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Cube Unwrapping

Cube Unwrapping
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2019-03-08 18:49
VectorSolid GeometryGeometric Construction
In collections SPATIAL VISUALISATION TASKS
This example demonstrates the process of unwrapping a cube from 3D space to a 2D plane, involving core concepts like solid geometry, polygon area calculation, and vector operations. It constructs the cube's vertices, edges, and faces using commands such as Intersect, Point, Cube, Vector, and Translate, then applies vector translation to unfold the surface. Suitable for high school geometry instruction or geometric construction practice.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, zAxis) → A
  2. Point(xAxis) → B
  3. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  4. Cube(A, B, C) → k, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  5. Vector(A, B) → u
  6. Vector(A, D) → v
  7. Vector(A, E) → w
  8. Vector(B, C) → p
  9. Vector(G, F) → l
  10. Translate(k, Vector[(6 * (-v)) + (6 * (-u)) + (a * l)]) → k'
  11. Translate(k, Vector[(6 * (-v)) + (5 * (-u)) + (a * l)]) → k'_1
  12. Translate(k, Vector[(6 * (-v)) + (4 * (-u)) + (a * l)]) → k'_2
  13. Translate(k, Vector[(6 * (-v)) + (3 * (-u)) + (a * l)]) → k'_3
  14. Translate(k, Vector[(6 * (-v)) + (2 * (-u)) + (a * l)]) → k'_4
  15. Translate(k, Vector[(6 * (-v)) + (-u) + (a * l)]) → k'_5
  16. Translate(k, Vector[(5 * (-v)) + (6 * (-u)) + (a * l)]) → k'_6
  17. Translate(k, Vector[(5 * (-v)) + (5 * (-u)) + (a * l)]) → k'_7
  18. Translate(k, Vector[(5 * (-v)) + (4 * (-u)) + (a * l)]) → k'_8
  19. Translate(k, Vector[(5 * (-v)) + (3 * (-u)) + (a * l)]) → k'_9
  20. Translate(k, Vector[(5 * (-v)) + (2 * (-u)) + (a * l)]) → k'_{10}
  21. Translate(k, Vector[(5 * (-v)) + (-u) + (a * l)]) → k'_{11}
  22. Translate(k, Vector[(4 * (-v)) + (6 * (-u)) + (a * l)]) → k'_{12}
  23. Translate(k, Vector[(4 * (-v)) + (5 * (-u)) + (a * l)]) → k'_{13}
  24. Translate(k, Vector[(4 * (-v)) + (4 * (-u)) + (a * l)]) → k'_{14}
  25. Translate(k, Vector[(4 * (-v)) + (3 * (-u)) + (a * l)]) → k'_{15}
  26. Translate(k, Vector[(4 * (-v)) + (2 * (-u)) + (a * l)]) → k'_{16}
  27. Translate(k, Vector[(4 * (-v)) + (-u) + (a * l)]) → k'_{17}
  28. Translate(k, Vector[(3 * (-v)) + (6 * (-u)) + (a * p)]) → k'_{18}
  29. Translate(k, Vector[(3 * (-v)) + (5 * (-u)) + (a * p)]) → k'_{19}
  30. Translate(k, Vector[(3 * (-v)) + (4 * (-u)) + (a * p)]) → k'_{20}
  31. Translate(k, Vector[(3 * (-v)) + (3 * (-u)) + (a * p)]) → k'_{21}
  32. Translate(k, Vector[(3 * (-v)) + (2 * (-u)) + (a * p)]) → k'_{22}
  33. Translate(k, Vector[(3 * (-v)) + (-u) + (a * p)]) → k'_{23}
