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Nets of Prisms: Construction and Deconstruction

Nets of Prisms: Construction and Deconstruction
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2016-04-19 15:43
PolygonSolid GeometryGeometric Construction
In collections Surface Area
This GeoGebra worksheet demonstrates the construction and deconstruction of the nets of various prisms, illustrating the transition between three-dimensional polyhedra and two-dimensional planar nets. Core mathematical concepts include prism geometry, polygon properties, vertex-edge topology, and spatial visualization. To construct these nets, the model utilizes the `Point` command to define vertices (A, C, D, B and their translated counterparts A_1 through A_4) and the `Polygon` command to draw the faces (poly1, poly1_1, etc.). By replicating and transforming vertex sequences, it dynamically shows how the bases and lateral faces unfold. This example is ideal for secondary school solid geometry lessons, spatial reasoning training, and interactive geometry classrooms.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw an isometric net of a prism, showing its base and lateral faces unfolded into a plane. The drawing should include multiple polygons with vertices such as A, B, C, D and their translated counterparts A1 to A4, connected by translation to represent the 3D prism. Clearly show how each face unfolds from the 3D structure to the 2D plane, illustrating prism geometry, vertex-edge topology, and spatial visualization.
The prompt above was compiled from the original drawing commands and is for reference only.