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Pentagonal Prism

Pentagonal Prism
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2020-05-22 20:19
PolygonMatrixTransformation
This example demonstrates the construction of a pentagonal prism. Key mathematical concepts include polygons, plane figures, matrices, and transformations. Using GeoGebra commands such as Point, Polygon, Translate, and Rotate, the various faces and edges of the pentagonal prism can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(yAxis) → OO
  2. Rotate(OO, (360°) / 16) → B
  3. Mirror(B, yAxis) → A
  4. Line(A, B) → n
  5. Polygon(A, B, 8) → veelhoek1, f, D, E, F, G, H, g, h, i, j, k, l, m, C
  6. Line(G, H) → r
  7. Intersect(n, r) → L
  8. Translate(L, Vector[(0, 0, -1.13)]) → L'_1
  9. Line(F, E) → q
  10. Intersect(q, r) → J
  11. Translate(J, Vector[(0, 0, -1.13)]) → J'_1
  12. Line(D, C) → p
  13. Intersect(p, q) → K
  14. Translate(K, Vector[(0, 0, -1.13)]) → K'_1
  15. Intersect(n, p) → I
  16. Translate(I, Vector[(0, 0, -1.13)]) → I'_1
  17. Polygon(I'_1, K'_1, J'_1, L'_1) → vierhoek15'_1, i'_1, k'_1, j'_1, l'_1
  18. Midpoint(B, C) → E_2
  19. Segment(E_2, I) → e_3
  20. Segment(J, L) → s
  21. Segment(L, I) → t
  22. Segment(I, K) → a
  23. Segment(K, J) → b
  24. Prism(veelhoek1, 2) → c, M, zijvlakBCPN, zijvlakCDQP, zijvlakDERQ, zijvlakEFSR, zijvlakFGTS, zijvlakGHUT, zijvlakAHUM, zijvlakMNPQRSTU, RibbeAM, RibbeBN, N, RibbeCP, RibbeDQ, RibbeER, RibbeFS, RibbeGT, RibbeHU, RibbeMN, RibbeNP, RibbePQ, RibbeQR, P, RibbeRS, RibbeST, RibbeTU, RibbeMU, Q, R, S, T, U, zijvlakABNM
  25. Midpoint(RibbePQ) → V
  26. Midpoint(RibbeST) → W
  27. Midpoint(T, P) → Z
  28. Segment(Z, P) → straal
  29. CircleArc(Z, P, A_1) → d
  30. Point(d) → C_1
  31. Point(d) → D_1
  32. Point(d) → E_1
  33. Point(d) → F_1
  34. Point(d) → G_1
  35. Rotate(L_1, (360°) / 8, zAxis) → M_1
  36. Rotate(K_1, (360°) / 8, zAxis) → N_1
  37. Rotate(J_1, (360°) / 8, zAxis) → O_1
  38. Rotate(H_1, (360°) / 8, zAxis) → P_1
  39. Rotate(I_1, (360°) / 8, zAxis) → Q_1
  40. Polygon(I_1, P, Q, Q_1) → vierhoek1, i_1, p_1, q_1, e
  41. Polygon(I_1, Q_1, P_1, H_1) → vierhoek2, f_1, g_1, h_1, j_1
  42. Polygon(J_1, H_1, P_1, O_1) → vierhoek3, k_1, l_1, m_1, o_1
  43. Polygon(K_1, J_1, O_1, N_1) → vierhoek4, n_1, r_1, s_1, t_1
  44. Polygon(L_1, K_1, N_1, M_1) → vierhoek5, a_1, b_1, c_1, d_1
  45. Polygon(L_1, M_1, B_1) → driehoek1, e_1, f_2, g_2
  46. Rotate(vierhoek1, (360°) / 8, zAxis) → vierhoek1'
  47. Rotate(vierhoek2, (360°) / 8, zAxis) → vierhoek2'
  48. Rotate(vierhoek3, (360°) / 8, zAxis) → vierhoek3'
  49. Rotate(vierhoek4, (360°) / 8, zAxis) → vierhoek4'
  50. Rotate(vierhoek5, (360°) / 8, zAxis) → vierhoek5'
  51. Rotate(driehoek1, (360°) / 8, zAxis) → driehoek1'
  52. Rotate(vierhoek1, (2 * (360°) / 8), zAxis) → vierhoek1'_1
