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球面模型-立方体与八面体

球面模型-立方体与八面体
几何画板及绘图内容加载中，请稍等……
2015-01-13 02:33
多边形立体几何不等式几何作图函数图像
①本范例演示了立方体与八面体在球面上的投影与关系；②涉及的核心数学概念包括立体几何、多边形、空间几何关系、不等式；③作图要点提炼自构造摘要，使用了Surface（曲面）、Segment（线段）、Circle（圆）等GeoGebra命令与对象；④适合高中及以上学生及数学爱好者用于理解空间几何体与球面关系，也可用于教学演示。

GeoGebra 命令及参数

  1. Surface(((4 + t) * cos(k)), ((4 + t) * sin(k)), 0, t, 0, 1, k, B1, B1 + π / 12) → C1
  2. Surface(((4 + t) * cos(k)), 0, ((4 + t) * sin(k)), t, 0, 1, k, B1, B1 + π / 12) → D1
  3. Surface(((4 + t) * cos(k)), ((4 + t) * sin(k)), 0, t, 0, 1, k, B2, B2 + π / 12) → C2
  4. Surface(((4 + t) * cos(k)), 0, ((4 + t) * sin(k)), t, 0, 1, k, B2, B2 + π / 12) → D2
  5. Surface(((4 + t) * cos(k)), ((4 + t) * sin(k)), 0, t, 0, 1, k, B3, B3 + π / 12) → C3
  6. Surface(((4 + t) * cos(k)), 0, ((4 + t) * sin(k)), t, 0, 1, k, B3, B3 + π / 12) → D3
  7. Surface(((4 + t) * cos(k)), ((4 + t) * sin(k)), 0, t, 0, 1, k, B4, B4 + π / 12) → C4
  8. Surface(((4 + t) * cos(k)), 0, ((4 + t) * sin(k)), t, 0, 1, k, B4, B4 + π / 12) → D4
  9. Surface(((4 + t) * cos(k)), ((4 + t) * sin(k)), 0, t, 0, 1, k, B5, B5 + π / 12) → C5
  10. Surface(((4 + t) * cos(k)), 0, ((4 + t) * sin(k)), t, 0, 1, k, B5, B5 + π / 12) → D5
  11. Surface(((4 + t) * cos(k)), ((4 + t) * sin(k)), 0, t, 0, 1, k, B6, B6 + π / 12) → C6
  12. Surface(((4 + t) * cos(k)), 0, ((4 + t) * sin(k)), t, 0, 1, k, B6, B6 + π / 12) → D6
  13. Surface(((4 + t) * cos(k)), ((4 + t) * sin(k)), 0, t, 0, 1, k, B7, B7 + π / 12) → C7
  14. Surface(((4 + t) * cos(k)), 0, ((4 + t) * sin(k)), t, 0, 1, k, B7, B7 + π / 12) → D7
  15. Surface(((4 + t) * cos(k)), ((4 + t) * sin(k)), 0, t, 0, 1, k, B8, B8 + π / 12) → C8
  16. Surface(((4 + t) * cos(k)), 0, ((4 + t) * sin(k)), t, 0, 1, k, B8, B8 + π / 12) → D8
  17. Surface(((4 + t) * cos(k)), ((4 + t) * sin(k)), 0, t, 0, 1, k, B9, B9 + π / 12) → C9
  18. Surface(((4 + t) * cos(k)), 0, ((4 + t) * sin(k)), t, 0, 1, k, B9, B9 + π / 12) → D9
  19. Surface(((4 + t) * cos(k)), ((4 + t) * sin(k)), 0, t, 0, 1, k, B10, B10 + π / 12) → C10
  20. Surface(((4 + t) * cos(k)), 0, ((4 + t) * sin(k)), t, 0, 1, k, B10, B10 + π / 12) → D10
  21. Surface(((4 + t) * cos(k)), ((4 + t) * sin(k)), 0, t, 0, 1, k, B11, B11 + π / 12) → C11
  22. Surface(((4 + t) * cos(k)), 0, ((4 + t) * sin(k)), t, 0, 1, k, B11, B11 + π / 12) → D11
  23. Surface(((4 + t) * cos(k)), ((4 + t) * sin(k)), 0, t, 0, 1, k, B12, B12 + π / 12) → C12
  24. Surface(((4 + t) * cos(k)), 0, ((4 + t) * sin(k)), t, 0, 1, k, B12, B12 + π / 12) → D12
  25. Surface(((4 + t) * cos(k)), ((4 + t) * sin(k)), 0, t, 0, 1, k, B13, B13 + π / 12) → C13
  26. Surface(((4 + t) * cos(k)), 0, ((4 + t) * sin(k)), t, 0, 1, k, B13, B13 + π / 12) → D13
  27. Surface(((4 + t) * cos(k)), ((4 + t) * sin(k)), 0, t, 0, 1, k, B14, B14 + π / 12) → C14
  28. Surface(((4 + t) * cos(k)), 0, ((4 + t) * sin(k)), t, 0, 1, k, B14, B14 + π / 12) → D14
  29. Surface(((4 + t) * cos(k)), ((4 + t) * sin(k)), 0, t, 0, 1, k, B15, B15 + π / 12) → C15
  30. Surface(((4 + t) * cos(k)), 0, ((4 + t) * sin(k)), t, 0, 1, k, B15, B15 + π / 12) → D15
  31. Surface(((4 + t) * cos(k)), ((4 + t) * sin(k)), 0, t, 0, 1, k, B16, B16 + π / 12) → C16
  32. Surface(((4 + t) * cos(k)), 0, ((4 + t) * sin(k)), t, 0, 1, k, B16, B16 + π / 12) → D16
  33. Surface(((4 + t) * cos(k)), ((4 + t) * sin(k)), 0, t, 0, 1, k, B17, B17 + π / 12) → C17
  34. Surface(((4 + t) * cos(k)), 0, ((4 + t) * sin(k)), t, 0, 1, k, B17, B17 + π / 12) → D17
  35. Surface(((4 + t) * cos(k)), ((4 + t) * sin(k)), 0, t, 0, 1, k, B18, B18 + π / 12) → C18
  36. Surface(((4 + t) * cos(k)), 0, ((4 + t) * sin(k)), t, 0, 1, k, B18, B18 + π / 12) → D18
  37. Surface(((4 + t) * cos(k)), ((4 + t) * sin(k)), 0, t, 0, 1, k, B19, B19 + π / 12) → C19
  38. Surface(((4 + t) * cos(k)), 0, ((4 + t) * sin(k)), t, 0, 1, k, B19, B19 + π / 12) → D19