  34. Translate(k, Vector[(2 * (-v)) + (6 * (-u)) + (a * p)]) → k'_{24}
  35. Translate(k, Vector[(2 * (-v)) + (5 * (-u)) + (a * p)]) → k'_{25}
  36. Translate(k, Vector[(2 * (-v)) + (4 * (-u)) + (a * p)]) → k'_{26}
  37. Translate(k, Vector[(2 * (-v)) + (3 * (-u)) + (a * p)]) → k'_{27}
  38. Translate(k, Vector[(2 * (-v)) + (2 * (-u)) + (a * p)]) → k'_{28}
  39. Translate(k, Vector[(2 * (-v)) + (-u) + (a * p)]) → k'_{29}
  40. Translate(k, Vector[(-v) + (6 * (-u)) + (a * p)]) → k'_{30}
  41. Translate(k, Vector[(-v) + (5 * (-u)) + (a * p)]) → k'_{31}
  42. Translate(k, Vector[(-v) + (4 * (-u)) + (a * p)]) → k'_{32}
  43. Translate(k, Vector[(-v) + (3 * (-u)) + (a * p)]) → k'_{33}
  44. Translate(k, Vector[(-v) + (2 * (-u)) + (a * p)]) → k'_{34}
  45. Translate(k, Vector[(-v) + (-u) + (a * p)]) → k'_{35}
  46. Translate(k, Vector[(6 * (-v)) + w + (6 * (-u)) + (a * l)]) → k'_{36}
  47. Translate(k, Vector[(6 * (-v)) + w + (5 * (-u)) + (a * l)]) → k'_{37}
  48. Translate(k, Vector[(6 * (-v)) + w + (4 * (-u)) + (a * l)]) → k'_{38}
  49. Translate(k, Vector[(6 * (-v)) + w + (3 * (-u)) + (a * l)]) → k'_{39}
  50. Translate(k, Vector[(6 * (-v)) + w + (2 * (-u)) + (a * l)]) → k'_{40}
  51. Translate(k, Vector[(6 * (-v)) + w + (-u) + (a * l)]) → k'_{41}
  52. Translate(k, Vector[(5 * (-v)) + w + (6 * (-u)) + (a * l)]) → k'_{42}
  53. Translate(k, Vector[(5 * (-v)) + w + (5 * (-u)) + (b * l)]) → k'_{43}
  54. Translate(k, Vector[(5 * (-v)) + w + (4 * (-u)) + (b * l)]) → k'_{44}
  55. Translate(k, Vector[(5 * (-v)) + w + (3 * (-u)) + (b * l)]) → k'_{45}
  56. Translate(k, Vector[(5 * (-v)) + w + (2 * (-u)) + (b * l)]) → k'_{46}
  57. Translate(k, Vector[(5 * (-v)) + w + (-u) + (a * l)]) → k'_{47}
  58. Translate(k, Vector[(4 * (-v)) + w + (6 * (-u)) + (a * l)]) → k'_{48}
  59. Translate(k, Vector[(4 * (-v)) + w + (5 * (-u)) + (b * l)]) → k'_{49}
  60. Translate(k, Vector[(4 * (-v)) + w + (4 * (-u)) + (b * l)]) → k'_{50}
  61. Translate(k, Vector[(4 * (-v)) + w + (3 * (-u)) + (b * l)]) → k'_{51}
  62. Translate(k, Vector[(4 * (-v)) + w + (2 * (-u)) + (b * l)]) → k'_{52}
  63. Translate(k, Vector[(4 * (-v)) + w + (-u) + (a * l)]) → k'_{53}
  64. Translate(k, Vector[(3 * (-v)) + w + (6 * (-u)) + (a * p)]) → k'_{54}
  65. Translate(k, Vector[(3 * (-v)) + w + (5 * (-u)) + (b * p)]) → k'_{55}
  66. Translate(k, Vector[(3 * (-v)) + w + (4 * (-u)) + (b * p)]) → k'_{56}
  67. Translate(k, Vector[(3 * (-v)) + w + (3 * (-u)) + (b * p)]) → k'_{57}
  68. Translate(k, Vector[(3 * (-v)) + w + (2 * (-u)) + (b * p)]) → k'_{58}
  69. Translate(k, Vector[(3 * (-v)) + w + (-u) + (a * p)]) → k'_{59}
  70. Translate(k, Vector[(2 * (-v)) + w + (6 * (-u)) + (a * p)]) → k'_{60}
