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立方体展开图工作表

立方体展开图工作表
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2018-11-24 06:45
多边形立体几何几何作图
①本范例演示立方体的展开图及其折叠过程；②涉及的核心数学概念包括立体几何、多边形、空间想象能力；③作图要点：使用 GeoGebra 的 Point（点）和 Polygon（多边形）命令创建了立方体的顶点和面，通过对象 A, C, D, B, poly1 及其变种构建了完整的展开图模型；④适合初中及以上学生学习立体几何，或用于几何作图教学演示。

GeoGebra 命令及参数

  1. Point(Circle[A, 1]) → C
  2. Polygon(A, C, D, B) → poly1, a, c, d, b
  3. Point(Circle[A_1, 1]) → C_1
  4. Polygon(A_1, C_1, D_1, B_1) → poly1_1, a_1, c_1, d_1, b_1
  5. Point(Circle[A_2, 1]) → C_2
  6. Polygon(A_2, C_2, D_2, B_2) → poly1_2, a_2, c_2, d_2, b_2
  7. Point(Circle[A_3, 1]) → C_3
  8. Polygon(A_3, C_3, D_3, B_3) → poly1_3, a_3, c_3, d_3, b_3
  9. Point(Circle[A_4, 1]) → C_4
  10. Polygon(A_4, C_4, D_4, B_4) → poly1_4, a_4, c_4, d_4, b_4
  11. Point(Circle[A_5, 1]) → C_5
  12. Polygon(A_5, C_5, D_5, B_5) → poly1_5, a_5, c_5, d_5, b_5
  13. Point(Circle[A_6, 1]) → C_6
  14. Polygon(A_6, C_6, D_6, B_6) → poly1_6, a_6, c_6, d_6, b_6
  15. Point(Circle[A_7, 1]) → C_7
  16. Polygon(A_7, C_7, D_7, B_7) → poly1_7, a_7, c_7, d_7, b_7
  17. Point(Circle[A_8, 1]) → C_8
  18. Polygon(A_8, C_8, D_8, B_8) → poly1_8, a_8, c_8, d_8, b_8
  19. Point(Circle[A_9, 1]) → C_9
  20. Polygon(A_9, C_9, D_9, B_9) → poly1_9, a_9, c_9, d_9, b_9
  21. Point(Circle[A_{10}, 1]) → C_{10}
  22. Polygon(A_{10}, C_{10}, D_{10}, B_{10}) → poly1_{10}, a_{10}, c_{10}, d_{10}, b_{10}
  23. Point(Circle[A_{11}, 1]) → C_{11}
  24. Polygon(A_{11}, C_{11}, D_{11}, B_{11}) → poly1_{11}, a_{11}, c_{11}, d_{11}, b_{11}
  25. Point(Circle[A_{12}, 1]) → C_{12}
  26. Polygon(A_{12}, C_{12}, D_{12}, B_{12}) → poly1_{12}, a_{12}, c_{12}, d_{12}, b_{12}
  27. Point(Circle[A_{13}, 1]) → C_{13}
  28. Polygon(A_{13}, C_{13}, D_{13}, B_{13}) → poly1_{13}, a_{13}, c_{13}, d_{13}, b_{13}
  29. Point(Circle[A_{14}, 1]) → C_{14}
  30. Polygon(A_{14}, C_{14}, D_{14}, B_{14}) → poly1_{14}, a_{14}, c_{14}, d_{14}, b_{14}
  31. Point(Circle[A_{15}, 1]) → C_{15}
  32. Polygon(A_{15}, C_{15}, D_{15}, B_{15}) → poly1_{15}, a_{15}, c_{15}, d_{15}, b_{15}
  33. Point(Circle[A_{16}, 1]) → C_{16}
  34. Polygon(A_{16}, C_{16}, D_{16}, B_{16}) → poly1_{16}, a_{16}, c_{16}, d_{16}, b_{16}
  35. Point(Circle[A_{17}, 1]) → C_{17}