  39. Surface(((4 + t) * cos(k)), ((4 + t) * sin(k)), 0, t, 0, 1, k, B20, B20 + π / 12) → C20
  40. Surface(((4 + t) * cos(k)), 0, ((4 + t) * sin(k)), t, 0, 1, k, B20, B20 + π / 12) → D20
  41. Surface(((4 + t) * cos(k)), ((4 + t) * sin(k)), 0, t, 0, 1, k, B21, B21 + π / 12) → C21
  42. Surface(((4 + t) * cos(k)), 0, ((4 + t) * sin(k)), t, 0, 1, k, B21, B21 + π / 12) → D21
  43. Surface(((4 + t) * cos(k)), ((4 + t) * sin(k)), 0, t, 0, 1, k, B22, B22 + π / 12) → C22
  44. Surface(((4 + t) * cos(k)), 0, ((4 + t) * sin(k)), t, 0, 1, k, B22, B22 + π / 12) → D22
  45. Surface(((4 + t) * cos(k)), ((4 + t) * sin(k)), 0, t, 0, 1, k, B23, B23 + π / 12) → C23
  46. Surface(((4 + t) * cos(k)), 0, ((4 + t) * sin(k)), t, 0, 1, k, B23, B23 + π / 12) → D23
  47. Surface(((4 + t) * cos(k)), ((4 + t) * sin(k)), 0, t, 0, 1, k, B24, B24 + π / 12) → C24
  48. Surface(((4 + t) * cos(k)), 0, ((4 + t) * sin(k)), t, 0, 1, k, B24, B24 + π / 12) → D24
  49. Surface(0, ((4 + t) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B1, B1 + π / 12) → E1
  50. Surface(0, ((4 + t) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B2, B2 + π / 12) → E2
  51. Surface(0, ((4 + t) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B3, B3 + π / 12) → E3
  52. Surface(0, ((4 + t) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B4, B4 + π / 12) → E4
  53. Surface(0, ((4 + t) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B5, B5 + π / 12) → E5
  54. Surface(0, ((4 + t) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B6, B6 + π / 12) → E6
  55. Surface(0, ((4 + t) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B7, B7 + π / 12) → E7
  56. Surface(0, ((4 + t) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B8, B8 + π / 12) → E8
  57. Surface(0, ((4 + t) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B9, B9 + π / 12) → E9
  58. Surface(0, ((4 + t) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B10, B10 + π / 12) → E10
  59. Surface(0, ((4 + t) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B11, B11 + π / 12) → E11
  60. Surface(0, ((4 + t) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B12, B12 + π / 12) → E12
  61. Surface(0, ((4 + t) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B13, B13 + π / 12) → E13
  62. Surface(0, ((4 + t) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B14, B14 + π / 12) → E14
  63. Surface(0, ((4 + t) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B15, B15 + π / 12) → E15
  64. Surface(0, ((4 + t) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B16, B16 + π / 12) → E16
  65. Surface(0, ((4 + t) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B17, B17 + π / 12) → E17
  66. Surface(0, ((4 + t) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B18, B18 + π / 12) → E18
  67. Surface(0, ((4 + t) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B19, B19 + π / 12) → E19
  68. Surface(0, ((4 + t) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B20, B20 + π / 12) → E20
  69. Surface(0, ((4 + t) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B21, B21 + π / 12) → E21
  70. Surface(0, ((4 + t) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B22, B22 + π / 12) → E22
  71. Surface(0, ((4 + t) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B23, B23 + π / 12) → E23
  72. Surface(0, ((4 + t) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B24, B24 + π / 12) → E24
  73. Surface(((a * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B1, B1 + π / 12) → F1
  74. Surface(((a * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B2, B2 + π / 12) → F2
  75. Surface(((a * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B3, B3 + π / 12) → F3
  76. Surface(((a * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B4, B4 + π / 12) → F4