  71. Translate(k, Vector[(2 * (-v)) + w + (65 * (-u)) + (b * p)]) → k'_{61}
  72. Translate(k, Vector[(2 * (-v)) + w + (5 * (-u)) + (b * p)]) → k'_{62}
  73. Translate(k, Vector[(2 * (-v)) + w + (4 * (-u)) + (b * p)]) → k'_{63}
  74. Translate(k, Vector[(2 * (-v)) + w + (3 * (-u)) + (b * p)]) → k'_{64}
  75. Translate(k, Vector[(2 * (-v)) + w + (4 * (-u)) + (b * p)]) → k'_{65}
  76. Translate(k, Vector[(2 * (-v)) + w + (2 * (-u)) + (b * p)]) → k'_{66}
  77. Translate(k, Vector[(2 * (-v)) + w + (-u) + (a * p)]) → k'_{67}
  78. Translate(k, Vector[(-v) + w + (6 * (-u)) + (a * p)]) → k'_{68}
  79. Translate(k, Vector[(-v) + w + (5 * (-u)) + (a * p)]) → k'_{69}
  80. Translate(k, Vector[(-v) + w + (4 * (-u)) + (a * p)]) → k'_{70}
  81. Translate(k, Vector[(-v) + w + (3 * (-u)) + (a * p)]) → k'_{71}
  82. Translate(k, Vector[(-v) + w + (2 * (-u)) + (a * p)]) → k'_{72}
  83. Translate(k, Vector[(-v) + w - u + (a * p)]) → k'_{73}
  84. Translate(k, Vector[(6 * (-v)) + (2 * w) + (6 * (-u)) + (a * l)]) → k'_{74}
  85. Translate(k, Vector[(6 * (-v)) + (2 * w) + (5 * (-u)) + (a * l)]) → k'_{75}
  86. Translate(k, Vector[(6 * (-v)) + (2 * w) + (4 * (-u)) + (a * l)]) → k'_{76}
  87. Translate(k, Vector[(6 * (-v)) + (2 * w) + (3 * (-u)) + (a * l)]) → k'_{77}
  88. Translate(k, Vector[(6 * (-v)) + (2 * w) + (2 * (-u)) + (a * l)]) → k'_{78}
  89. Translate(k, Vector[(6 * (-v)) + (2 * w) + (-u) + (a * l)]) → k'_{79}
  90. Translate(k, Vector[(6 * (-v)) + (2 * w) + (6 * (-u)) + (a * l)]) → k'_{80}
  91. Translate(k, Vector[(5 * (-v)) + (2 * w) + (6 * (-u)) + (a * l)]) → k'_{81}
  92. Translate(k, Vector[(5 * (-v)) + (2 * w) + (5 * (-u)) + (b * l)]) → k'_{82}
  93. Translate(k, Vector[(5 * (-v)) + (2 * w) + (4 * (-u)) + (b * l)]) → k'_{83}
  94. Translate(k, Vector[(5 * (-v)) + (2 * w) + (3 * (-u)) + (b * l)]) → k'_{84}
  95. Translate(k, Vector[(5 * (-v)) + (2 * w) + (2 * (-u)) + (b * l)]) → k'_{85}
  96. Translate(k, Vector[(5 * (-v)) + (2 * w) + (-u) + (a * l)]) → k'_{86}
  97. Translate(k, Vector[(4 * (-v)) + (2 * w) + (6 * (-u)) + (a * l)]) → k'_{87}
  98. Translate(k, Vector[(4 * (-v)) + (2 * w) + (5 * (-u)) + (b * l)]) → k'_{88}
  99. Translate(k, Vector[(4 * (-v)) + (2 * w) + (4 * (-u)) + (c * l)]) → k'_{89}
  100. Translate(k, Vector[(4 * (-v)) + (2 * w) + (3 * (-u)) + (c * l)]) → k'_{90}
  101. Translate(k, Vector[(4 * (-v)) + (2 * w) + (2 * (-u)) + (b * l)]) → k'_{91}
  102. Translate(k, Vector[(4 * (-v)) + (2 * w) + (-u) + (a * l)]) → k'_{92}
  103. Translate(k, Vector[(3 * (-v)) + (2 * w) + (6 * (-u)) + (a * p)]) → k'_{93}
  104. Translate(k, Vector[(3 * (-v)) + (2 * w) + (5 * (-u)) + (b * p)]) → k'_{94}
  105. Translate(k, Vector[(3 * (-v)) + (2 * w) + (4 * (-u)) + (c * p)]) → k'_{95}
