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6 Pyramid Cube Cutouts

6 Pyramid Cube Cutouts
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2014-07-27 11:29
Solid GeometryDerivativeGeometric Construction
This example demonstrates a 3D geometric model of a cube with a hexagonal pyramid cut out. Key mathematical concepts include solid geometry, rotation, and volume calculation. Using GeoGebra commands such as Segment, Point, Rotate, Vector, and Translate, the model is constructed. Suitable for high school or university solid geometry courses.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Segment(B, C) → b
  3. Segment(C, D) → c
  4. Segment(D, A) → d
  5. Point(b) → E
  6. Point(a) → H
  7. Segment(B, I) → e
  8. Segment(I, C) → f
  9. Rotate(I, 90*°, J) → I'
  10. Rotate(I', 90*°, J) → I''
  11. Rotate(I'', 90*°, J) → I'''
  12. Segment(C, I') → g
  13. Segment(D, I') → h
  14. Segment(D, I'') → i
  15. Segment(I'', A) → j
  16. Segment(A, I''') → k
  17. Segment(I''', B) → l
  18. Segment(A_1, B_1) → a_1
  19. Segment(B_1, C_1) → b_1
  20. Segment(C_1, D_1) → c_1
  21. Segment(D_1, A_1) → d_1
  22. Point(b_1) → E_1
  23. Point(a_1) → H_1
  24. Segment(B_1, I_1) → e_1
  25. Segment(I_1, C_1) → f_1
  26. Rotate(I_1, 90*°, J_1) → I'_1
  27. Rotate(I'_1, 90*°, J_1) → I''_1
  28. Rotate(I''_1, 90*°, J_1) → I'''_1
  29. Segment(C_1, I'_1) → g_1
  30. Segment(D_1, I'_1) → h_1
  31. Segment(D_1, I''_1) → i_1
  32. Segment(I''_1, A_1) → j_1
  33. Segment(A_1, I'''_1) → k_1
  34. Segment(I'''_1, B_1) → l_1
  35. Vector(I''_1, C) → u
  36. Translate(A_1, u) → K
  37. Translate(B_1, u) → L
  38. Segment(K, L) → m
  39. Translate(B_1, u) → M
  40. Translate(C_1, u) → N
  41. Segment(M, N) → n
  42. Translate(C_1, u) → O
  43. Translate(D_1, u) → P
  44. Segment(O, P) → p
  45. Translate(D_1, u) → Q
  46. Translate(A_1, u) → R
  47. Segment(Q, R) → q
  48. Translate(B_1, u) → S
  49. Translate(I_1, u) → T
  50. Segment(S, T) → r
  51. Translate(I_1, u) → U
  52. Translate(C_1, u) → V
  53. Segment(U, V) → s
  54. Translate(C_1, u) → W
  55. Translate(I'_1, u) → Z
  56. Segment(W, Z) → t
  57. Translate(D_1, u) → F_1
  58. Translate(I'_1, u) → G_1
  59. Segment(F_1, G_1) → m_1
  60. Translate(D_1, u) → K_1
  61. Translate(I''_1, u) → L_1
  62. Segment(K_1, L_1) → n_1
  63. Translate(I''_1, u) → M_1
  64. Translate(A_1, u) → N_1
  65. Segment(M_1, N_1) → p_1
  66. Translate(A_1, u) → O_1
  67. Translate(I'''_1, u) → P_1
  68. Segment(O_1, P_1) → q_1
  69. Translate(I'''_1, u) → Q_1
  70. Translate(B_1, u) → R_1
  71. Segment(Q_1, R_1) → r_1
  72. Translate(E_1, u) → S_1
  73. Translate(H_1, u) → T_1
  74. Translate(J_1, u) → U_1
  75. Vector(I'''_1, D) → v
  76. Translate(A_1, v) → V_1
