MathPlotAI Logo MathPlotAI

Filling a Cuboid with Unit Cubes: Counting, Volume, and Scale Change

Filling a Cuboid with Unit Cubes: Counting, Volume, and Scale Change
Loading the math board and drawing, please wait…
2023-03-23 20:00
FunctionSequenceSolid GeometryGeometric ConstructionSlider Animation
In collections Quader und Würfel - Volumen
This GeoGebra example demonstrates how to fill a cuboid using unit cubes and then investigate what happens when you switch to larger unit cubes (i.e., unit cubes with volume 1 in a different scale). The main math ideas are cuboid volume as a count of unit volumes (decomposition into matching cubes), the formula-based reasoning V = (area of base) × height, and the careful relationship between “number of cubes” and “volume units” when the unit cube size changes (e.g., moving between 1 m³ and 1 mm³ scales). Construction and interaction highlights include building the cuboid and the unit-cube arrangement using polygons, then using rotations and joins to replicate faces/blocks into a grid; CountIf together with If logic checks how many unit cubes fit, while Textfield outputs explanations and correction messages for open questions. From the provided construction summary, the model uses Join, Rotate, Polygon, CountIf, If, Segment, Textfield, and Midpoint, along with objects such as A_1…A_16, ListA, sliderA/sliderB/sliderC, questionCount, nums, lNums, and lA/lB/lC to support geometric construction, parameter control, and on-screen text feedback. Suitable for grades 5–6 for solid-geometry volume understanding, decomposition-based counting, and discussion of unit-scale effects.

GeoGebra Commands & Parameters

  1. Join({{1}, nums}) → lNums
  2. Rotate(B + ((sliderB * verzerrung), 0), winkel, B) → C
  3. Rotate(F + ((sliderB * verzerrung), 0), winkel, F) → G
  4. Rotate(E + ((sliderB * verzerrung), 0), winkel, E) → H
  5. Polygon(I, J, K, L) → region, i_{16}, j_{16}, k_{16}, l_{16}
  6. CountIf(IsInRegion[P, region], P, {A_{10}, A_{11}, A_{12}, A_{13}, A_{14}, A_{15}, A_{2}, A_{3}, A_{4}, A_{5}, A_{6}, A_{7}, A_{8}, A_{9}, A_1, A_{16}}) → objectsInRegion
  7. If(bsp ≟ 1, CountIf[x > 1, Bsp1], If[bsp ≟ 2, CountIf[x > 1, Bsp2], If[bsp ≟ 3, CountIf[x > 1, Bsp3], If[bsp ≟ 4, CountIf[x > 1, Bsp4], If[bsp ≟ 5, CountIf[x > 1, Bsp5], If[bsp ≟ 6, CountIf[x > 1, Bsp6], If[bsp ≟ 7, CountIf[x > 1, Bsp7], If[bsp ≟ 8, CountIf[x > 1, Bsp8]]]]]]]]) → double
  8. Rotate(A + ((sliderB * verzerrung), 0), winkel, A) → D
  9. Segment(A, B) → f
  10. Segment(A, D) → g