  53. Rotate(vierhoek2, (2 * (360°) / 8), zAxis) → vierhoek2'_1
  54. Rotate(vierhoek3, (2 * (360°) / 8), zAxis) → vierhoek3'_1
  55. Rotate(vierhoek4, (2 * (360°) / 8), zAxis) → vierhoek4'_1
  56. Rotate(vierhoek5, (2 * (360°) / 8), zAxis) → vierhoek5'_1
  57. Rotate(driehoek1, (2 * (360°) / 8), zAxis) → driehoek1'_1
  58. Rotate(vierhoek1, (3 * (360°) / 8), zAxis) → vierhoek1'_2
  59. Rotate(vierhoek2, (3 * (360°) / 8), zAxis) → vierhoek2'_2
  60. Rotate(vierhoek3, (3 * (360°) / 8), zAxis) → vierhoek3'_2
  61. Rotate(vierhoek4, (3 * (360°) / 8), zAxis) → vierhoek4'_2
  62. Rotate(vierhoek5, (3 * (360°) / 8), zAxis) → vierhoek5'_2
  63. Rotate(driehoek1, (3 * (360°) / 8), zAxis) → driehoek1'_2
  64. Plane(V, W, W + (0, 0, 1)) → p_2
  65. Intersect(l_1, p_2) → S_1
  66. Intersect(f_1, p_2) → R_1
  67. Intersect(r_1, p_2) → T_1
  68. Intersect(b_1, p_2) → U_1
  69. Intersect(c_1, p_2) → V_1
  70. Intersect(Segment[Rotate[N_1, (360°) / 8, zAxis], Rotate[M_1, (360°) / 8, zAxis]], p_2) → W_1
  71. Intersect(Segment[Rotate[N_1, (2 * (360°) / 8), zAxis], Rotate[M_1, (2 * (360°) / 8), zAxis]], p_2) → Z_1
  72. Intersect(Segment[Rotate[K_1, (3 * (360°) / 8), zAxis], Rotate[N_1, (3 * (360°) / 8), zAxis]], p_2) → A_2
  73. Intersect(Segment[Rotate[J_1, (3 * (360°) / 8), zAxis], Rotate[O_1, (3 * (360°) / 8), zAxis]], p_2) → B_2
  74. Intersect(Segment[Rotate[H_1, (3 * (360°) / 8), zAxis], Rotate[P_1, (3 * (360°) / 8), zAxis]], p_2) → C_2
  75. Intersect(Segment[Rotate[I_1, (3 * (360°) / 8), zAxis], Rotate[Q_1, (3 * (360°) / 8), zAxis]], p_2) → D_2
  76. Segment(V, R_1) → h_2
  77. Segment(R_1, S_1) → i_2
  78. Segment(S_1, T_1) → j_2
  79. Segment(T_1, U_1) → k_2
  80. Segment(U_1, V_1) → l_2
  81. Segment(V_1, W_1) → m_2
  82. Segment(W_1, Z_1) → n_2
  83. Segment(Z_1, A_2) → q_2
  84. Segment(A_2, B_2) → r_2
  85. Segment(B_2, C_2) → s_2
  86. Segment(C_2, D_2) → t_2
  87. Segment(D_2, W) → a_2
  88. Sequence(Rotate[l1, (nn * (360°) / 8), zAxis], nn, 1, 11) → l2
  89. Segment(O, I) → b_2
  90. Sequence(Rotate[vierhoek1, (nn * (360°) / 8), zAxis], nn, 4, 7) → l3
  91. Sequence(Rotate[vierhoek2, (nn * (360°) / 8), zAxis], nn, 4, 7) → l4
  92. Sequence(Rotate[vierhoek3, (nn * (360°) / 8), zAxis], nn, 4, 7) → l5
  93. Sequence(Rotate[vierhoek4, (nn * (360°) / 8), zAxis], nn, 4, 7) → l6
  94. Sequence(Rotate[vierhoek5, (nn * (360°) / 8), zAxis], nn, 4, 7) → l7
  95. Sequence(Rotate[driehoek1, (nn * (360°) / 8), zAxis], nn, 4, 7) → l8
  96. Segment(N, P) → e_2
  97. Sequence(Segment[Rotate[N, (nn * (360°) / 8), zAxis], Rotate[P, (nn * (360°) / 8), zAxis]], nn, 1, 7) → l9
  98. Segment(B, C) → f_3
  99. Segment(O, K) → t_3
  100. Segment(J_2, E_2) → a_3
  101. OrthogonalLine(I, a_3, space) → d_3
  102. Midpoint(a_3) → U_2
  103. Intersect(zAxis, d_3) → V_2