  77. Translate(B_1, v) → W_1
  78. Segment(V_1, W_1) → s_1
  79. Translate(B_1, v) → Z_1
  80. Translate(C_1, v) → A_2
  81. Segment(Z_1, A_2) → t_1
  82. Translate(C_1, v) → B_2
  83. Translate(D_1, v) → C_2
  84. Segment(B_2, C_2) → a_2
  85. Translate(D_1, v) → D_2
  86. Translate(A_1, v) → E_2
  87. Segment(D_2, E_2) → b_2
  88. Translate(B_1, v) → F_2
  89. Translate(I_1, v) → G_2
  90. Segment(F_2, G_2) → c_2
  91. Translate(I_1, v) → H_2
  92. Translate(C_1, v) → I_2
  93. Segment(H_2, I_2) → d_2
  94. Translate(C_1, v) → J_2
  95. Translate(I'_1, v) → K_2
  96. Segment(J_2, K_2) → e_2
  97. Translate(D_1, v) → L_2
  98. Translate(I'_1, v) → M_2
  99. Segment(L_2, M_2) → f_2
  100. Translate(D_1, v) → N_2
  101. Translate(I''_1, v) → O_2
  102. Segment(N_2, O_2) → g_2
  103. Translate(I''_1, v) → P_2
  104. Translate(A_1, v) → Q_2
  105. Segment(P_2, Q_2) → h_2
  106. Translate(A_1, v) → R_2
  107. Translate(I'''_1, v) → S_2
  108. Segment(R_2, S_2) → i_2
  109. Translate(I'''_1, v) → T_2
  110. Translate(B_1, v) → U_2
  111. Segment(T_2, U_2) → j_2
  112. Translate(E_1, v) → V_2
  113. Translate(H_1, v) → W_2
  114. Translate(J_1, v) → Z_2
  115. Vector(I'''_1, P) → w
  116. Translate(A_1, w) → A_3
  117. Translate(B_1, w) → B_3
  118. Segment(A_3, B_3) → k_2
  119. Translate(B_1, w) → C_3
  120. Translate(C_1, w) → D_3
  121. Segment(C_3, D_3) → l_2
  122. Translate(C_1, w) → E_3
  123. Translate(D_1, w) → F_3
  124. Segment(E_3, F_3) → m_2
  125. Translate(D_1, w) → G_3
  126. Translate(A_1, w) → H_3
  127. Segment(G_3, H_3) → n_2
  128. Translate(B_1, w) → I_3
  129. Translate(I_1, w) → J_3
  130. Segment(I_3, J_3) → p_2
  131. Translate(I_1, w) → K_3
  132. Translate(C_1, w) → L_3
  133. Segment(K_3, L_3) → q_2
  134. Translate(C_1, w) → M_3
  135. Translate(I'_1, w) → N_3
  136. Segment(M_3, N_3) → r_2
  137. Translate(D_1, w) → O_3
  138. Translate(I'_1, w) → P_3
  139. Segment(O_3, P_3) → s_2
  140. Translate(D_1, w) → Q_3
  141. Translate(I''_1, w) → R_3
  142. Segment(Q_3, R_3) → t_2
  143. Translate(I''_1, w) → S_3
  144. Translate(A_1, w) → T_3
  145. Segment(S_3, T_3) → a_3
  146. Translate(A_1, w) → U_3
  147. Translate(I'''_1, w) → V_3
  148. Segment(U_3, V_3) → b_3
  149. Translate(I'''_1, w) → W_3
  150. Translate(B_1, w) → Z_3
  151. Segment(W_3, Z_3) → c_3
  152. Translate(E_1, w) → A_4
  153. Translate(H_1, w) → B_4
  154. Translate(J_1, w) → C_4
  155. Vector(I''_1, Z) → u_1
  156. Translate(A_1, u_1) → D_4
  157. Translate(B_1, u_1) → E_4
  158. Segment(D_4, E_4) → d_3
  159. Translate(B_1, u_1) → F_4
  160. Translate(C_1, u_1) → G_4
  161. Segment(F_4, G_4) → e_3
  162. Translate(C_1, u_1) → H_4
  163. Translate(D_1, u_1) → I_4
  164. Segment(H_4, I_4) → f_3
