] < 180°) ∧ (Angle[E2, F2, F3] < 180°), Polygon[D2, C2, C3]) → многоугольник36
  48. If((Angle[D1, C1, C2] < 180°) ∧ (Angle[E1, F1, F2] < 180°), Polygon[D1, C1, C2]) → многоугольник37
  49. If((Angle[D4, C4, C1] < 180°) ∧ (Angle[E4, F4, F1] < 180°), Polygon[D4, C4, C1]) → многоугольник38
  50. If(Angle[B2, B1, D1] < 180°, Polygon[B1, B2, D1]) → многоугольник39
  51. Polygon(Corner[1], Corner[2], Corner[3], Corner[4]) → многоугольник31, f, g, h_1, i

AI Drawing Prompt Reference

Draw a combination of a cube and an octahedral prism to demonstrate their geometric relationship and symmetry. Start by constructing the vertices and edges of the cube, then find the midpoints of each edge and vertex to form the base for the octahedral prism. Connect these midpoints to create the triangular faces of the octahedral prism, ensuring they connect seamlessly to the cube's top and bottom faces. Finally, use polygon tools to complete the sides and bases of both shapes, highlighting their integration and spatial symmetry.
The prompt above was compiled from the original drawing commands and is for reference only.