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Cube Dissection Examples

Cube Dissection Examples
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2019-05-03 17:22
Solid GeometryTransformationGeometric Construction
This example demonstrates various ways to dissect a cube and explore its geometric properties. It involves core math concepts like solid geometry, symmetry, centroid, and midpoint calculations. GeoGebra commands used include Intersect, Polygon, Point, Midpoint, Segment, Circle, Line, Mirror, LineBisector, and Rotate. Suitable for high school students and math enthusiasts studying spatial geometry and geometric transformations.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  3. Point(xAxis) → E
  4. Polygon(E, F, 4) → poly2, j, k, l, m, G, H
  5. Midpoint(h) → I
  6. Midpoint(f) → J
  7. Midpoint(l) → K
  8. Midpoint(j) → L
  9. Segment(I, J) → n
  10. Segment(K, L) → p
  11. Point(n) → M
  12. Midpoint(I, J) → N
  13. Circle(M, 0.2) → c
  14. Intersect(c, n, 2) → O
  15. Line(M, h) → q
  16. Line(O, q) → r
  17. Point(q) → P
  18. Line(P, n) → s
  19. Intersect(r, s) → Q
  20. Mirror(P, N) → P'
  21. Mirror(Q, N) → Q'
  22. Mirror(O, N) → O'
  23. Mirror(M, N) → M'
  24. Polygon(D, I, J, A, M, P, Q, O, O', Q', P', M') → poly3, d, m', j_1, a, i_1, m_1, p_1, q_1, o, o', q', p'
  25. Polygon(C, I, J, B, M, P, Q, O, O', Q', P', M') → poly4, c_1, m'_1, j_2, b, i_2, m_2, p_2, q_2, o_1, o'_1, q'_1, p'_1
  26. Midpoint(m) → R
  27. Midpoint(k) → S
  28. Segment(R, S) → t
  29. Point(p) → T
  30. Point(p) → U
  31. LineBisector(T, U) → e
  32. Point(e) → V
  33. Intersect(t, p) → W
  34. Rotate(T, 90°, W) → T'
  35. Rotate(V, 90°, W) → V'
  36. Rotate(U, 90°, W) → U'
  37. Polygon(K, H, R, T', V', U', W, U, V, T) → poly5, k_1, t_1, h_1, r_1, t', v', u', w, u, v
  38. Rotate(K, 90°, W) → K'
  39. Rotate(H, 90°, W) → H'
  40. Rotate(R, 90°, W) → R'
  41. Rotate(T', 90°, W) → T''
  42. Rotate(V', 90°, W) → V''
  43. Rotate(U', 90°, W) → U''
  44. Rotate(W, 90°, W) → W'
  45. Rotate(U, 90°, W) → U'_1
  46. Rotate(V, 90°, W) → V'_1
  47. Rotate(T, 90°, W) → T'_1
  48. Polygon(K', H', R', T'', V'', U'', W', U'_1, V'_1, T'_1) → poly5', k', t'_1, h', r', t'', v'', u'', w', u'_1, v'_1
  49. Rotate(K', 90°, W) → K''
  50. Rotate(H', 90°, W) → H''
  51. Rotate(R', 90°, W) → R''
  52. Rotate(T'', 90°, W) → T'''
  53. Rotate(V'', 90°, W) → V'''
  54. Rotate(U'', 90°, W) → U'''
  55. Rotate(W', 90°, W) → W''
  56. Rotate(U'_1, 90°, W) → Z
  57. Rotate(V'_1, 90°, W) → A_1
  58. Rotate(T'_1, 90°, W) → B_1
  59. Polygon(K'', H'', R'', T''', V''', U''', W'', Z, A_1, B_1) → poly5'', k'', b_1, h'', r'', t''', v''', u''', w'', z_1, a_1
  60. Rotate(K'', 90°, W) → K'''
  61. Rotate(H'', 90°, W) → H'''
  62. Rotate(R'', 90°, W) → R'''
  63. Rotate(T''', 90°, W) → C_1
  64. Rotate(V''', 90°, W) → D_1
  65. Rotate(U''', 90°, W) → E_1
  66. Rotate(W'', 90°, W) → W'''
  67. Rotate(Z, 90°, W) → Z'
  68. Rotate(A_1, 90°, W) → F_1
  69. Rotate(B_1, 90°, W) → G_1
  70. Polygon(K''', H''', R''', C_1, D_1, E_1, W''', Z', F_1, G_1) → poly5''', k''', g_1, h''', r''', c_2, d_1, e_1, w''', z', f_1

AI Drawing Prompt Reference

Draw a cube and demonstrate various ways to dissect it, start by sketching three visible faces of the cube, find the centroids and midpoints of each face, connect the centroids of opposite faces to form diagonals, draw circles on the diagonals to locate intersection points, then perform mirror and rotation operations based on these points, finally create multiple symmetrical geometric shapes to show the cube's symmetry and geometric transformation process.
The prompt above was compiled from the original drawing commands and is for reference only.