  36. Polygon(A_{17}, C_{17}, D_{17}, B_{17}) → poly1_{17}, a_{17}, c_{17}, d_{17}, b_{17}
  37. Point(Circle[A_{18}, 1]) → C_{18}
  38. Polygon(A_{18}, C_{18}, D_{18}, B_{18}) → poly1_{18}, a_{18}, c_{18}, d_{18}, b_{18}
  39. Point(Circle[A_{19}, 1]) → C_{19}
  40. Polygon(A_{19}, C_{19}, D_{19}, B_{19}) → poly1_{19}, a_{19}, c_{19}, d_{19}, b_{19}
  41. Point(Circle[A_{20}, 1]) → C_{20}
  42. Polygon(A_{20}, C_{20}, D_{20}, B_{20}) → poly1_{20}, a_{20}, c_{20}, d_{20}, b_{20}
  43. Point(Circle[A_{21}, 1]) → C_{21}
  44. Polygon(A_{21}, C_{21}, D_{21}, B_{21}) → poly1_{21}, a_{21}, c_{21}, d_{21}, b_{21}
  45. Point(Circle[A_{22}, 1]) → C_{22}
  46. Polygon(A_{22}, C_{22}, D_{22}, B_{22}) → poly1_{22}, a_{22}, c_{22}, d_{22}, b_{22}
  47. Point(Circle[A_{23}, 1]) → C_{23}
  48. Polygon(A_{23}, C_{23}, D_{23}, B_{23}) → poly1_{23}, a_{23}, c_{23}, d_{23}, b_{23}
  49. Point(Circle[A_{24}, 1]) → C_{24}
  50. Polygon(A_{24}, C_{24}, D_{24}, B_{24}) → poly1_{24}, a_{24}, c_{24}, d_{24}, b_{24}
  51. Point(Circle[A_{25}, 1]) → C_{25}
  52. Polygon(A_{25}, C_{25}, D_{25}, B_{25}) → poly1_{25}, a_{25}, c_{25}, d_{25}, b_{25}
  53. Point(Circle[A_{26}, 1]) → C_{26}
  54. Polygon(A_{26}, C_{26}, D_{26}, B_{26}) → poly1_{26}, a_{26}, c_{26}, d_{26}, b_{26}
  55. Point(Circle[A_{27}, 1]) → C_{27}
  56. Polygon(A_{27}, C_{27}, D_{27}, B_{27}) → poly1_{27}, a_{27}, c_{27}, d_{27}, b_{27}
  57. Point(Circle[A_{28}, 1]) → C_{28}
  58. Polygon(A_{28}, C_{28}, D_{28}, B_{28}) → poly1_{28}, a_{28}, c_{28}, d_{28}, b_{28}
  59. Point(Circle[A_{29}, 1]) → C_{29}
  60. Polygon(A_{29}, C_{29}, D_{29}, B_{29}) → poly1_{29}, a_{29}, c_{29}, d_{29}, b_{29}
  61. Point(Circle[A_{30}, 1]) → C_{30}
  62. Polygon(A_{30}, C_{30}, D_{30}, B_{30}) → poly1_{30}, a_{30}, c_{30}, d_{30}, b_{30}
  63. Point(Circle[A_{31}, 1]) → C_{31}
  64. Polygon(A_{31}, C_{31}, D_{31}, B_{31}) → poly1_{31}, a_{31}, c_{31}, d_{31}, b_{31}
  65. Point(Circle[A_{32}, 1]) → C_{32}
  66. Polygon(A_{32}, C_{32}, D_{32}, B_{32}) → poly1_{32}, a_{32}, c_{32}, d_{32}, b_{32}
  67. Point(Circle[A_{33}, 1]) → C_{33}
  68. Polygon(A_{33}, C_{33}, D_{33}, B_{33}) → poly1_{33}, a_{33}, c_{33}, d_{33}, b_{33}
  69. Point(Circle[A_{34}, 1]) → C_{34}
  70. Polygon(A_{34}, C_{34}, D_{34}, B_{34}) → poly1_{34}, a_{34}, c_{34}, d_{34}, b_{34}