  11. Segment(D, C) → h
  12. Segment(C, B) → i
  13. Segment(B, F) → j
  14. Segment(F, G) → k
  15. Segment(G, C) → l
  16. Segment(G, H) → m
  17. Segment(H, E) → n
  18. Segment(E, A) → p
  19. Segment(H, D) → q
  20. Segment(F, E) → r
  21. Rotate(B_1 + ((sliderB_1 * verzerrung), 0), winkel, B_1) → C_1
  22. Rotate(A_1 + ((sliderB_1 * verzerrung), 0), winkel, A_1) → D_1
  23. Rotate(F_1 + ((sliderB_1 * verzerrung), 0), winkel, F_1) → G_1
  24. Rotate(E_1 + ((sliderB_1 * verzerrung), 0), winkel, E_1) → H_1
  25. Segment(A_1, B_1) → s
  26. Segment(B_1, F_1) → t
  27. Segment(F_1, E_1) → a
  28. Segment(E_1, A_1) → b
  29. Segment(A_1, D_1) → c
  30. Segment(D_1, H_1) → d
  31. Segment(B_1, C_1) → e
  32. Segment(E_1, H_1) → f_1
  33. Segment(H_1, G_1) → g_1
  34. Segment(F_1, G_1) → h_1
  35. Segment(G_1, C_1) → i_1
  36. Segment(D_1, C_1) → j_1
  37. Polygon(E_1, H_1, G_1, C_1, B_1, A_1) → poly1, e_1, k_1, l_1, c_1, b_1, a_1
  38. Rotate(B_{2} + ((sliderB_1 * verzerrung), 0), winkel, B_{2}) → C_{2}
  39. Rotate(A_{2} + ((sliderB_1 * verzerrung), 0), winkel, A_{2}) → D_{2}
  40. Rotate(F_{2} + ((sliderB_1 * verzerrung), 0), winkel, F_{2}) → G_{2}
  41. Rotate(E_{2} + ((sliderB_1 * verzerrung), 0), winkel, E_{2}) → H_{2}
  42. Segment(A_{2}, B_{2}) → s_{1}
  43. Segment(B_{2}, F_{2}) → t_{1}
  44. Segment(F_{2}, E_{2}) → a_{2}
  45. Segment(E_{2}, A_{2}) → b_{2}
  46. Segment(A_{2}, D_{2}) → c_{2}
  47. Segment(D_{2}, H_{2}) → d_{1}
  48. Segment(B_{2}, C_{2}) → e_{2}
  49. Segment(E_{2}, H_{2}) → f_{2}
  50. Segment(H_{2}, G_{2}) → g_{2}
  51. Segment(F_{2}, G_{2}) → h_{2}
  52. Segment(G_{2}, C_{2}) → i_{2}
  53. Segment(D_{2}, C_{2}) → j_{2}
  54. Polygon(E_{2}, H_{2}, G_{2}, C_{2}, B_{2}, A_{2}) → poly1_{1}, e_{3}, k_{2}, l_{2}, c_{3}, b_{3}, a_{3}
  55. Rotate(B_{3} + ((sliderB_1 * verzerrung), 0), winkel, B_{3}) → C_{3}
  56. Rotate(A_{3} + ((sliderB_1 * verzerrung), 0), winkel, A_{3}) → D_{3}
  57. Rotate(F_{3} + ((sliderB_1 * verzerrung), 0), winkel, F_{3}) → G_{3}
  58. Rotate(E_{3} + ((sliderB_1 * verzerrung), 0), winkel, E_{3}) → H_{3}
  59. Segment(A_{3}, B_{3}) → s_{2}
  60. Segment(B_{3}, F_{3}) → t_{2}
  61. Segment(F_{3}, E_{3}) → a_{4}
  62. Segment(E_{3}, A_{3}) → b_{4}
  63. Segment(A_{3}, D_{3}) → c_{4}
  64. Segment(D_{3}, H_{3}) → d_{2}
  65. Segment(B_{3}, C_{3}) → e_{4}
  66. Segment(E_{3}, H_{3}) → f_{3}
  67. Segment(H_{3}, G_{3}) → g_{3}
  68. Segment(F_{3}, G_{3}) → h_{3}
  69. Segment(G_{3}, C_{3}) → i_{3}
  70. Segment(D_{3}, C_{3}) → j_{3}