  77. Surface(((a * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B5, B5 + π / 12) → F5
  78. Surface(((a * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B6, B6 + π / 12) → F6
  79. Surface(((a * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B7, B7 + π / 12) → F7
  80. Surface(((a * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B8, B8 + π / 12) → F8
  81. Surface(((a * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B9, B9 + π / 12) → F9
  82. Surface(((a * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B10, B10 + π / 12) → F10
  83. Surface(((a * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B11, B11 + π / 12) → F11
  84. Surface(((a * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B12, B12 + π / 12) → F12
  85. Surface(((a * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B13, B13 + π / 12) → F13
  86. Surface(((a * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B14, B14 + π / 12) → F14
  87. Surface(((a * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B15, B15 + π / 12) → F15
  88. Surface(((a * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B16, B16 + π / 12) → F16
  89. Surface(((a * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B17, B17 + π / 12) → F17
  90. Surface(((a * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B18, B18 + π / 12) → F18
  91. Surface(((a * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B19, B19 + π / 12) → F19
  92. Surface(((a * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B20, B20 + π / 12) → F20
  93. Surface(((a * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B21, B21 + π / 12) → F21
  94. Surface(((a * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B22, B22 + π / 12) → F22
  95. Surface(((a * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B23, B23 + π / 12) → F23
  96. Surface(((a * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B24, B24 + π / 12) → F24
  97. Surface((((-a) * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B1, B1 + π / 12) → G1
  98. Surface((((-a) * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B2, B2 + π / 12) → G2
  99. Surface((((-a) * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B3, B3 + π / 12) → G3
  100. Surface((((-a) * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B4, B4 + π / 12) → G4
  101. Surface((((-a) * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B5, B5 + π / 12) → G5
  102. Surface((((-a) * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B6, B6 + π / 12) → G6
  103. Surface((((-a) * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B7, B7 + π / 12) → G7
  104. Surface((((-a) * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B8, B8 + π / 12) → G8
  105. Surface((((-a) * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B9, B9 + π / 12) → G9
  106. Surface((((-a) * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B10, B10 + π / 12) → G10
  107. Surface((((-a) * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B11, B11 + π / 12) → G11
  108. Surface((((-a) * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B12, B12 + π / 12) → G12
  109. Surface((((-a) * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B13, B13 + π / 12) → G13
  110. Surface((((-a) * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B14, B14 + π / 12) → G14
  111. Surface((((-a) * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B15, B15 + π / 12) → G15
  112. Surface((((-a) * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B16, B16 + π / 12) → G16
  113. Surface((((-a) * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B17, B17 + π / 12) → G17
  114. Surface((((-a) * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B18, B18 + π / 12) → G18
  115. Surface((((-a) * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B19, B19 + π / 12) → G19