  104. CircleArc(V_2, E_2, J_2) → c_4
  105. Rotate(c_4, 90°, zAxis) → d_4
  106. Point(c_4) → W_2
  107. Point(c_4) → Z_2
  108. Point(c_4) → A_3
  109. Polygon(J_2, I, B) → driehoek2, b_4, f_4, i_4
  110. Segment(B, C) → g_4
  111. Line(W_2, g_4) → h_4
  112. Line(Z_2, g_4) → j_4
  113. Line(A_3, g_4) → k_4
  114. Polygon(C, I, J_2) → driehoek3, l_4, c_5, i_5
  115. Midpoint(a) → K_3
  116. Segment(K_3, V) → n_5
  117. Point(n_5) → L_3
  118. PointIn(zijvlakCDQP) → M_3
  119. PointIn(zijvlakCDQP) → N_3
  120. CircumcircleArc(M_3, L_3, N_3) → d_5
  121. Line(N_3, n_5) → p_5
  122. Line(M_3, n_5) → q_5
  123. Intersect(a, zijvlakCDQP) → O_3
  124. Segment(C, D) → r_5
  125. Intersect(p_5, r_5) → P_3
  126. Intersect(r_5, q_5) → Q_3
  127. Segment(N_3, P_3) → s_5
  128. Segment(M_3, Q_3) → t_5
  129. Translate(d_5, Vector[(0, 0, -0.75)]) → c_2
  130. Translate(C, Vector[(1.5 * vert)]) → C'
  131. Translate(D, Vector[(1.5 * vert)]) → D'
  132. Segment(C', D') → d_2
  133. Translate(P_3, Vector[(1.5 * vert)]) → F_2
  134. Translate(Q_3, Vector[(1.5 * vert)]) → G_2
  135. Translate(N_3, vert) → H_2
  136. Translate(M_3, vert) → I_2
  137. Segment(H_2, F_2) → g_3
  138. Segment(I_2, G_2) → h_3
  139. Point(n_5) → O_2
  140. Translate(veelhoek1, Vector[(0, 0, z(O_2))]) → veelhoek1'
  141. Translate(veelhoek1, Vector[(0, 0, z(C'))]) → veelhoek1'_1
  142. Polygon(C', D', Q, P) → vierhoek6, c', d', q_3, p_3
  143. Sequence(Rotate[vierhoek6, (nn * (360°) / 8), zAxis], nn, 1, 7) → l10
  144. Sequence(Rotate[c_2, (nn * (360°) / 8), zAxis], nn, 1, 7) → l11
  145. Sequence(Segment[Rotate[H_2, (nn * (360°) / 8), zAxis], Rotate[F_2, (nn * (360°) / 8), zAxis]], nn, 1, 7) → l12
  146. Sequence(Segment[Rotate[I_2, (nn * (360°) / 8), zAxis], Rotate[G_2, (nn * (360°) / 8), zAxis]], nn, 1, 7) → l13
  147. Line(R_2, O_2) → i_3
  148. Rotate(P_2, 90°, i_3) → S_2
  149. Midpoint(P, Q) → B_3
  150. Translate(Q, Vector[(0, 0, -0.81)]) → Q'
  151. Translate(P, Vector[(0, 0, -0.81)]) → P'
  152. Segment(Q', P') → j_3
  153. Rotate(Q', 90°, i_3) → Q''
  154. CircleArc(O_2, Q', Q'') → c_3
  155. Point(c_3) → C_3
  156. Point(c_3) → D_3
  157. Point(c_3) → E_3
  158. Point(c_3) → F_3
  159. Segment(V, G_3) → k_3
  160. Segment(V, G_3) → l_3
  161. Segment(G_3, H_3) → m_3
  162. Segment(H_3, I_3) → n_3
  163. Segment(I_3, J_3) → r_3
  164. Segment(J_3, Q') → s_3
  165. Mirror(G_3, p_4) → R_3
  166. Mirror(H_3, p_4) → S_3
  167. Mirror(I_3, p_4) → T_3
  168. Mirror(J_3, p_4) → U_3
  169. Line(V_3, Q') → b_3
  170. Line(W_3, P') → m_4
  171. Line(J_3, b_3) → n_4
  172. Line(I_3, b_3) → q_4
  173. Line(H_3, b_3) → r_4
  174. Line(G_3, b_3) → s_4
  175. Line(U_3, m_4) → t_4
  176. Line(T_3, m_4) → a_4
  177. Line(S_3, m_4) → e_4
  178. Line(R_3, m_4) → f_5
  179. Intersect(m_4, b_3) → Z_3