  71. Point(Circle[A_{35}, 1]) → C_{35}
  72. Polygon(A_{35}, C_{35}, D_{35}, B_{35}) → poly1_{35}, a_{35}, c_{35}, d_{35}, b_{35}
  73. Point(Circle[A_{36}, 1]) → C_{36}
  74. Polygon(A_{36}, C_{36}, D_{36}, B_{36}) → poly1_{36}, a_{36}, c_{36}, d_{36}, b_{36}
  75. Point(Circle[A_{37}, 1]) → C_{37}
  76. Polygon(A_{37}, C_{37}, D_{37}, B_{37}) → poly1_{37}, a_{37}, c_{37}, d_{37}, b_{37}
  77. Point(Circle[A_{38}, 1]) → C_{38}
  78. Polygon(A_{38}, C_{38}, D_{38}, B_{38}) → poly1_{38}, a_{38}, c_{38}, d_{38}, b_{38}
  79. Point(Circle[A_{39}, 1]) → C_{39}
  80. Polygon(A_{39}, C_{39}, D_{39}, B_{39}) → poly1_{39}, a_{39}, c_{39}, d_{39}, b_{39}
  81. Point(Circle[A_{40}, 1]) → C_{40}
  82. Polygon(A_{40}, C_{40}, D_{40}, B_{40}) → poly1_{40}, a_{40}, c_{40}, d_{40}, b_{40}
  83. Point(Circle[A_{41}, 1]) → C_{41}
  84. Polygon(A_{41}, C_{41}, D_{41}, B_{41}) → poly1_{41}, a_{41}, c_{41}, d_{41}, b_{41}
  85. Point(Circle[A_{42}, 1]) → C_{42}
  86. Polygon(A_{42}, C_{42}, D_{42}, B_{42}) → poly1_{42}, a_{42}, c_{42}, d_{42}, b_{42}
  87. Point(Circle[A_{43}, 1]) → C_{43}
  88. Polygon(A_{43}, C_{43}, D_{43}, B_{43}) → poly1_{43}, a_{43}, c_{43}, d_{43}, b_{43}
  89. Point(Circle[A_{44}, 1]) → C_{44}
  90. Polygon(A_{44}, C_{44}, D_{44}, B_{44}) → poly1_{44}, a_{44}, c_{44}, d_{44}, b_{44}
  91. Point(Circle[A_{45}, 1]) → C_{45}
  92. Polygon(A_{45}, C_{45}, D_{45}, B_{45}) → poly1_{45}, a_{45}, c_{45}, d_{45}, b_{45}
  93. Point(Circle[A_{46}, 1]) → C_{46}
  94. Polygon(A_{46}, C_{46}, D_{46}, B_{46}) → poly1_{46}, a_{46}, c_{46}, d_{46}, b_{46}
  95. Point(Circle[A_{47}, 1]) → C_{47}
  96. Polygon(A_{47}, C_{47}, D_{47}, B_{47}) → poly1_{47}, a_{47}, c_{47}, d_{47}, b_{47}
  97. Point(Circle[A_{48}, 1]) → C_{48}
  98. Polygon(A_{48}, C_{48}, D_{48}, B_{48}) → poly1_{48}, a_{48}, c_{48}, d_{48}, b_{48}
  99. Point(Circle[A_{49}, 1]) → C_{49}
  100. Polygon(A_{49}, C_{49}, D_{49}, B_{49}) → poly1_{49}, a_{49}, c_{49}, d_{49}, b_{49}
  101. Point(Circle[A_{50}, 1]) → C_{50}
  102. Polygon(A_{50}, C_{50}, D_{50}, B_{50}) → poly1_{50}, a_{50}, c_{50}, d_{50}, b_{50}
  103. Point(Circle[A_{51}, 1]) → C_{51}
  104. Polygon(A_{51}, C_{51}, D_{51}, B_{51}) → poly1_{51}, a_{51}, c_{51}, d_{51}, b_{51}