  116. Surface((((-a) * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B20, B20 + π / 12) → G20
  117. Surface((((-a) * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B21, B21 + π / 12) → G21
  118. Surface((((-a) * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B22, B22 + π / 12) → G22
  119. Surface((((-a) * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B23, B23 + π / 12) → G23
  120. Surface((((-a) * (4 + t)) * cos(k)), ((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), t, 0, 1, k, B24, B24 + π / 12) → G24
  121. Surface(((4 + t) * cos(k)), ((a * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B1, B1 + π / 12) → H1
  122. Surface(((4 + t) * cos(k)), ((a * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B2, B2 + π / 12) → H2
  123. Surface(((4 + t) * cos(k)), ((a * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B3, B3 + π / 12) → H3
  124. Surface(((4 + t) * cos(k)), ((a * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B4, B4 + π / 12) → H4
  125. Surface(((4 + t) * cos(k)), ((a * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B5, B5 + π / 12) → H5
  126. Surface(((4 + t) * cos(k)), ((a * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B6, B6 + π / 12) → H6
  127. Surface(((4 + t) * cos(k)), ((a * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B7, B7 + π / 12) → H7
  128. Surface(((4 + t) * cos(k)), ((a * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B8, B8 + π / 12) → H8
  129. Surface(((4 + t) * cos(k)), ((a * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B9, B9 + π / 12) → H9
  130. Surface(((4 + t) * cos(k)), ((a * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B10, B10 + π / 12) → H10
  131. Surface(((4 + t) * cos(k)), ((a * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B11, B11 + π / 12) → H11
  132. Surface(((4 + t) * cos(k)), ((a * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B12, B12 + π / 12) → H12
  133. Surface(((4 + t) * cos(k)), ((a * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B13, B13 + π / 12) → H13
  134. Surface(((4 + t) * cos(k)), ((a * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B14, B14 + π / 12) → H14
  135. Surface(((4 + t) * cos(k)), ((a * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B15, B15 + π / 12) → H15
  136. Surface(((4 + t) * cos(k)), ((a * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B16, B16 + π / 12) → H16
  137. Surface(((4 + t) * cos(k)), ((a * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B17, B17 + π / 12) → H17
  138. Surface(((4 + t) * cos(k)), ((a * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B18, B18 + π / 12) → H18
  139. Surface(((4 + t) * cos(k)), ((a * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B19, B19 + π / 12) → H19
  140. Surface(((4 + t) * cos(k)), ((a * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B20, B20 + π / 12) → H20
  141. Surface(((4 + t) * cos(k)), ((a * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B21, B21 + π / 12) → H21
  142. Surface(((4 + t) * cos(k)), ((a * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B22, B22 + π / 12) → H22
  143. Surface(((4 + t) * cos(k)), ((a * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B23, B23 + π / 12) → H23
  144. Surface(((4 + t) * cos(k)), ((a * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B24, B24 + π / 12) → H24
  145. Surface(((4 + t) * cos(k)), (((-a) * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B1, B1 + π / 12) → I1
  146. Surface(((4 + t) * cos(k)), (((-a) * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B2, B2 + π / 12) → I2
  147. Surface(((4 + t) * cos(k)), (((-a) * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B3, B3 + π / 12) → I3
  148. Surface(((4 + t) * cos(k)), (((-a) * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B4, B4 + π / 12) → I4
