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Pyramid in a Cube

Pyramid in a Cube
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2020-05-28 17:46
PolygonCoordinate GeometrySolid Geometry
This example demonstrates a pyramid within a cube. It involves basic concepts of solid geometry, such as polyhedra and spatial figures. Using GeoGebra commands like Polygon, Segment, and PointIn, the pyramid's faces and vertices can be constructed. Suitable for middle and high school students learning solid geometry.

GeoGebra Commands & Parameters

  1. OrthogonalLine(I, xAxis) → l_1
  2. OrthogonalLine(I, l_1) → m_1
  3. Point(m_1) → K
  4. Point(l_1) → P
  5. Sequence(Mat * Element[cube, k], k, 1, 8) → cube'
  6. Element(Element[AE, 3], 1) → droite
  7. Sequence((Element[cube', k, 1, 1], Element[cube', k, 2, 1]), k, 1, 8) → listepoints
  8. Point(listepoints) → A
  9. Point(listepoints) → E
  10. Point(listepoints) → C_1
  11. Point(listepoints) → D
  12. Polygon(A, E, C_1, D) → poly1, a_1, b, c_1, d
  13. Point(listepoints) → B
  14. Point(listepoints) → F
  15. Point(listepoints) → G
  16. Point(listepoints) → H
  17. Polygon(B, F, G, H) → poly2, e, f, g, h
  18. Point(listepoints) → C
  19. Polygon(F, C, A, B) → poly3, f_1, i, a_2, b_1
  20. Element(AB, 3, 1) → avant
  21. Polygon(C_1, G, H, E) → poly4, c_2, g_1, h_1, e_1
  22. Element(AC, 3, 1) → dessus
  23. Polygon(F, C, C_1, G) → poly5, f_2, c_3, c_4, g_2
  24. Polygon(A, B, H, E) → poly6, a_3, b_2, h_2, e_2
  25. Segment(E, A) → c
  26. Segment(A, C) → j
  27. Segment(A, B) → k
  28. Segment(C, C_1) → l
  29. Segment(C_1, E) → m
  30. Segment(H, E) → n
  31. Segment(A, B) → p
  32. Segment(B, H) → q
  33. Segment(H, E) → r
  34. Segment(H, G) → s
  35. Segment(B, F) → t
  36. Segment(G, C_1) → d_1
  37. Segment(F, G) → i_1
  38. Segment(F, C) → j_1
  39. PointIn(poly5) → J
  40. Segment(J, E) → k_1
  41. Polygon(J, E, H) → poly7, h_3, j_2, e_3
  42. Polygon(J, H, B) → poly8, b_3, j_3, h_4
  43. Polygon(J, E, A) → poly9, a_4, j_4, e_4
  44. Polygon(J, A, B) → poly10, b_4, j_5, a_5
  45. Angle(Line[A, E], Line[A, J]) → ang1
  46. Angle(Line[E, H], Line[E, J]) → ang2
  47. Angle(Line[H, B], Line[H, J]) → ang3
  48. Angle(Line[B, A], Line[B, J]) → ang4
  49. Polygon(A, B, H, E) → poly11, a_6, b_5, h_5, e_5
  50. Angle(Line[B, H], Line[B, A]) → ang5

AI Drawing Prompt Reference

Draw a cube and construct a pyramid inside it. Start by defining the cube's eight vertices and connecting edges to form its six faces. Choose an interior point on one side face of the cube as the apex of the pyramid. Connect this apex to the four vertices of that face to create the pyramid's four triangular side faces. Also draw auxiliary segments on other faces to clearly show the spatial relationship between the pyramid and the cube. Finally, mark the angles between the apex and the edges of the base to illustrate the angular relationships in solid geometry.
The prompt above was compiled from the original drawing commands and is for reference only.