  71. Polygon(E_{3}, H_{3}, G_{3}, C_{3}, B_{3}, A_{3}) → poly1_{2}, e_{5}, k_{3}, l_{3}, c_{5}, b_{5}, a_{5}
  72. Rotate(B_{4} + ((sliderB_1 * verzerrung), 0), winkel, B_{4}) → C_{4}
  73. Rotate(A_{4} + ((sliderB_1 * verzerrung), 0), winkel, A_{4}) → D_{4}
  74. Rotate(F_{4} + ((sliderB_1 * verzerrung), 0), winkel, F_{4}) → G_{4}
  75. Rotate(E_{4} + ((sliderB_1 * verzerrung), 0), winkel, E_{4}) → H_{4}
  76. Segment(A_{4}, B_{4}) → s_{3}
  77. Segment(B_{4}, F_{4}) → t_{3}
  78. Segment(F_{4}, E_{4}) → a_{6}
  79. Segment(E_{4}, A_{4}) → b_{6}
  80. Segment(A_{4}, D_{4}) → c_{6}
  81. Segment(D_{4}, H_{4}) → d_{3}
  82. Segment(B_{4}, C_{4}) → e_{6}
  83. Segment(E_{4}, H_{4}) → f_{4}
  84. Segment(H_{4}, G_{4}) → g_{4}
  85. Segment(F_{4}, G_{4}) → h_{4}
  86. Segment(G_{4}, C_{4}) → i_{4}
  87. Segment(D_{4}, C_{4}) → j_{4}
  88. Polygon(E_{4}, H_{4}, G_{4}, C_{4}, B_{4}, A_{4}) → poly1_{3}, e_{7}, k_{4}, l_{4}, c_{7}, b_{7}, a_{7}
  89. Rotate(B_{5} + ((sliderB_1 * verzerrung), 0), winkel, B_{5}) → C_{5}
  90. Rotate(A_{5} + ((sliderB_1 * verzerrung), 0), winkel, A_{5}) → D_{5}
  91. Rotate(F_{5} + ((sliderB_1 * verzerrung), 0), winkel, F_{5}) → G_{5}
  92. Rotate(E_{5} + ((sliderB_1 * verzerrung), 0), winkel, E_{5}) → H_{5}
  93. Segment(A_{5}, B_{5}) → s_{4}
  94. Segment(B_{5}, F_{5}) → t_{4}
  95. Segment(F_{5}, E_{5}) → a_{8}
  96. Segment(E_{5}, A_{5}) → b_{8}
  97. Segment(A_{5}, D_{5}) → c_{8}
  98. Segment(D_{5}, H_{5}) → d_{4}
  99. Segment(B_{5}, C_{5}) → e_{8}
  100. Segment(E_{5}, H_{5}) → f_{5}
  101. Segment(H_{5}, G_{5}) → g_{5}
  102. Segment(F_{5}, G_{5}) → h_{5}
  103. Segment(G_{5}, C_{5}) → i_{5}
  104. Segment(D_{5}, C_{5}) → j_{5}
  105. Polygon(E_{5}, H_{5}, G_{5}, C_{5}, B_{5}, A_{5}) → poly1_{4}, e_{9}, k_{5}, l_{5}, c_{9}, b_{9}, a_{9}
  106. Rotate(B_{6} + ((sliderB_1 * verzerrung), 0), winkel, B_{6}) → C_{6}
  107. Rotate(A_{6} + ((sliderB_1 * verzerrung), 0), winkel, A_{6}) → D_{6}
  108. Rotate(F_{6} + ((sliderB_1 * verzerrung), 0), winkel, F_{6}) → G_{6}
  109. Rotate(E_{6} + ((sliderB_1 * verzerrung), 0), winkel, E_{6}) → H_{6}
  110. Segment(A_{6}, B_{6}) → s_{5}
  111. Segment(B_{6}, F_{6}) → t_{5}
  112. Segment(F_{6}, E_{6}) → a_{10}
  113. Segment(E_{6}, A_{6}) → b_{10}
  114. Segment(A_{6}, D_{6}) → c_{10}
  115. Segment(D_{6}, H_{6}) → d_{5}
  116. Segment(B_{6}, C_{6}) → e_{10}
  117. Segment(E_{6}, H_{6}) → f_{6}
  118. Segment(H_{6}, G_{6}) → g_{6}
  119. Segment(F_{6}, G_{6}) → h_{6}
  120. Segment(G_{6}, C_{6}) → i_{6}
