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A Cube Removed From Another Cube

A Cube Removed From Another Cube
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2016-05-02 19:09
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the process of removing one cube from another. It involves the concept of intersection in solid geometry. Using GeoGebra commands such as Polygon, Midpoint, Segment, Vector, and Point, the intersection of two cubes can be constructed. Suitable for students at the junior high school level and above.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 6) → poly1, a, F, b, c, d, e, f, C, D, E
  2. Midpoint(D, A) → G
  3. Segment(D, G) → g
  4. Segment(B, G) → h
  5. Segment(G, F) → i
  6. Vector(G, D) → u
  7. Point(u) → H
  8. Segment(G, H) → j
  9. Circle(G, H) → k
  10. Intersect(k, i) → I,
  11. Intersect(k, h) → J,
  12. Segment(E, G) → l
  13. Segment(G, A) → m
  14. Segment(G, C) → p
  15. Intersect(k, l) → K,
  16. Intersect(k, m) → L,
  17. Intersect(k, p) → M,
  18. Segment(K, H) → q
  19. Segment(K, I) → r
  20. Segment(I, L) → s
  21. Segment(L, J) → t
  22. Segment(J, M) → a_1
  23. Segment(M, H) → b_1
  24. Segment(F, I) → c_1
  25. Segment(K, G) → d_1
  26. Segment(G, L) → e_1
  27. Segment(J, B) → f_1
  28. Segment(G, M) → g_1
  29. Segment(D, H) → h_1
  30. Polygon(B, C, D, H, M, J) → poly2, b_2, c_2, d_2, h_2, m_1, j_1
  31. Polygon(I, K, G, L) → poly3, i_1, k_1, g_2, l_1
  32. Polygon(H, K, I, F, E, D) → poly4, h_3, k_2, i_2, f_2, e_2, d_3
  33. Polygon(L, G, M, J) → poly5, l_2, g_3, m_2, j_2
  34. Polygon(F, I, L, J, B, A) → poly6, f_3, i_3, l_3, j_3, b_3, a_2
  35. Polygon(G, M, H, K) → poly8, g_5, m_4, h_5, k_4
  36. Ray(O, N) → n_1