  149. Surface(((4 + t) * cos(k)), (((-a) * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B5, B5 + π / 12) → I5
  150. Surface(((4 + t) * cos(k)), (((-a) * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B6, B6 + π / 12) → I6
  151. Surface(((4 + t) * cos(k)), (((-a) * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B7, B7 + π / 12) → I7
  152. Surface(((4 + t) * cos(k)), (((-a) * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B8, B8 + π / 12) → I8
  153. Surface(((4 + t) * cos(k)), (((-a) * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B9, B9 + π / 12) → I9
  154. Surface(((4 + t) * cos(k)), (((-a) * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B10, B10 + π / 12) → I10
  155. Surface(((4 + t) * cos(k)), (((-a) * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B11, B11 + π / 12) → I11
  156. Surface(((4 + t) * cos(k)), (((-a) * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B12, B12 + π / 12) → I12
  157. Surface(((4 + t) * cos(k)), (((-a) * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B13, B13 + π / 12) → I13
  158. Surface(((4 + t) * cos(k)), (((-a) * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B14, B14 + π / 12) → I14
  159. Surface(((4 + t) * cos(k)), (((-a) * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B15, B15 + π / 12) → I15
  160. Surface(((4 + t) * cos(k)), (((-a) * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B16, B16 + π / 12) → I16
  161. Surface(((4 + t) * cos(k)), (((-a) * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B17, B17 + π / 12) → I17
  162. Surface(((4 + t) * cos(k)), (((-a) * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B18, B18 + π / 12) → I18
  163. Surface(((4 + t) * cos(k)), (((-a) * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B19, B19 + π / 12) → I19
  164. Surface(((4 + t) * cos(k)), (((-a) * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B20, B20 + π / 12) → I20
  165. Surface(((4 + t) * cos(k)), (((-a) * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B21, B21 + π / 12) → I21
  166. Surface(((4 + t) * cos(k)), (((-a) * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B22, B22 + π / 12) → I22
  167. Surface(((4 + t) * cos(k)), (((-a) * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B23, B23 + π / 12) → I23
  168. Surface(((4 + t) * cos(k)), (((-a) * (4 + t)) * sin(k)), ((a * (4 + t)) * sin(k)), t, 0, 1, k, B24, B24 + π / 12) → I24
  169. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), (((-a) * (4 + t)) * cos(k)), t, 0, 1, k, B1, B1 + π / 12) → J1
  170. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), (((-a) * (4 + t)) * cos(k)), t, 0, 1, k, B2, B2 + π / 12) → J2
  171. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), (((-a) * (4 + t)) * cos(k)), t, 0, 1, k, B3, B3 + π / 12) → J3
  172. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), (((-a) * (4 + t)) * cos(k)), t, 0, 1, k, B4, B4 + π / 12) → J4
  173. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), (((-a) * (4 + t)) * cos(k)), t, 0, 1, k, B5, B5 + π / 12) → J5
  174. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), (((-a) * (4 + t)) * cos(k)), t, 0, 1, k, B6, B6 + π / 12) → J6
  175. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), (((-a) * (4 + t)) * cos(k)), t, 0, 1, k, B7, B7 + π / 12) → J7
  176. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), (((-a) * (4 + t)) * cos(k)), t, 0, 1, k, B8, B8 + π / 12) → J8
  177. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), (((-a) * (4 + t)) * cos(k)), t, 0, 1, k, B9, B9 + π / 12) → J9
  178. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), (((-a) * (4 + t)) * cos(k)), t, 0, 1, k, B10, B10 + π / 12) → J10
  179. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), (((-a) * (4 + t)) * cos(k)), t, 0, 1, k, B11, B11 + π / 12) → J11