  121. Segment(D_{6}, C_{6}) → j_{6}
  122. Polygon(E_{6}, H_{6}, G_{6}, C_{6}, B_{6}, A_{6}) → poly1_{5}, e_{11}, k_{6}, l_{6}, c_{11}, b_{11}, a_{11}
  123. Rotate(B_{7} + ((sliderB_1 * verzerrung), 0), winkel, B_{7}) → C_{7}
  124. Rotate(A_{7} + ((sliderB_1 * verzerrung), 0), winkel, A_{7}) → D_{7}
  125. Rotate(F_{7} + ((sliderB_1 * verzerrung), 0), winkel, F_{7}) → G_{7}
  126. Rotate(E_{7} + ((sliderB_1 * verzerrung), 0), winkel, E_{7}) → H_{7}
  127. Segment(A_{7}, B_{7}) → s_{6}
  128. Segment(B_{7}, F_{7}) → t_{6}
  129. Segment(F_{7}, E_{7}) → a_{12}
  130. Segment(E_{7}, A_{7}) → b_{12}
  131. Segment(A_{7}, D_{7}) → c_{12}
  132. Segment(D_{7}, H_{7}) → d_{6}
  133. Segment(B_{7}, C_{7}) → e_{12}
  134. Segment(E_{7}, H_{7}) → f_{7}
  135. Segment(H_{7}, G_{7}) → g_{7}
  136. Segment(F_{7}, G_{7}) → h_{7}
  137. Segment(G_{7}, C_{7}) → i_{7}
  138. Segment(D_{7}, C_{7}) → j_{7}
  139. Polygon(E_{7}, H_{7}, G_{7}, C_{7}, B_{7}, A_{7}) → poly1_{6}, e_{13}, k_{7}, l_{7}, c_{13}, b_{13}, a_{13}
  140. Rotate(B_{8} + ((sliderB_1 * verzerrung), 0), winkel, B_{8}) → C_{8}
  141. Rotate(A_{8} + ((sliderB_1 * verzerrung), 0), winkel, A_{8}) → D_{8}
  142. Rotate(F_{8} + ((sliderB_1 * verzerrung), 0), winkel, F_{8}) → G_{8}
  143. Rotate(E_{8} + ((sliderB_1 * verzerrung), 0), winkel, E_{8}) → H_{8}
  144. Segment(A_{8}, B_{8}) → s_{7}
  145. Segment(B_{8}, F_{8}) → t_{7}
  146. Segment(F_{8}, E_{8}) → a_{14}
  147. Segment(E_{8}, A_{8}) → b_{14}
  148. Segment(A_{8}, D_{8}) → c_{14}
  149. Segment(D_{8}, H_{8}) → d_{7}
  150. Segment(B_{8}, C_{8}) → e_{14}
  151. Segment(E_{8}, H_{8}) → f_{8}
  152. Segment(H_{8}, G_{8}) → g_{8}
  153. Segment(F_{8}, G_{8}) → h_{8}
  154. Segment(G_{8}, C_{8}) → i_{8}
  155. Segment(D_{8}, C_{8}) → j_{8}
  156. Polygon(E_{8}, H_{8}, G_{8}, C_{8}, B_{8}, A_{8}) → poly1_{7}, e_{15}, k_{8}, l_{8}, c_{15}, b_{15}, a_{15}
  157. Rotate(B_{9} + ((sliderB_1 * verzerrung), 0), winkel, B_{9}) → C_{9}
  158. Rotate(A_{9} + ((sliderB_1 * verzerrung), 0), winkel, A_{9}) → D_{9}
  159. Rotate(F_{9} + ((sliderB_1 * verzerrung), 0), winkel, F_{9}) → G_{9}
  160. Rotate(E_{9} + ((sliderB_1 * verzerrung), 0), winkel, E_{9}) → H_{9}
  161. Segment(A_{9}, B_{9}) → s_{8}
  162. Segment(B_{9}, F_{9}) → t_{8}
  163. Segment(F_{9}, E_{9}) → a_{16}
  164. Segment(E_{9}, A_{9}) → b_{16}
  165. Segment(A_{9}, D_{9}) → c_{16}
  166. Segment(D_{9}, H_{9}) → d_{8}
  167. Segment(B_{9}, C_{9}) → e_{16}
  168. Segment(E_{9}, H_{9}) → f_{9}
