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14 Types of Cube Section Figures

14 Types of Cube Section Figures
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2020-05-13 15:41
TrigonometrySolid GeometryGeometric Construction
This example demonstrates the 14 different types of section figures obtained by intersecting a cube with various planes; Core math concepts include solid geometry, cross-sections, polygons, and trigonometry; Construction highlights involve GeoGebra commands/objects like Point, Cube, Segment, Plane, IntersectPath, Midpoint, Line, Intersect, and Polygon; Suitable for high school and above students to learn and understand the properties of complex geometric body cross-sections, or for mathematical teaching demonstrations.

GeoGebra Commands & Parameters

  1. Point(Circle[B, Distance[A, B], Segment[A, B]]) → E
  2. Cube(A, B, E) → a, F, FlächeEFJI, FlächeGHIJ, KanteAF, KanteAB, KanteBE, KanteEF, KanteAG, KanteFJ, KanteGJ, KanteGH, G, KanteBH, KanteHI, KanteEI, KanteIJ, H, I, J, FlächeABEF, FlächeAFJG, FlächeABHG, FlächeBEIH
  3. Segment(H, I) → f
  4. Point(KanteGH) → D
  5. Point(KanteBH) → K
  6. Point(KanteHI) → L
  7. Plane(D, K, L) → d
  8. IntersectPath(d, a) → Vieleck1, M, N, O, g, h, i
  9. Midpoint(G, H) → P
  10. Midpoint(H, I) → Q
  11. Point(KanteBH) → R
  12. Plane(P, R, Q) → e
  13. IntersectPath(e, a) → Vieleck2, S, T, U, j, k, l
  14. Midpoint(G, H) → V
  15. Midpoint(H, I) → W
  16. Midpoint(H, B) → Z
  17. Plane(V, Z, W) → m
  18. IntersectPath(m, a) → Vieleck3, A_1, B_1, C_1, n, p, q
  19. Point(KanteBE) → F_1
  20. Plane(D_1, E_1, F_1) → o
  21. IntersectPath(o, a) → Vieleck4, G_1, H_1, I_1, J_1, r, s, t, f_1
  22. Point(KanteGH) → K_1
  23. Point(KanteHI) → L_1
  24. Plane(K_1, L_1, M_1) → u
  25. IntersectPath(u, a) → Vieleck5, N_1, O_1, P_1, Q_1, g_1, h_1, i_1, j_1
  26. Point(KanteBE) → R_1
  27. Plane(A, R_1, I) → v
  28. IntersectPath(v, a) → Vieleck6, S_1, T_1, U_1, V_1, k_1, l_1, m_1, n_1
  29. Point(KanteAG) → W_1
  30. Point(KanteBH) → Z_1
  31. Point(KanteEI) → A_2
  32. Plane(W_1, Z_1, A_2) → w
  33. IntersectPath(w, a) → Vieleck7, B_2, C_2, D_2, E_2, p_1, q_1, r_1, s_1
  34. Point(KanteGH) → F_2
  35. Line(F_2, KanteHI) → t_1
  36. Intersect(KanteIJ, t_1) → G_2
  37. Line(F_2, KanteBH) → a_1
  38. Intersect(a_1, KanteAB) → H_2
  39. Plane(F_2, H_2, G_2) → b_1
  40. IntersectPath(b_1, a) → Vieleck8, I_2, J_2, K_2, L_2, c_1, d_1, e_1, f_2
  41. Point(KanteAG) → M_2
  42. Point(KanteAB) → N_2
  43. Point(KanteEI) → O_2
  44. Plane(M_2, N_2, O_2) → o_1
  45. IntersectPath(o_1, a) → Vieleck9, P_2, j_2, k_2, l_2, Q_2, R_2, S_2, T_2, U_2, g_2, h_2, i_2
  46. Midpoint(KanteGJ) → V_2
  47. Midpoint(KanteAG) → W_2
  48. Midpoint(KanteAB) → Z_2
  49. Midpoint(KanteBE) → A_3
  50. Midpoint(KanteEI) → B_3
  51. Midpoint(KanteIJ) → C_3
  52. Plane(V_2, W_2, C_3) → u_1
  53. IntersectPath(u_1, a) → Vieleck10, D_3, q_2, r_2, s_2, E_3, F_3, G_3, H_3, I_3, m_2, n_2, p_2
  54. Point(KanteAG) → J_3
  55. Point(KanteAB) → K_3
  56. Point(KanteBE) → L_3
  57. Plane(J_3, K_3, L_3) → v_1
  58. IntersectPath(v_1, a) → Vieleck11, M_3, c_2, d_2, e_2, N_3, O_3, P_3, Q_3, R_3, t_2, a_2, b_2
  59. Point(KanteGH) → S_3
  60. Point(KanteHI) → T_3
  61. Point(KanteAB) → U_3
  62. Segment(S_3, T_3) → f_3
  63. Line(U_3, f_3) → g_3
  64. Intersect(KanteBE, g_3) → V_3
  65. Polygon(S_3, U_3, V_3, T_3) → v1, s_3, u_3, v_3, t_3
  66. Plane(S_3, U_3, T_3) → p_3

AI Drawing Prompt Reference

Draw a cube and intersect it with various planes to display 14 different types of section shapes, including triangles and quadrilaterals, label key points and section shapes, showcasing core concepts of solid geometry, cross-sections, polygons, and trigonometry.
The prompt above was compiled from the original drawing commands and is for reference only.