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Duality of Interesting Solids

Duality of Interesting Solids
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2019-05-19 18:12
Solid GeometryGeometric ConstructionGraphing
This example demonstrates the duality relationships between various geometric solids like cubes and spheres. It involves core math concepts including solid geometry, linear regression, quadratic equations, and tangent lines. Construction highlights the use of commands such as Polygon, Sphere, Intersect, and Distance in GeoGebra. Suitable for high school students and math enthusiasts exploring spatial geometry and algebraic connections.

GeoGebra Commands & Parameters

  1. Polygon(V0, V6, V22, V30, V18) → A1, v0, v6, v22, v30, v18
  2. Polygon(V0, V18, V16, V34, V8) → A2, f, g, v16, v34, v8
  3. Polygon(V0, V8, V24, V36, V20) → A3, h, i, v24, v36, v20
  4. Polygon(V0, V20, V14, V32, V6) → A4, j, k, v14, v32, l
  5. Polygon(V1, V7, V23, V33, V19) → A5, v1, v7, v23, v33, v19
  6. Polygon(V1, V19, V17, V37, V9) → A6, m, n, v17, v37, v9
  7. Polygon(V1, V9, V25, V35, V21) → A7, p, q, v25, v35, v21
  8. Polygon(V1, V21, V15, V31, V7) → A8, r, s, v15, v31, a
  9. Polygon(V2, V10, V27, V33, V23) → A9, v2, v10, v27, b, c
  10. Polygon(V2, V23, V7, V31, V11) → A10, d, e, f_1, g_1, v11
  11. Polygon(V2, V11, V26, V30, V22) → A11, h_1, i_1, v26, j_1, k_1
  12. Polygon(V2, V22, V6, V32, V10) → A12, l_1, m_1, n_1, p_1, q_1
  13. Polygon(V3, V12, V29, V35, V25) → A13, v3, v12, v29, r_1, s_1
  14. Polygon(V3, V25, V9, V37, V13) → A14, t_1, a_1, b_1, c_1, v13
  15. Polygon(V3, V13, V28, V36, V24) → A15, d_1, e_1, v28, f_2, g_2
  16. Polygon(V3, V24, V8, V34, V12) → A16, h_2, i_2, j_2, k_2, l_2
  17. Polygon(V4, V15, V21, V35, V29) → A17, v4, m_2, n_2, p_2, q_2
  18. Polygon(V4, V29, V12, V34, V16) → A18, r_2, s_2, t_2, a_2, b_2
  19. Polygon(V4, V16, V18, V30, V26) → A19, c_2, d_2, e_2, f_3, g_3
  20. Polygon(V4, V26, V11, V31, V15) → A20, h_3, i_3, j_3, k_3, l_3
  21. Polygon(V5, V14, V20, V36, V28) → A21, v5, m_3, n_3, p_3, q_3
  22. Polygon(V5, V28, V13, V37, V17) → A22, r_3, s_3, t_3, a_3, b_3
  23. Polygon(V5, V17, V19, V33, V27) → A23, c_3, d_3, e_3, f_4, g_4
  24. Polygon(V5, V27, V10, V32, V14) → A24, h_4, i_4, j_4, k_4, l_4
  25. Polygon(W2, W12, W0, W14) → B0, m_4, w12, n_4, w14
  26. Polygon(W3, W13, W1, W15) → B1, w3, w13, p_4, w15
  27. Polygon(W4, W16, W5, W17) → B2, w4, w16, w5, w17
  28. Polygon(W7, W19, W6, W18) → B3, w7, w19, w6, w18
  29. Polygon(W8, W21, W11, W22) → B4, w8, w21, w11, w22
  30. Polygon(W9, W20, W10, W23) → B5, w9, w20, w10, w23
  31. Polygon(W0, W8, W14) → B6, q_4, r_4, s_4
  32. Polygon(W1, W9, W15) → B7, t_4, a_4, b_4
  33. Polygon(W2, W10, W12) → B8, c_4, d_4, e_4
  34. Polygon(W3, W11, W13) → B9, f_5, g_5, h_5
  35. Polygon(W4, W0, W16) → B10, i_5, j_5, k_5
  36. Polygon(W5, W1, W17) → B11, l_5, m_5, n_5
  37. Polygon(W6, W2, W18) → B12, p_5, q_5, r_5
  38. Polygon(W7, W3, W19) → B13, s_5, t_5, a_5
  39. Polygon(W8, W4, W21) → B14, b_5, c_5, d_5
  40. Polygon(W9, W5, W20) → B15, e_5, f_6, g_6
  41. Polygon(W10, W6, W23) → B16, h_6, i_6, j_6
  42. Polygon(W11, W7, W22) → B17, k_6, l_6, m_6
  43. Polygon(W13, W17, W1) → B19, r_6, s_6, t_6
  44. Polygon(W14, W18, W2) → B20, a_6, b_6, c_6
  45. Polygon(W15, W19, W3) → B21, d_6, e_6, f_7
  46. Polygon(W16, W20, W5) → B22, g_7, h_7, i_7
  47. Polygon(W17, W21, W4) → B23, j_7, k_7, l_7
  48. Polygon(W18, W22, W7) → B24, m_7, n_7, p_7
  49. Polygon(W19, W23, W6) → B25, q_7, r_7, s_7
  50. Polygon(W20, W12, W10) → B26, t_7, a_7, b_7
  51. Polygon(W22, W14, W8) → B28, c_7, d_7, e_7
  52. Polygon(W23, W15, W9) → B29, f_8, g_8, h_8
  53. Polygon(W8, W0, W4) → B30, i_8, j_8, k_8
  54. Polygon(W9, W1, W5) → B31, l_8, m_8, n_8
  55. Polygon(W10, W2, W6) → B32, p_8, q_8, r_8
  56. Polygon(W11, W3, W7) → B33, s_8, t_8, a_8
  57. Polygon(W12, W20, W16) → B34, b_8, c_8, d_8
  58. Polygon(W13, W21, W17) → B35, e_8, f_9, g_9
  59. Polygon(W14, W22, W18) → B36, h_9, i_9, j_9
  60. Polygon(W15, W23, W19) → B37, k_9, l_9, m_9
  61. Polygon(W12, W16, W0) → B18, n_6, p_6, q_6
  62. Sphere(O, r1e) → Kg1e
  63. Sphere(O, r1i) → Kg1i
  64. Sphere(O, r2c) → Kg2c
  65. Sphere(O, r2m) → Kg2m
  66. Polygon(W21, W13, W11) → B27, n_9, p_9, q_9
  67. Intersect(f, s_4) → S001
  68. Intersect(d_7, d_2) → S002
  69. Intersect(i_8, e_2) → S003
  70. Distance(V0, O) → r1c
  71. Sphere(O, r2sq) → Kg2sq
  72. Sphere(O, r2t) → Kg2t
  73. Intersect(h_9, a_2) → S004
  74. Intersect(j_9, j_2) → S005
  75. Intersect(h, c_6) → S006