  169. Segment(H_{9}, G_{9}) → g_{9}
  170. Segment(F_{9}, G_{9}) → h_{9}
  171. Segment(G_{9}, C_{9}) → i_{9}
  172. Segment(D_{9}, C_{9}) → j_{9}
  173. Polygon(E_{9}, H_{9}, G_{9}, C_{9}, B_{9}, A_{9}) → poly1_{8}, e_{17}, k_{9}, l_{9}, c_{17}, b_{17}, a_{17}
  174. Rotate(B_{10} + ((sliderB_1 * verzerrung), 0), winkel, B_{10}) → C_{10}
  175. Rotate(A_{10} + ((sliderB_1 * verzerrung), 0), winkel, A_{10}) → D_{10}
  176. Rotate(F_{10} + ((sliderB_1 * verzerrung), 0), winkel, F_{10}) → G_{10}
  177. Rotate(E_{10} + ((sliderB_1 * verzerrung), 0), winkel, E_{10}) → H_{10}
  178. Segment(A_{10}, B_{10}) → s_{9}
  179. Segment(B_{10}, F_{10}) → t_{9}
  180. Segment(F_{10}, E_{10}) → a_{18}
  181. Segment(E_{10}, A_{10}) → b_{18}
  182. Segment(A_{10}, D_{10}) → c_{18}
  183. Segment(D_{10}, H_{10}) → d_{9}
  184. Segment(B_{10}, C_{10}) → e_{18}
  185. Segment(E_{10}, H_{10}) → f_{10}
  186. Segment(H_{10}, G_{10}) → g_{10}
  187. Segment(F_{10}, G_{10}) → h_{10}
  188. Segment(G_{10}, C_{10}) → i_{10}
  189. Segment(D_{10}, C_{10}) → j_{10}
  190. Polygon(E_{10}, H_{10}, G_{10}, C_{10}, B_{10}, A_{10}) → poly1_{9}, e_{19}, k_{10}, l_{10}, c_{19}, b_{19}, a_{19}
  191. Rotate(B_{11} + ((sliderB_1 * verzerrung), 0), winkel, B_{11}) → C_{11}
  192. Rotate(A_{11} + ((sliderB_1 * verzerrung), 0), winkel, A_{11}) → D_{11}
  193. Rotate(F_{11} + ((sliderB_1 * verzerrung), 0), winkel, F_{11}) → G_{11}
  194. Rotate(E_{11} + ((sliderB_1 * verzerrung), 0), winkel, E_{11}) → H_{11}
  195. Segment(A_{11}, B_{11}) → s_{10}
  196. Segment(B_{11}, F_{11}) → t_{10}
  197. Segment(F_{11}, E_{11}) → a_{20}
  198. Segment(E_{11}, A_{11}) → b_{20}
  199. Segment(A_{11}, D_{11}) → c_{20}
  200. Segment(D_{11}, H_{11}) → d_{10}
  201. Segment(B_{11}, C_{11}) → e_{20}
  202. Segment(E_{11}, H_{11}) → f_{11}
  203. Segment(H_{11}, G_{11}) → g_{11}
  204. Segment(F_{11}, G_{11}) → h_{11}
  205. Segment(G_{11}, C_{11}) → i_{11}
  206. Segment(D_{11}, C_{11}) → j_{11}
  207. Polygon(E_{11}, H_{11}, G_{11}, C_{11}, B_{11}, A_{11}) → poly1_{10}, e_{21}, k_{11}, l_{11}, c_{21}, b_{21}, a_{21}
  208. Rotate(B_{12} + ((sliderB_1 * verzerrung), 0), winkel, B_{12}) → C_{12}
  209. Rotate(A_{12} + ((sliderB_1 * verzerrung), 0), winkel, A_{12}) → D_{12}
  210. Rotate(F_{12} + ((sliderB_1 * verzerrung), 0), winkel, F_{12}) → G_{12}
  211. Rotate(E_{12} + ((sliderB_1 * verzerrung), 0), winkel, E_{12}) → H_{12}
  212. Segment(A_{12}, B_{12}) → s_{11}
  213. Segment(B_{12}, F_{12}) → t_{11}
  214. Segment(F_{12}, E_{12}) → a_{22}