  106. Translate(k, Vector[(3 * (-v)) + (2 * w) + (3 * (-u)) + (c * p)]) → k'_{96}
  107. Translate(k, Vector[(3 * (-v)) + (2 * w) + (2 * (-u)) + (b * p)]) → k'_{97}
  108. Translate(k, Vector[(3 * (-v)) + (2 * w) + (-u) + (a * p)]) → k'_{98}
  109. Translate(k, Vector[(2 * (-v)) + (2 * w) + (6 * (-u)) + (a * p)]) → k'_{99}
  110. Translate(k, Vector[(2 * (-v)) + (2 * w) + (5 * (-u)) + (b * p)]) → k'_{100}
  111. Translate(k, Vector[(2 * (-v)) + (2 * w) + (4 * (-u)) + (b * p)]) → k'_{101}
  112. Translate(k, Vector[(2 * (-v)) + (2 * w) + (3 * (-u)) + (b * p)]) → k'_{102}
  113. Translate(k, Vector[(2 * (-v)) + (2 * w) + (2 * (-u)) + (b * p)]) → k'_{103}
  114. Translate(k, Vector[(2 * (-v)) + (2 * w) + (-u) + (a * p)]) → k'_{104}
  115. Translate(k, Vector[(-v) + (2 * w) + (6 * (-u)) + (a * p)]) → k'_{105}
  116. Translate(k, Vector[(-v) + (2 * w) + (5 * (-u)) + (a * p)]) → k'_{106}
  117. Translate(k, Vector[(-v) + (2 * w) + (4 * (-u)) + (a * p)]) → k'_{107}
  118. Translate(k, Vector[(-v) + (2 * w) + (3 * (-u)) + (a * p)]) → k'_{108}
  119. Translate(k, Vector[(-v) + (2 * w) + (2 * (-u)) + (a * p)]) → k'_{109}
  120. Translate(k, Vector[(-v) + (2 * w) + (-u) + (a * p)]) → k'_{110}
  121. Translate(k, Vector[(6 * (-v)) + (3 * w) + (6 * (-u)) + (a * l)]) → k'_{111}
  122. Translate(k, Vector[(6 * (-v)) + (3 * w) + (5 * (-u)) + (a * l)]) → k'_{112}
  123. Translate(k, Vector[(6 * (-v)) + (3 * w) + (4 * (-u)) + (a * l)]) → k'_{113}
  124. Translate(k, Vector[(6 * (-v)) + (3 * w) + (3 * (-u)) + (a * l)]) → k'_{114}
  125. Translate(k, Vector[(6 * (-v)) + (3 * w) + (2 * (-u)) + (a * l)]) → k'_{115}
  126. Translate(k, Vector[(6 * (-v)) + (3 * w) + (-u) + (a * l)]) → k'_{116}
  127. Translate(k, Vector[(5 * (-v)) + (3 * w) + (6 * (-u)) + (a * l)]) → k'_{117}
  128. Translate(k, Vector[(5 * (-v)) + (3 * w) + (5 * (-u)) + (b * l)]) → k'_{118}
  129. Translate(k, Vector[(5 * (-v)) + (3 * w) + (4 * (-u)) + (b * l)]) → k'_{119}
  130. Translate(k, Vector[(5 * (-v)) + (3 * w) + (3 * (-u)) + (b * l)]) → k'_{120}
  131. Translate(k, Vector[(5 * (-v)) + (3 * w) + (2 * (-u)) + (b * l)]) → k'_{121}
  132. Translate(k, Vector[(5 * (-v)) + (3 * w) + (-u) + (a * l)]) → k'_{122}
  133. Translate(k, Vector[(4 * (-v)) + (3 * w) + (6 * (-u)) + (a * l)]) → k'_{123}
  134. Translate(k, Vector[(4 * (-v)) + (3 * w) + (5 * (-u)) + (b * l)]) → k'_{124}
  135. Translate(k, Vector[(4 * (-v)) + (3 * w) + (4 * (-u)) + (c * l)]) → k'_{125}
  136. Translate(k, Vector[(4 * (-v)) + (3 * w) + (3 * (-u)) + (c * l)]) → k'_{126}
  137. Translate(k, Vector[(4 * (-v)) + (3 * w) + (2 * (-u)) + (b * l)]) → k'_{127}
  138. Translate(k, Vector[(4 * (-v)) + (3 * w) + (-u) + (a * l)]) → k'_{128}