  180. Intersect(t_4, n_4) → A_4
  181. Intersect(a_4, q_4) → B_4
  182. Intersect(e_4, r_4) → C_4
  183. Intersect(s_4, f_5) → D_4
  184. Polygon(Z_3, Q', J_3, A_4) → vierhoek7, z_3, q', g_5, h_5
  185. Polygon(A_4, J_3, I_3, B_4) → vierhoek8, j_5, k_5, l_5, m_5
  186. Polygon(B_4, I_3, H_3, C_4) → vierhoek9, a_5, b_5, e_5, f_6
  187. Polygon(C_4, H_3, G_3, D_4) → vierhoek10, g_6, h_6, i_6, j_6
  188. Polygon(D_4, G_3, V) → driehoek4, v, k_6, l_6
  189. Polygon(P', Z_3, A_4, U_3) → vierhoek11, p', m_6, n_6, u_3
  190. Polygon(U_3, A_4, B_4, T_3) → vierhoek12, p_6, q_6, r_6, s_6
  191. Polygon(T_3, B_4, C_4, S_3) → vierhoek13, t_6, a_6, b_6, c_6
  192. Polygon(S_3, C_4, D_4, R_3) → vierhoek14, d_6, e_6, f_7, g_7
  193. Polygon(R_3, D_4, V) → driehoek5, v_1, h_7, i_7
  194. Segment(V, D_4) → j_7
  195. Segment(D_4, C_4) → k_7
  196. Segment(C_4, B_4) → l_7
  197. Segment(B_4, A_4) → m_7
  198. Segment(A_4, Z_3) → n_7
  199. Mirror(G_3, p_4) → E_4
  200. Mirror(H_3, p_4) → F_4
  201. Segment(E_4, F_4) → p_7
  202. Mirror(H_3, p_4) → G_4
  203. Mirror(I_3, p_4) → H_4
  204. Segment(G_4, H_4) → q_7
  205. Mirror(I_3, p_4) → I_4
  206. Mirror(J_3, p_4) → J_4
  207. Segment(I_4, J_4) → r_7
  208. Mirror(J_3, p_4) → K_4
  209. Mirror(Q', p_4) → Q''_1
  210. Segment(K_4, Q''_1) → s_7
  211. Sequence(Rotate[l14, (nn * 90°), zAxis], nn, 1, 3) → l15
  212. Sequence(Rotate[l16, (nn * 90°), zAxis], nn, 1, 3) → l17
  213. Sequence(Rotate[l18, (nn * 90°), zAxis], nn, 1, 3) → l19
  214. Sequence(Rotate[l20, (nn * 90°), zAxis], nn, 1, 3) → l21
  215. Point(n_7) → L_4
  216. Segment(L_4, Q') → t_7
  217. Segment(P', L_4) → a_7
  218. Sequence(Rotate[l22, (nn * 90°), zAxis], nn, 1, 3) → l23
  219. Polygon(I, K, J, L) → vierhoek15, i_8, k_8, j_8, l_8
  220. Translate(I, Vector[(0, 0, -1)]) → I'
  221. Translate(K, Vector[(0, 0, -1)]) → K'
  222. Translate(J, Vector[(0, 0, -1)]) → J'
  223. Translate(L, Vector[(0, 0, -1)]) → L'
  224. Rotate(vierhoek15'_1, (360°) / 8, zAxis) → vierhoek15''
  225. Segment(L_4, M_4) → b_7
  226. Sequence(Segment[Rotate[L_4, (nn * 90°), zAxis], Rotate[M_4, (nn * 90°), zAxis]], nn, 1, 3) → l24
  227. Polygon(A, B, 8) → veelhoek2, c_7, O_4, P_4, Q_4, R_4, S_4, d_7, e_7, f_8, g_8, h_8, m_8, n_8, N_4
  228. Segment(L, I) → p_8
  229. Segment(I, K) → q_8
  230. Midpoint(c_7) → T_4
  231. Midpoint(a) → U_4
  232. Midpoint(E, D) → V_4
  233. Midpoint(F, G) → W_4
  234. Midpoint(S_4, A) → Z_4
  235. Midpoint(B, C) → A_5
  236. Segment(W_4, T_4) → r_8
  237. Segment(W_4, U_4) → s_8
  238. Intersect(s, xAxis) → B_5
  239. Segment(A_5, B_5) → b_8
  240. Segment(B_5, V_4) → c_8
  241. Segment(T_4, V_4) → d_8
  242. Midpoint(b) → C_5
  243. Segment(C_5, Z_4) → e_8
  244. Segment(C_5, A_5) → f_9
  245. Segment(Z_4, U_4) → t_8
  246. Segment(O, S_4) → a_8
  247. Segment(O, A) → g_9