  215. Segment(E_{12}, A_{12}) → b_{22}
  216. Segment(A_{12}, D_{12}) → c_{22}
  217. Segment(D_{12}, H_{12}) → d_{11}
  218. Segment(B_{12}, C_{12}) → e_{22}
  219. Segment(E_{12}, H_{12}) → f_{12}
  220. Segment(H_{12}, G_{12}) → g_{12}
  221. Segment(F_{12}, G_{12}) → h_{12}
  222. Segment(G_{12}, C_{12}) → i_{12}
  223. Segment(D_{12}, C_{12}) → j_{12}
  224. Polygon(E_{12}, H_{12}, G_{12}, C_{12}, B_{12}, A_{12}) → poly1_{11}, e_{23}, k_{12}, l_{12}, c_{23}, b_{23}, a_{23}
  225. Rotate(B_{13} + ((sliderB_1 * verzerrung), 0), winkel, B_{13}) → C_{13}
  226. Rotate(A_{13} + ((sliderB_1 * verzerrung), 0), winkel, A_{13}) → D_{13}
  227. Rotate(F_{13} + ((sliderB_1 * verzerrung), 0), winkel, F_{13}) → G_{13}
  228. Rotate(E_{13} + ((sliderB_1 * verzerrung), 0), winkel, E_{13}) → H_{13}
  229. Segment(A_{13}, B_{13}) → s_{12}
  230. Segment(B_{13}, F_{13}) → t_{12}
  231. Segment(F_{13}, E_{13}) → a_{24}
  232. Segment(E_{13}, A_{13}) → b_{24}
  233. Segment(A_{13}, D_{13}) → c_{24}
  234. Segment(D_{13}, H_{13}) → d_{12}
  235. Segment(B_{13}, C_{13}) → e_{24}
  236. Segment(E_{13}, H_{13}) → f_{13}
  237. Segment(H_{13}, G_{13}) → g_{13}
  238. Segment(F_{13}, G_{13}) → h_{13}
  239. Segment(G_{13}, C_{13}) → i_{13}
  240. Segment(D_{13}, C_{13}) → j_{13}
  241. Polygon(E_{13}, H_{13}, G_{13}, C_{13}, B_{13}, A_{13}) → poly1_{12}, e_{25}, k_{13}, l_{13}, c_{25}, b_{25}, a_{25}
  242. Rotate(B_{14} + ((sliderB_1 * verzerrung), 0), winkel, B_{14}) → C_{14}
  243. Rotate(A_{14} + ((sliderB_1 * verzerrung), 0), winkel, A_{14}) → D_{14}
  244. Rotate(F_{14} + ((sliderB_1 * verzerrung), 0), winkel, F_{14}) → G_{14}
  245. Rotate(E_{14} + ((sliderB_1 * verzerrung), 0), winkel, E_{14}) → H_{14}
  246. Segment(A_{14}, B_{14}) → s_{13}
  247. Segment(B_{14}, F_{14}) → t_{13}
  248. Segment(F_{14}, E_{14}) → a_{26}
  249. Segment(E_{14}, A_{14}) → b_{26}
  250. Segment(A_{14}, D_{14}) → c_{26}
  251. Segment(D_{14}, H_{14}) → d_{13}
  252. Segment(B_{14}, C_{14}) → e_{26}
  253. Segment(E_{14}, H_{14}) → f_{14}
  254. Segment(H_{14}, G_{14}) → g_{14}
  255. Segment(F_{14}, G_{14}) → h_{14}
  256. Segment(G_{14}, C_{14}) → i_{14}
  257. Segment(D_{14}, C_{14}) → j_{14}
  258. Polygon(E_{14}, H_{14}, G_{14}, C_{14}, B_{14}, A_{14}) → poly1_{13}, e_{27}, k_{14}, l_{14}, c_{27}, b_{27}, a_{27}
  259. Rotate(B_{15} + ((sliderB_1 * verzerrung), 0), winkel, B_{15}) → C_{15}
  260. Rotate(A_{15} + ((sliderB_1 * verzerrung), 0), winkel, A_{15}) → D_{15}
