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A Quarter of a Cube

A Quarter of a Cube
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2019-01-17 10:49
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates how a cube can be divided into four parts. It involves basic concepts in solid geometry, such as points, lines, and planes, and their relationships. Using GeoGebra commands like Point, Polygon, Segment, etc., the division process of the cube can be visually understood. Suitable for middle school and above students to learn solid geometry.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  4. Polygon(E, F, 4) → poly2, j, k, l, m, G, H
  5. Segment(H, F) → n
  6. Segment(E, G) → p
  7. Midpoint(i) → I
  8. Midpoint(m) → J
  9. Midpoint(l) → K
  10. Midpoint(k) → L
  11. Midpoint(j) → M
  12. Midpoint(n) → N
  13. Midpoint(h) → O
  14. Midpoint(g) → P
  15. Centroid(poly1) → Q
  16. Centroid(poly1) → R
  17. Midpoint(f) → S
  18. Polygon(D, I, J, E, N, H, K, O) → poly3, d, i_1, j_1, e, n_1, h_1, k_1, o
  19. Polygon(O, K, H, N, G, L, P, C) → poly4, o_1, k_2, h_2, n_2, g_1, l_1, p_1, c
  20. Polygon(L, G, N, F, M, S, B, P) → poly5, l_2, g_2, n_3, f_1, m_1, s, b, p_2
  21. Polygon(I, A, S, M, F, N, E, J) → poly6, i_2, a, s_1, m_2, f_2, n_4, e_1, j_2
  22. Circle(N, r) → q
  23. Intersect(q, h_2) → T,
  24. Intersect(q, g_2) → U,
  25. Vector(N, T) → u
  26. Vector(N, U) → v
  27. Translate(O, v) → O'
  28. Translate(K, v) → K'
  29. Translate(H, v) → H'
  30. Translate(N, v) → N'
  31. Translate(G, v) → G'
  32. Translate(L, v) → L'
  33. Translate(P, v) → P'
  34. Translate(C, v) → C'
  35. Polygon(O', K', H', N', G', L', P', C') → poly4', o', k', h', n', g', l', p', c'
  36. Translate(D, u) → D'
  37. Translate(I, u) → I'
  38. Translate(J, u) → J'
  39. Translate(E, u) → E'
  40. Translate(N, u) → N'_1
  41. Translate(H, u) → H'_1
  42. Translate(K, u) → K'_1
  43. Translate(O, u) → O'_1
  44. Polygon(D', I', J', E', N'_1, H'_1, K'_1, O'_1) → poly3', d', i', j', e', n'_1, h'_1, k'_1, o'_1
  45. Translate(I, Vector[(-v)]) → I'_1
  46. Translate(A, Vector[(-v)]) → A'
  47. Translate(S, Vector[(-v)]) → S'
  48. Translate(M, Vector[(-v)]) → M'
  49. Translate(F, Vector[(-v)]) → F'
  50. Translate(N, Vector[(-v)]) → N'_2
  51. Translate(E, Vector[(-v)]) → E'_1
  52. Translate(J, Vector[(-v)]) → J'_1
  53. Polygon(I'_1, A', S', M', F', N'_2, E'_1, J'_1) → poly6', i'_1, a', s', m', f', n'_2, e'_1, j'_1
  54. Translate(L, Vector[(-u)]) → L'_1
  55. Translate(G, Vector[(-u)]) → G'_1
  56. Translate(N, Vector[(-u)]) → N'_3
  57. Translate(F, Vector[(-u)]) → F'_1
  58. Translate(M, Vector[(-u)]) → M'_1
  59. Translate(S, Vector[(-u)]) → S'_1
  60. Translate(B, Vector[(-u)]) → B'
  61. Translate(P, Vector[(-u)]) → P'_1
  62. Polygon(L'_1, G'_1, N'_3, F'_1, M'_1, S'_1, B', P'_1) → poly5', l'_1, g'_1, n'_3, f'_1, m'_1, s'_1, b', p'_1
  63. Prism(poly3', a_1) → b_1, F_1, face10, face11, face12, face13, face14, face15, face9, face16, edge12, edge13, G_1, edge14, edge15, edge16, edge17, edge18, edge19, edge20, edge22, edge23, edge24, H_1, edge25, edge26, edge27, edge21, I_1, J_1, K_1, L_1, M_1, face8
  64. Prism(poly4', q_1) → r_1, V_1, face28, face29, face30, face31, face32, face33, face27, face34, edge28, edge45, W_1, edge46, edge47, edge48, edge49, edge50, edge51, edge52, edge54, edge55, edge56, Z_1, edge57, edge58, edge59, edge53, A_2, B_2, C_2, D_2, E_2, face17
  65. Prism(poly6', d_1) → t_1, N_1, face21, face22, face23, face24, face25, face26, face20, face35, edge30, edge31, O_1, edge32, edge33, edge34, edge35, edge36, edge37, edge38, edge40, edge41, edge42, P_1, edge43, edge44, edge60, edge39, Q_1, R_1, S_1, T_1, U_1, face19
  66. Prism(poly5', u_1) → v_1, F_2, face39, face40, face41, face42, face43, face44, face38, face45, edge63, edge64, G_2, edge65, edge66, edge67, edge68, edge69, edge70, edge71, edge73, edge74, edge75, H_2, edge76, edge77, edge78, edge72, I_2, J_2, K_2, L_2, M_2, face37