  139. Translate(k, Vector[(3 * (-v)) + (3 * w) + (6 * (-u)) + (a * p)]) → k'_{129}
  140. Translate(k, Vector[(3 * (-v)) + (3 * w) + (5 * (-u)) + (b * p)]) → k'_{130}
  141. Translate(k, Vector[(3 * (-v)) + (3 * w) + (4 * (-u)) + (c * p)]) → k'_{131}
  142. Translate(k, Vector[(3 * (-v)) + (3 * w) + (3 * (-u)) + (c * p)]) → k'_{132}
  143. Translate(k, Vector[(3 * (-v)) + (3 * w) + (2 * (-u)) + (b * p)]) → k'_{133}
  144. Translate(k, Vector[(3 * (-v)) + (3 * w) + (-u) + (a * p)]) → k'_{134}
  145. Translate(k, Vector[(2 * (-v)) + (3 * w) + (6 * (-u)) + (a * p)]) → k'_{135}
  146. Translate(k, Vector[(2 * (-v)) + (3 * w) + (5 * (-u)) + (b * p)]) → k'_{136}
  147. Translate(k, Vector[(2 * (-v)) + (3 * w) + (4 * (-u)) + (b * p)]) → k'_{137}
  148. Translate(k, Vector[(2 * (-v)) + (3 * w) + (3 * (-u)) + (b * p)]) → k'_{138}
  149. Translate(k, Vector[(2 * (-v)) + (3 * w) + (2 * (-u)) + (b * p)]) → k'_{139}
  150. Translate(k, Vector[(2 * (-v)) + (3 * w) + (-u) + (a * p)]) → k'_{140}
  151. Translate(k, Vector[(-v) + (3 * w) + (6 * (-u)) + (a * p)]) → k'_{141}
  152. Translate(k, Vector[(-v) + (3 * w) + (5 * (-u)) + (a * p)]) → k'_{142}
  153. Translate(k, Vector[(-v) + (3 * w) + (4 * (-u)) + (a * p)]) → k'_{143}
  154. Translate(k, Vector[(-v) + (3 * w) + (3 * (-u)) + (a * p)]) → k'_{144}
  155. Translate(k, Vector[(-v) + (3 * w) + (2 * (-u)) + (a * p)]) → k'_{145}
  156. Translate(k, Vector[(-v) + (3 * w) + (-u) + (a * p)]) → k'_{146}
  157. Translate(k, Vector[(6 * (-v)) + (4 * w) + (6 * (-u)) + (a * l)]) → k'_{147}
  158. Translate(k, Vector[(6 * (-v)) + (4 * w) + (5 * (-u)) + (a * l)]) → k'_{148}
  159. Translate(k, Vector[(6 * (-v)) + (4 * w) + (4 * (-u)) + (a * l)]) → k'_{149}
  160. Translate(k, Vector[(6 * (-v)) + (4 * w) + (3 * (-u)) + (a * l)]) → k'_{150}
  161. Translate(k, Vector[(6 * (-v)) + (4 * w) + (2 * (-u)) + (a * l)]) → k'_{151}
  162. Translate(k, Vector[(6 * (-v)) + (4 * w) + (-u) + (a * l)]) → k'_{152}
  163. Translate(k, Vector[(5 * (-v)) + (4 * w) + (6 * (-u)) + (a * l)]) → k'_{153}
  164. Translate(k, Vector[(5 * (-v)) + (4 * w) + (5 * (-u)) + (b * l)]) → k'_{154}
  165. Translate(k, Vector[(5 * (-v)) + (4 * w) + (4 * (-u)) + (b * l)]) → k'_{155}
  166. Translate(k, Vector[(5 * (-v)) + (4 * w) + (3 * (-u)) + (b * l)]) → k'_{156}
  167. Translate(k, Vector[(5 * (-v)) + (4 * w) + (2 * (-u)) + (b * l)]) → k'_{157}
  168. Translate(k, Vector[(5 * (-v)) + (4 * w) + (-u) + (a * l)]) → k'_{158}
  169. Translate(k, Vector[(4 * (-v)) + (4 * w) + (6 * (-u)) + (a * l)]) → k'_{159}
  170. Translate(k, Vector[(4 * (-v)) + (4 * w) + (5 * (-u)) + (b * l)]) → k'_{160}