  180. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), (((-a) * (4 + t)) * cos(k)), t, 0, 1, k, B12, B12 + π / 12) → J12
  181. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), (((-a) * (4 + t)) * cos(k)), t, 0, 1, k, B13, B13 + π / 12) → J13
  182. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), (((-a) * (4 + t)) * cos(k)), t, 0, 1, k, B14, B14 + π / 12) → J14
  183. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), (((-a) * (4 + t)) * cos(k)), t, 0, 1, k, B15, B15 + π / 12) → J15
  184. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), (((-a) * (4 + t)) * cos(k)), t, 0, 1, k, B16, B16 + π / 12) → J16
  185. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), (((-a) * (4 + t)) * cos(k)), t, 0, 1, k, B17, B17 + π / 12) → J17
  186. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), (((-a) * (4 + t)) * cos(k)), t, 0, 1, k, B18, B18 + π / 12) → J18
  187. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), (((-a) * (4 + t)) * cos(k)), t, 0, 1, k, B19, B19 + π / 12) → J19
  188. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), (((-a) * (4 + t)) * cos(k)), t, 0, 1, k, B20, B20 + π / 12) → J20
  189. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), (((-a) * (4 + t)) * cos(k)), t, 0, 1, k, B21, B21 + π / 12) → J21
  190. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), (((-a) * (4 + t)) * cos(k)), t, 0, 1, k, B22, B22 + π / 12) → J22
  191. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), (((-a) * (4 + t)) * cos(k)), t, 0, 1, k, B23, B23 + π / 12) → J23
  192. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), (((-a) * (4 + t)) * cos(k)), t, 0, 1, k, B24, B24 + π / 12) → J24
  193. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), ((a * (4 + t)) * cos(k)), t, 0, 1, k, B1, B1 + π / 12) → K1
  194. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), ((a * (4 + t)) * cos(k)), t, 0, 1, k, B2, B2 + π / 12) → K2
  195. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), ((a * (4 + t)) * cos(k)), t, 0, 1, k, B3, B3 + π / 12) → K3
  196. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), ((a * (4 + t)) * cos(k)), t, 0, 1, k, B4, B4 + π / 12) → K4
  197. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), ((a * (4 + t)) * cos(k)), t, 0, 1, k, B5, B5 + π / 12) → K5
  198. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), ((a * (4 + t)) * cos(k)), t, 0, 1, k, B6, B6 + π / 12) → K6
  199. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), ((a * (4 + t)) * cos(k)), t, 0, 1, k, B7, B7 + π / 12) → K7
  200. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), ((a * (4 + t)) * cos(k)), t, 0, 1, k, B8, B8 + π / 12) → K8
  201. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), ((a * (4 + t)) * cos(k)), t, 0, 1, k, B9, B9 + π / 12) → K9
  202. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), ((a * (4 + t)) * cos(k)), t, 0, 1, k, B10, B10 + π / 12) → K10
  203. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), ((a * (4 + t)) * cos(k)), t, 0, 1, k, B11, B11 + π / 12) → K11
  204. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), ((a * (4 + t)) * cos(k)), t, 0, 1, k, B12, B12 + π / 12) → K12
  205. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), ((a * (4 + t)) * cos(k)), t, 0, 1, k, B13, B13 + π / 12) → K13
  206. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), ((a * (4 + t)) * cos(k)), t, 0, 1, k, B14, B14 + π / 12) → K14
  207. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), ((a * (4 + t)) * cos(k)), t, 0, 1, k, B15, B15 + π / 12) → K15
  208. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), ((a * (4 + t)) * cos(k)), t, 0, 1, k, B16, B16 + π / 12) → K16
  209. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), ((a * (4 + t)) * cos(k)), t, 0, 1, k, B17, B17 + π / 12) → K17