  165. Translate(D_1, u_1) → J_4
  166. Translate(A_1, u_1) → K_4
  167. Segment(J_4, K_4) → g_3
  168. Translate(B_1, u_1) → L_4
  169. Translate(I_1, u_1) → M_4
  170. Segment(L_4, M_4) → h_3
  171. Translate(I_1, u_1) → N_4
  172. Translate(C_1, u_1) → O_4
  173. Segment(N_4, O_4) → i_3
  174. Translate(C_1, u_1) → P_4
  175. Translate(I'_1, u_1) → Q_4
  176. Segment(P_4, Q_4) → j_3
  177. Translate(D_1, u_1) → R_4
  178. Translate(I'_1, u_1) → S_4
  179. Segment(R_4, S_4) → k_3
  180. Translate(D_1, u_1) → T_4
  181. Translate(I''_1, u_1) → U_4
  182. Segment(T_4, U_4) → l_3
  183. Translate(I''_1, u_1) → V_4
  184. Translate(A_1, u_1) → W_4
  185. Segment(V_4, W_4) → m_3
  186. Translate(A_1, u_1) → Z_4
  187. Translate(I'''_1, u_1) → A_5
  188. Segment(Z_4, A_5) → n_3
  189. Translate(I'''_1, u_1) → B_5
  190. Translate(B_1, u_1) → C_5
  191. Segment(B_5, C_5) → p_3
  192. Translate(E_1, u_1) → D_5
  193. Translate(H_1, u_1) → E_5
  194. Translate(J_1, u_1) → F_5
  195. Vector(I''_1, L) → v_1
  196. Translate(A_1, v_1) → G_5
  197. Translate(B_1, v_1) → H_5
  198. Segment(G_5, H_5) → q_3
  199. Translate(B_1, v_1) → I_5
  200. Translate(C_1, v_1) → J_5
  201. Segment(I_5, J_5) → r_3
  202. Translate(C_1, v_1) → K_5
  203. Translate(D_1, v_1) → L_5
  204. Segment(K_5, L_5) → s_3
  205. Translate(D_1, v_1) → M_5
  206. Translate(A_1, v_1) → N_5
  207. Segment(M_5, N_5) → t_3
  208. Translate(B_1, v_1) → O_5
  209. Translate(I_1, v_1) → P_5
  210. Segment(O_5, P_5) → a_4
  211. Translate(I_1, v_1) → Q_5
  212. Translate(C_1, v_1) → R_5
  213. Segment(Q_5, R_5) → b_4
  214. Translate(C_1, v_1) → S_5
  215. Translate(I'_1, v_1) → T_5
  216. Segment(S_5, T_5) → c_4
  217. Translate(D_1, v_1) → U_5
  218. Translate(I'_1, v_1) → V_5
  219. Segment(U_5, V_5) → d_4
  220. Translate(D_1, v_1) → W_5
  221. Translate(I''_1, v_1) → Z_5
  222. Segment(W_5, Z_5) → e_4
  223. Translate(I''_1, v_1) → A_6
  224. Translate(A_1, v_1) → B_6
  225. Segment(A_6, B_6) → f_4
  226. Translate(A_1, v_1) → C_6
  227. Translate(I'''_1, v_1) → D_6
  228. Segment(C_6, D_6) → g_4
  229. Translate(I'''_1, v_1) → E_6
  230. Translate(B_1, v_1) → F_6
  231. Segment(E_6, F_6) → h_4
  232. Translate(E_1, v_1) → G_6
  233. Translate(H_1, v_1) → H_6
  234. Translate(J_1, v_1) → I_6

AI Drawing Prompt Reference

Draw a cube and then cut out a hexagonal pyramid from it. Start by creating the six faces of the cube, then select a center point I on one face and rotate I to generate the pyramid's vertices. Connect these vertices to form the pyramid. Finally, translate the pyramid's base to align with the cube's base to create the cutting effect.
The prompt above was compiled from the original drawing commands and is for reference only.