  171. Translate(k, Vector[(4 * (-v)) + (4 * w) + (4 * (-u)) + (b * l)]) → k'_{161}
  172. Translate(k, Vector[(4 * (-v)) + (4 * w) + (3 * (-u)) + (b * l)]) → k'_{162}
  173. Translate(k, Vector[(4 * (-v)) + (4 * w) + (2 * (-u)) + (b * l)]) → k'_{163}
  174. Translate(k, Vector[(4 * (-v)) + (4 * w) + (-u) + (a * l)]) → k'_{164}
  175. Translate(k, Vector[(3 * (-v)) + (4 * w) + (6 * (-u)) + (a * p)]) → k'_{165}
  176. Translate(k, Vector[(3 * (-v)) + (4 * w) + (5 * (-u)) + (b * p)]) → k'_{166}
  177. Translate(k, Vector[(3 * (-v)) + (4 * w) + (4 * (-u)) + (b * p)]) → k'_{167}
  178. Translate(k, Vector[(3 * (-v)) + (4 * w) + (3 * (-u)) + (b * p)]) → k'_{168}
  179. Translate(k, Vector[(3 * (-v)) + (4 * w) + (2 * (-u)) + (b * p)]) → k'_{169}
  180. Translate(k, Vector[(3 * (-v)) + (4 * w) + (-u) + (a * p)]) → k'_{170}
  181. Translate(k, Vector[(2 * (-v)) + (4 * w) + (6 * (-u)) + (a * p)]) → k'_{171}
  182. Translate(k, Vector[(2 * (-v)) + (4 * w) + (5 * (-u)) + (b * p)]) → k'_{172}
  183. Translate(k, Vector[(2 * (-v)) + (4 * w) + (4 * (-u)) + (b * p)]) → k'_{173}
  184. Translate(k, Vector[(2 * (-v)) + (4 * w) + (3 * (-u)) + (b * p)]) → k'_{174}
  185. Translate(k, Vector[(2 * (-v)) + (4 * w) + (2 * (-u)) + (b * p)]) → k'_{175}
  186. Translate(k, Vector[(2 * (-v)) + (4 * w) + (-u) + (a * p)]) → k'_{176}
  187. Translate(k, Vector[(-v) + (4 * w) + (6 * (-u)) + (a * p)]) → k'_{177}
  188. Translate(k, Vector[(-v) + (4 * w) + (5 * (-u)) + (a * p)]) → k'_{178}
  189. Translate(k, Vector[(-v) + (4 * w) + (4 * (-u)) + (a * p)]) → k'_{179}
  190. Translate(k, Vector[(-v) + (4 * w) + (3 * (-u)) + (a * p)]) → k'_{180}
  191. Translate(k, Vector[(-v) + (4 * w) + (2 * (-u)) + (a * p)]) → k'_{181}
  192. Translate(k, Vector[(-v) + (4 * w) + (-u) + (a * p)]) → k'_{182}
  193. Translate(k, Vector[(6 * (-v)) + (5 * w) + (6 * (-u)) + (a * l)]) → k'_{183}
  194. Translate(k, Vector[(6 * (-v)) + (5 * w) + (5 * (-u)) + (a * l)]) → k'_{184}
  195. Translate(k, Vector[(6 * (-v)) + (5 * w) + (4 * (-u)) + (a * l)]) → k'_{185}
  196. Translate(k, Vector[(6 * (-v)) + (5 * w) + (3 * (-u)) + (a * l)]) → k'_{186}
  197. Translate(k, Vector[(6 * (-v)) + (5 * w) + (2 * (-u)) + (a * l)]) → k'_{187}
  198. Translate(k, Vector[(6 * (-v)) + (5 * w) + (-u) + (a * l)]) → k'_{188}
  199. Translate(k, Vector[(5 * (-v)) + (5 * w) + (6 * (-u)) + (a * l)]) → k'_{189}
  200. Translate(k, Vector[(5 * (-v)) + (5 * w) + (5 * (-u)) + (a * l)]) → k'_{190}
  201. Translate(k, Vector[(5 * (-v)) + (5 * w) + (4 * (-u)) + (a * l)]) → k'_{191}
  202. Translate(k, Vector[(5 * (-v)) + (5 * w) + (3 * (-u)) + (a * l)]) → k'_{192}
  203. Translate(k, Vector[(5 * (-v)) + (5 * w) + (2 * (-u)) + (a * l)]) → k'_{193}
