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Tetrahedron and CubeOctahedron

Tetrahedron and CubeOctahedron
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2013-02-06 23:02
Solid GeometryTransformationGeometric Construction
This example demonstrates the construction of a tetrahedron and a cubeoctahedron. Key mathematical concepts include solid geometry and geometric construction. Using GeoGebra commands such as Circle, Point, Angle, Segment, Line, etc., the properties of these geometric bodies can be visually understood. Suitable for high school students and teachers.

GeoGebra Commands & Parameters

  1. Circle(N_9, N_8) → c
  2. Point(c) → Наклон
  3. Angle(N_8, N_9, Наклон) → α
  4. Circle(P_9, P_8) → d
  5. Point(d) → Поворот
  6. Angle(P_8, P_9, Поворот) → β
  7. Segment(N_9, N_8) → a_3
  8. Segment(N_9, Наклон) → b_3
  9. Segment(P_9, P_8) → e
  10. Segment(P_9, Поворот) → f
  11. Segment(F, T) → h_2
  12. Line(U, h_2) → i_2
  13. Point(i_2) → V
  14. Segment(U, V) → j_2
  15. Distance(C_1, D_1) → расстояниеC1D1
  16. Distance(F_1, G_1) → расстояниеF1G1
  17. Midpoint(B_1, N_1) → O
  18. Midpoint(N_1, L_1) → J_1
  19. Midpoint(L_1, K_1) → Q_1
  20. Midpoint(K_1, B_1) → R_1
  21. Midpoint(B_1, P_1) → S_1
  22. Midpoint(P_1, O_1) → T_1
  23. Midpoint(O_1, N_1) → U_1
  24. Segment(V_1, W_1) → e_3
  25. Segment(Z_1, A_2) → f_3
  26. Segment(C_2, B_2) → g_3
  27. Midpoint(R_1, Q_1) → D_2
  28. Midpoint(O_1, B_1) → G_2
  29. Midpoint(O_1, L_1) → I_2
  30. Midpoint(P_1, K_1) → N_2
  31. Midpoint(K_1, N_1) → P_2
  32. Midpoint(N_1, P_1) → R_2
  33. If(Angle[M_2, K_2, L_2] > 180°, Polygon[M_2, K_2, L_2]) → многоугольник3
  34. RotateText("\copyright uStas\;\;Strelets", 90*°) → надпись5
  35. If(Angle[F_2, J_2, H_2] > 180°, Polygon[J_2, H_2, F_2]) → многоугольник4
  36. Segment(H_1, E_1) → d_3
  37. Segment(Q_2, O_2) → p_4
  38. Segment(T_2, S_2) → n_4
  39. Conic(S_1, T_1, U_1, J_1, Q_1) → q_4
  40. Midpoint(M_2, L_2) → U_2
  41. Midpoint(K_2, M_2) → V_2
  42. Dilate(U_2, 1.3333333333333333, K_2) → A_3
  43. Dilate(V_2, 1.3333333333333333, L_2) → B_3
  44. Conic(B_3, M_2, A_3, L_2, K_2) → r_4
  45. Dilate(A_3, -1, O) → W_2
  46. Dilate(B_3, -1, O) → Z_2
  47. Conic(H_2, W_2, F_2, J_2, Z_2) → s_4
  48. If(Angle[J_1, Q_1, L_2] < 180°, Polygon[Q_1, L_2, J_1]) → многоугольник1
  49. If(Angle[J_2, J_1, U_1] < 180°, Polygon[J_1, U_1, J_2]) → многоугольник2
  50. If(Angle[H_2, R_1, Q_1] < 180°, Polygon[R_1, Q_1, H_2]) → многоугольник5
  51. If(Angle[F_2, T_1, S_1] < 180°, Polygon[T_1, S_1, F_2]) → многоугольник6
  52. If(Angle[K_2, S_1, R_1] > 180°, Polygon[S_1, K_2, R_1]) → многоугольник7
  53. If(Angle[M_2, U_1, T_1] > 180°, Polygon[U_1, M_2, T_1]) → многоугольник8
  54. If(Angle[S_1, T_1, M_2] < 180°, Polygon[T_1, M_2, K_2, S_1]) → многоугольник9
  55. If(Angle[Q_1, R_1, K_2] < 180°, Polygon[K_2, L_2, Q_1, R_1]) → многоугольник10
  56. If(Angle[U_1, J_1, L_2] < 180°, Polygon[L_2, M_2, U_1, J_1]) → многоугольник11
  57. If(Angle[H_2, F_2, S_1] < 180°, Polygon[S_1, R_1, H_2, F_2]) → многоугольник12
  58. If(Angle[J_2, H_2, Q_1] < 180°, Polygon[Q_1, J_1, J_2, H_2]) → многоугольник13
  59. If(Angle[F_2, J_2, U_1] < 180°, Polygon[U_1, T_1, F_2, J_2]) → многоугольник14
  60. Segment(M_2, K_2) → i
  61. Segment(L_2, K_2) → j
  62. Segment(M_2, L_2) → k
  63. Segment(K_2, R_1) → l
  64. Segment(R_1, Q_1) → m
  65. Segment(L_2, Q_1) → n
  66. Segment(R_1, H_2) → p_2
  67. Segment(Q_1, H_2) → q_2
  68. Segment(Q_1, J_1) → r
  69. Segment(L_2, J_1) → s
  70. Segment(J_1, J_2) → t
  71. Segment(J_2, H_2) → a_1
  72. Segment(J_2, U_1) → b_1
  73. Segment(U_1, J_1) → c_1
  74. Segment(M_2, U_1) → d_1
  75. Segment(M_2, T_1) → e_1
  76. Segment(T_1, U_1) → f_1
  77. Segment(T_1, F_2) → g_1
  78. Segment(F_2, J_2) → h_1
  79. Segment(T_1, S_1) → i_1
  80. Segment(K_2, S_1) → j_1
  81. Segment(S_1, R_1) → k_1
  82. Segment(S_1, F_2) → l_1
  83. Segment(H_2, F_2) → m_1
  84. Distance(M_2, K_2) → расстояниеM2K2
  85. Distance(M_2, T_1) → расстояниеM2T1
  86. Distance(F_2, S_1) → расстояниеF2S1
  87. Distance(S_1, R_1) → расстояниеS1R1
  88. Circle(O, B) → p_1
  89. Отрезок3D(C_1, G_1, F_1, D_1) → b, n_1
  90. Отрезок3D(C_1, F_1, D_1, G_1) → q_1, r_1
  91. Отрезок3D(C_1, D_1, G_1, F_1) → s_1, t_1
  92. Отрезок3D(F_1, G_1, D_1, C_1) → a_2, b_2
  93. Отрезок3D(D_1, F_1, G_1, C_1) → c_2, d_2
  94. Отрезок3D(G_1, D_1, F_1, C_1) → e_2, f_2

AI Drawing Prompt Reference

Draw a tetrahedron and a cubeoctahedron. Start by drawing a circle with points N9 and N8 as centers, select point Naklon, and construct angle α. Then draw a circle with points P9 and P8 as centers, select point Povorot, and construct angle β. Next, draw line segments N9N8, N9Naklon, P9P8, and P9Povorot. Draw line segment F to T, line segment U to h2, and select point V. Draw line segment UV. Finally, construct the lengths of C1D1 and F1G1, find the midpoints of B1N1, N1L1, L1K1, K1B1, B1P1, P1O1, and O1N1, and construct polygons 1, 3, 4, and 5.
The prompt above was compiled from the original drawing commands and is for reference only.