  210. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), ((a * (4 + t)) * cos(k)), t, 0, 1, k, B18, B18 + π / 12) → K18
  211. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), ((a * (4 + t)) * cos(k)), t, 0, 1, k, B19, B19 + π / 12) → K19
  212. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), ((a * (4 + t)) * cos(k)), t, 0, 1, k, B20, B20 + π / 12) → K20
  213. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), ((a * (4 + t)) * cos(k)), t, 0, 1, k, B21, B21 + π / 12) → K21
  214. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), ((a * (4 + t)) * cos(k)), t, 0, 1, k, B22, B22 + π / 12) → K22
  215. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), ((a * (4 + t)) * cos(k)), t, 0, 1, k, B23, B23 + π / 12) → K23
  216. Surface(((a * (4 + t)) * cos(k)), ((4 + t) * sin(k)), ((a * (4 + t)) * cos(k)), t, 0, 1, k, B24, B24 + π / 12) → K24
  217. Segment((0, 0, 0) + (4 * P1), (0, 0, 0) + (5 * P1)) → Q1
  218. Segment((0, 0, 0) + (4 * P2), (0, 0, 0) + (5 * P2)) → Q2
  219. Segment((0, 0, 0) + (4 * P3), (0, 0, 0) + (5 * P3)) → Q3
  220. Segment((0, 0, 0) + (4 * P4), (0, 0, 0) + (5 * P4)) → Q4
  221. Segment((0, 0, 0) + (4 * P5), (0, 0, 0) + (5 * P5)) → Q5
  222. Segment((0, 0, 0) + (4 * P6), (0, 0, 0) + (5 * P6)) → Q6
  223. Segment((0, 0, 0) + (4 * P7), (0, 0, 0) + (5 * P7)) → Q7
  224. Segment((0, 0, 0) + (4 * P8), (0, 0, 0) + (5 * P8)) → Q8
  225. Segment((0, 0, 0) + (4 * P9), (0, 0, 0) + (5 * P9)) → Q9
  226. Segment((0, 0, 0) + (4 * P10), (0, 0, 0) + (5 * P10)) → Q10
  227. Segment((0, 0, 0) + (4 * P11), (0, 0, 0) + (5 * P11)) → Q11
  228. Segment((0, 0, 0) + (4 * P12), (0, 0, 0) + (5 * P12)) → Q12
  229. Segment((0, 0, 0) + (4 * P13), (0, 0, 0) + (5 * P13)) → Q13
  230. Segment((0, 0, 0) + (4 * P14), (0, 0, 0) + (5 * P14)) → Q14
  231. Segment((0, 0, 0) + (4 * P15), (0, 0, 0) + (5 * P15)) → Q15
  232. Segment((0, 0, 0) + (4 * P16), (0, 0, 0) + (5 * P16)) → Q16
  233. Segment((0, 0, 0) + (4 * P17), (0, 0, 0) + (5 * P17)) → Q17
  234. Segment((0, 0, 0) + (4 * P18), (0, 0, 0) + (5 * P18)) → Q18
  235. Segment((0, 0, 0) + (4 * P19), (0, 0, 0) + (5 * P19)) → Q19
  236. Segment((0, 0, 0) + (4 * P20), (0, 0, 0) + (5 * P20)) → Q20
  237. Segment((0, 0, 0) + (4 * P21), (0, 0, 0) + (5 * P21)) → Q21
  238. Segment((0, 0, 0) + (4 * P22), (0, 0, 0) + (5 * P22)) → Q22
  239. Segment((0, 0, 0) + (4 * P23), (0, 0, 0) + (5 * P23)) → Q23
  240. Segment((0, 0, 0) + (4 * P24), (0, 0, 0) + (5 * P24)) → Q24
  241. Segment((0, 0, 0) + (4 * P25), (0, 0, 0) + (5 * P25)) → Q25
  242. Segment((0, 0, 0) + (4 * P26), (0, 0, 0) + (5 * P26)) → Q26
  243. Circle((0, 0, 0), 4, Line[(0, 0, 0), (1, 0, 0)]) → c
  244. Circle((0, 0, 0), 5, Line[(0, 0, 0), (1, 0, 0)]) → d
  245. Circle((0, 0, 0), 5, Line[(0, 0, 0), (1, 1, 0)]) → e
  246. Circle((0, 0, 0), 4, Line[(0, 0, 0), (1, 1, 0)]) → f
  247. Circle((0, 0, 0), 4, Line[(0, 0, 0), (0, 1, 0)]) → g
  248. Circle((0, 0, 0), 5, Line[(0, 0, 0), (0, 1, 0)]) → h
  249. Circle((0, 0, 0), 5, Line[(0, 0, 0), (-1, 1, 0)]) → k
  250. Circle((0, 0, 0), 4, Line[(0, 0, 0), (-1, 1, 0)]) → p
  251. Circle((0, 0, 0), 4, Line[(0, 0, 0), (0, 0, 1)]) → q
  252. Circle((0, 0, 0), 5, Line[(0, 0, 0), (0, 0, 1)]) → r
  253. Circle((0, 0, 0), 5, Line[(0, 0, 0), (0, 1, 1)]) → s
  254. Circle((0, 0, 0), 4, Line[(0, 0, 0), (0, 1, 1)]) → t
  255. Circle((0, 0, 0), 4, Line[(0, 0, 0), (0, -1, 1)]) → c_1
  256. Circle((0, 0, 0), 5, Line[(0, 0, 0), (0, -1, 1)]) → d_1
  257. Circle((0, 0, 0), 5, Line[(0, 0, 0), (1, 0, 1)]) → e_1
  258. Circle((0, 0, 0), 4, Line[(0, 0, 0), (1, 0, 1)]) → f_1
  259. Circle((0, 0, 0), 4, Line[(0, 0, 0), (-1, 0, 1)]) → g_1
  260. Circle((0, 0, 0), 5, Line[(0, 0, 0), (-1, 0, 1)]) → h_1

AI 绘图提示语参考

在球面上绘制一个立方体和一个八面体的投影，展示它们之间的关系。使用多个曲面来构建球体，并通过曲面和线段来描绘立方体和八面体的轮廓。注意立方体和八面体的顶点与球面的交点，以及它们在球面上的投影关系。先绘制球面，再逐步添加立方体和八面体的投影，最后调整视角以突出空间几何关系。
以上提示语为根据原始绘图命令整理而来，仅供参考。