  248. Segment(O, B) → h_9
  249. Segment(O, C) → i_9
  250. Segment(O, D) → j_9
  251. Segment(O, E) → k_9
  252. Segment(O, F) → l_9
  253. Segment(O, G) → m_9
  254. Segment(V_4, K) → n_9
  255. Segment(W_4, J) → p_9
  256. Segment(Z_4, L) → q_9
  257. Intersect(a, p_8) → D_5
  258. Segment(A_5, D_5) → r_9
  259. Translate(l23, Vector[(0, 0, -2.32)]) → l23'
  260. Translate(T, Vector[(0, 0, -3.13)]) → T'
  261. Translate(S, Vector[(0, 0, -3.13)]) → S'
  262. Segment(T', S') → RibbeST'
  263. Sequence(Segment[Rotate[T', (nn * 90°), zAxis], Rotate[S', (nn * 90°), zAxis]], nn, 1, 3) → l25
  264. Rotate(T', (360°) / 8, zAxis) → T''
  265. Mirror(F_2, zAxis) → E_5
  266. Mirror(G_2, zAxis) → F_5
  267. Segment(T', E_5) → s_9
  268. Segment(F_5, T'') → t_9
  269. Sequence(Segment[Rotate[T', (nn * 90°), zAxis], Rotate[E_5, (nn * 90°), zAxis]], nn, 1, 3) → l26
  270. Sequence(Segment[Rotate[F_5, (nn * 90°), zAxis], Rotate[T'', (nn * 90°), zAxis]], nn, 1, 3) → l27
  271. Mirror(W_1, zAxis) → G_5
  272. Segment(W_1, G_5) → a_9
  273. Midpoint(W_1, G_5) → H_5
  274. Rotate(W_1, 90°, zAxis) → I_5
  275. Rotate(W_1, (-(90°)), zAxis) → J_5
  276. Segment(J_5, I_5) → b_9
  277. Rotate(G_5, 90°, b_9) → K_5
  278. CircleArc(H_5, G_5, K_5) → c_9
  279. Point(c_9) → L_5
  280. Point(c_9) → M_5
  281. Point(c_9) → N_5
  282. Point(c_9) → O_5
  283. Rotate(Q_5, ((-(360°))) / 8, zAxis) → U_5
  284. Rotate(R_5, ((-(360°))) / 8, zAxis) → V_5
  285. Rotate(S_5, ((-(360°))) / 8, zAxis) → W_5
  286. Rotate(T_5, ((-(360°))) / 8, zAxis) → Z_5
  287. Rotate(G_5, ((-(360°))) / 8, zAxis) → A_6
  288. Polygon(P_5, U_5, Q_5) → driehoek6, d_9, e_9, u_5
  289. Polygon(U_5, V_5, R_5, Q_5) → vierhoek16, f_{10}, v_5, g_{10}, h_{10}
  290. Polygon(V_5, W_5, S_5, R_5) → vierhoek17, i_{10}, w_5, j_{10}, k_{10}
  291. Polygon(W_5, Z_5, T_5, S_5) → vierhoek18, l_{10}, z_5, m_{10}, n_{10}
  292. Polygon(A_6, G_5, T_5, Z_5) → vierhoek19, p_{10}, q_{10}, r_{10}, s_{10}
  293. Point(l2) → B_6
  294. Polygon(A_6, B_6, G_5) → driehoek7, t_{10}, a_{10}, b_{10}
  295. Sequence(Rotate[l28, (nn * (360°) / 8), zAxis], nn, 1, 7) → l29
  296. Segment(A_6, Z_5) → c_{10}
  297. Segment(Z_5, W_5) → d_{10}
  298. Segment(W_5, V_5) → e_{10}
  299. Segment(V_5, U_5) → f_{11}
  300. Segment(U_5, P_5) → g_{11}
  301. Sequence(Rotate[l30, (nn * (360°) / 8), zAxis], nn, 1, 7) → l31

AI Drawing Prompt Reference

Draw a pentagonal prism by first creating a pentagon base, then generating the prism's faces and edges through rotation and translation. Specifically, create the pentagon's vertices, rotate to generate new vertices, use these to create polygons and segments, and finally construct the prism's faces using these segments and polygons.
The prompt above was compiled from the original drawing commands and is for reference only.