  204. Translate(k, Vector[(5 * (-v)) + (5 * w) + (-u) + (a * l)]) → k'_{194}
  205. Translate(k, Vector[(4 * (-v)) + (5 * w) + (6 * (-u)) + (a * l)]) → k'_{195}
  206. Translate(k, Vector[(4 * (-v)) + (5 * w) + (5 * (-u)) + (a * l)]) → k'_{196}
  207. Translate(k, Vector[(4 * (-v)) + (5 * w) + (4 * (-u)) + (a * l)]) → k'_{197}
  208. Translate(k, Vector[(4 * (-v)) + (5 * w) + (3 * (-u)) + (a * l)]) → k'_{198}
  209. Translate(k, Vector[(4 * (-v)) + (5 * w) + (2 * (-u)) + (a * l)]) → k'_{199}
  210. Translate(k, Vector[(4 * (-v)) + (5 * w) + (-u) + (a * l)]) → k'_{200}
  211. Translate(k, Vector[(3 * (-v)) + (5 * w) + (6 * (-u)) + (a * p)]) → k'_{201}
  212. Translate(k, Vector[(3 * (-v)) + (5 * w) + (5 * (-u)) + (a * p)]) → k'_{202}
  213. Translate(k, Vector[(3 * (-v)) + (5 * w) + (4 * (-u)) + (a * p)]) → k'_{203}
  214. Translate(k, Vector[(3 * (-v)) + (5 * w) + (3 * (-u)) + (a * p)]) → k'_{204}
  215. Translate(k, Vector[(3 * (-v)) + (5 * w) + (2 * (-u)) + (a * p)]) → k'_{205}
  216. Translate(k, Vector[(3 * (-v)) + (5 * w) + (-u) + (a * p)]) → k'_{206}
  217. Translate(k, Vector[(2 * (-v)) + (5 * w) + (6 * (-u)) + (a * p)]) → k'_{207}
  218. Translate(k, Vector[(2 * (-v)) + (5 * w) + (5 * (-u)) + (a * p)]) → k'_{208}
  219. Translate(k, Vector[(2 * (-v)) + (5 * w) + (4 * (-u)) + (a * p)]) → k'_{209}
  220. Translate(k, Vector[(2 * (-v)) + (5 * w) + (3 * (-u)) + (a * p)]) → k'_{210}
  221. Translate(k, Vector[(2 * (-v)) + (5 * w) + (2 * (-u)) + (a * p)]) → k'_{211}
  222. Translate(k, Vector[(2 * (-v)) + (5 * w) + (-u) + (a * p)]) → k'_{212}
  223. Translate(k, Vector[(-v) + (5 * w) + (6 * (-u)) + (a * p)]) → k'_{213}
  224. Translate(k, Vector[(-v) + (5 * w) + (5 * (-u)) + (a * p)]) → k'_{214}
  225. Translate(k, Vector[(-v) + (5 * w) + (4 * (-u)) + (a * p)]) → k'_{215}
  226. Translate(k, Vector[(-v) + (5 * w) + (3 * (-u)) + (a * p)]) → k'_{216}
  227. Translate(k, Vector[(-v) + (5 * w) + (2 * (-u)) + (a * p)]) → k'_{217}
  228. Translate(k, Vector[(-v) + (5 * w) + (-u) + (a * p)]) → k'_{218}

AI Drawing Prompt Reference

Draw a cube and demonstrate the process of unwrapping it. Start by plotting the coordinate axes and finding their intersection point to construct the cube's vertices. Then, draw the edges and faces of the cube. Create three vectors representing directions along the cube. Using these vectors, apply translation operations to unfold each face of the cube onto a 2D plane sequentially. The final image should show both the original 3D cube and its unwrapped 2D layout, clearly illustrating the transformation from three-dimensional to two-dimensional space.
The prompt above was compiled from the original drawing commands and is for reference only.