  261. Rotate(F_{15} + ((sliderB_1 * verzerrung), 0), winkel, F_{15}) → G_{15}
  262. Rotate(E_{15} + ((sliderB_1 * verzerrung), 0), winkel, E_{15}) → H_{15}
  263. Segment(A_{15}, B_{15}) → s_{14}
  264. Segment(B_{15}, F_{15}) → t_{14}
  265. Segment(F_{15}, E_{15}) → a_{28}
  266. Segment(E_{15}, A_{15}) → b_{28}
  267. Segment(A_{15}, D_{15}) → c_{28}
  268. Segment(D_{15}, H_{15}) → d_{14}
  269. Segment(B_{15}, C_{15}) → e_{28}
  270. Segment(E_{15}, H_{15}) → f_{15}
  271. Segment(H_{15}, G_{15}) → g_{15}
  272. Segment(F_{15}, G_{15}) → h_{15}
  273. Segment(G_{15}, C_{15}) → i_{15}
  274. Segment(D_{15}, C_{15}) → j_{15}
  275. Polygon(E_{15}, H_{15}, G_{15}, C_{15}, B_{15}, A_{15}) → poly1_{14}, e_{29}, k_{15}, l_{15}, c_{29}, b_{29}, a_{29}
  276. If(bsp ≟ 1, CountIf[x ≟ 0, Bsp1], If[bsp ≟ 2, CountIf[x ≟ 0, Bsp2], If[bsp ≟ 3, CountIf[x ≟ 0, Bsp3], If[bsp ≟ 4, CountIf[x ≟ 0, Bsp4], If[bsp ≟ 5, CountIf[x ≟ 0, Bsp5], If[bsp ≟ 6, CountIf[x ≟ 0, Bsp6], If[bsp ≟ 7, CountIf[x ≟ 0, Bsp7], If[bsp ≟ 8, CountIf[x ≟ 0, Bsp8]]]]]]]]) → every
  277. Textfield(aInput) → InputBox1
  278. Midpoint(A, B) → M
  279. Midpoint(B, C) → N
  280. Midpoint(A, E) → O
  281. Rotate(B_{16} + ((sliderB_1 * verzerrung), 0), winkel, B_{16}) → C_{16}
  282. Rotate(F_{16} + ((sliderB_1 * verzerrung), 0), winkel, F_{16}) → G_{16}
  283. Rotate(E_{16} + ((sliderB_1 * verzerrung), 0), winkel, E_{16}) → H_{16}
  284. Segment(A_{16}, B_{16}) → s_{15}
  285. Segment(B_{16}, F_{16}) → t_{15}
  286. Segment(F_{16}, E_{16}) → a_{31}
  287. Segment(E_{16}, A_{16}) → b_{31}
  288. Segment(B_{16}, C_{16}) → e_{31}
  289. Segment(E_{16}, H_{16}) → f_{16}
  290. Segment(H_{16}, G_{16}) → g_{16}
  291. Segment(F_{16}, G_{16}) → h_{16}
  292. Segment(G_{16}, C_{16}) → i_{17}
  293. Polygon(E_{16}, H_{16}, G_{16}, C_{16}, B_{16}, A_{16}) → poly1_{15}, e_{30}, k_{17}, l_{17}, c_{30}, b_{30}, a_{30}
  294. Rotate(A_{16} + ((sliderB_1 * verzerrung), 0), winkel, A_{16}) → P
  295. Segment(A_{16}, P) → m_1
  296. Segment(P, C_{16}) → n_1
  297. Segment(P, H_{16}) → p_1
  298. Polygon(A, B, C, G, H, E) → poly2, q_1, r_1, m_2, n_2, p_2, q_2

AI Drawing Prompt Reference

Draw a cuboid and fill it with unit cubes. Start by creating the six faces of the cuboid, then use rotation and translation to replicate and arrange these faces into a grid. Next, count and display how many unit cubes fit and the total volume in different unit cube sizes.
The prompt above was compiled from the original drawing commands and is for reference only.