  105. Point(Circle[A_{52}, 1]) → C_{52}
  106. Polygon(A_{52}, C_{52}, D_{52}, B_{52}) → poly1_{52}, a_{52}, c_{52}, d_{52}, b_{52}
  107. Point(Circle[A_{53}, 1]) → C_{53}
  108. Polygon(A_{53}, C_{53}, D_{53}, B_{53}) → poly1_{53}, a_{53}, c_{53}, d_{53}, b_{53}
  109. Point(Circle[A_{54}, 1]) → C_{54}
  110. Point(Circle[A_{55}, 1]) → C_{55}
  111. Point(Circle[A_{56}, 1]) → C_{56}
  112. Point(Circle[A_{57}, 1]) → C_{57}
  113. Point(Circle[A_{58}, 1]) → C_{58}
  114. Point(Circle[A_{59}, 1]) → C_{59}
  115. Point(Circle[A_{60}, 1]) → C_{60}
  116. Polygon(A_{60}, C_{60}, D_{60}, B_{60}) → poly1_{60}, a_{60}, c_{60}, d_{60}, b_{60}
  117. Point(Circle[A_{61}, 1]) → C_{61}
  118. Polygon(A_{61}, C_{61}, D_{61}, B_{61}) → poly1_{61}, a_{61}, c_{61}, d_{61}, b_{61}
  119. Point(Circle[A_{62}, 1]) → C_{62}
  120. Polygon(A_{62}, C_{62}, D_{62}, B_{62}) → poly1_{62}, a_{62}, c_{62}, d_{62}, b_{62}
  121. Point(Circle[A_{63}, 1]) → C_{63}
  122. Polygon(A_{63}, C_{63}, D_{63}, B_{63}) → poly1_{63}, a_{63}, c_{63}, d_{63}, b_{63}
  123. Point(Circle[A_{64}, 1]) → C_{64}
  124. Polygon(A_{64}, C_{64}, D_{64}, B_{64}) → poly1_{64}, a_{64}, c_{64}, d_{64}, b_{64}
  125. Point(Circle[A_{65}, 1]) → C_{65}
  126. Polygon(A_{65}, C_{65}, D_{65}, B_{65}) → poly1_{65}, a_{65}, c_{65}, d_{65}, b_{65}
  127. Point(Circle[A_{66}, 1]) → C_{66}
  128. Polygon(A_{66}, C_{66}, D_{66}, B_{66}) → poly1_{66}, a_{66}, c_{66}, d_{66}, b_{66}
  129. Point(Circle[A_{67}, 1]) → C_{67}
  130. Polygon(A_{67}, C_{67}, D_{67}, B_{67}) → poly1_{67}, a_{67}, c_{67}, d_{67}, b_{67}
  131. Point(Circle[A_{68}, 1]) → C_{68}
  132. Polygon(A_{68}, C_{68}, D_{68}, B_{68}) → poly1_{68}, a_{68}, c_{68}, d_{68}, b_{68}
  133. Point(Circle[A_{69}, 1]) → C_{69}
  134. Polygon(A_{69}, C_{69}, D_{69}, B_{69}) → poly1_{69}, a_{69}, c_{69}, d_{69}, b_{69}
  135. Point(Circle[A_{70}, 1]) → C_{70}
  136. Polygon(A_{70}, C_{70}, D_{70}, B_{70}) → poly1_{70}, a_{70}, c_{70}, d_{70}, b_{70}
  137. Point(Circle[A_{71}, 1]) → C_{71}
  138. Polygon(A_{71}, C_{71}, D_{71}, B_{71}) → poly1_{71}, a_{71}, c_{71}, d_{71}, b_{71}

AI 绘图提示语参考

绘制一个立方体的展开图，包含多个相连的多边形，展示如何折叠成三维立方体。首先画出中心点，然后围绕该点依次绘制多个相同大小的正方形，每个正方形与其他正方形共享边，形成一个网状结构。最后将这个网状结构折叠，形成立体的立方体形状，突出几何构造和空间想象能力。
以上提示语为根据原始绘图命令整理而来，仅供参考。