正方体的展开图

GeoGebra 命令及参数

1. Line(A, B) → g
2. Line(B, C) → r
3. Line(A, D) → s
4. Line(D, C) → t
5. Rotate(U_1, (-rt), g) → K_6
6. Rotate(V_1, (-rt), g) → L_6
7. Rotate(D, rt, t) → D'
8. Rotate(C_2, rt, t) → M_6
9. Rotate(D_2, rt, t) → N_6
10. Rotate(B_2, (-rt), r) → O_6
11. Rotate(A_2, (-rt), r) → P_6
12. Rotate(Z_1, rt, s) → Q_6
13. Rotate(W_1, rt, s) → R_6
14. Polygon(A, B, C, D) → q1, a, b, c, d
15. Polygon(L_6, B, A, K_6) → q2, l_6, b_2, a_1, k_6
16. Polygon(P_6, O_6, C, B) → q3, p_6, o_6, c_2, b_3
17. Polygon(R_6, A, D, Q_6) → q4, r_6, a_2, d_1, q_6
18. Polygon(N_6, M_6, D, C) → q5, n_6, m_6, d_2, c_7
19. Line(I_1, L_1) → i_1
20. Line(J_1, K_1) → j_1
21. Rotate(P_5, rt, i_1) → S_6
22. Rotate(O_5, rt, i_1) → T_6
23. Rotate(Q_5, (-rt), j_1) → U_6
24. Rotate(R_5, (-rt), j_1) → V_6
25. Polygon(J_1, K_1, L_1, I_1) → q6, k_1, l_1, q_1, e_1
26. Polygon(V_6, J_1, K_1, U_6) → q7, v_6, f_2, k_2, u_6
27. Polygon(T_6, I_1, L_1, S_6) → q8, t_6, n_2, e_2, s_6
28. Rotate(V_5, (-rt), g) → W_6
29. Rotate(W_5, (-rt), g) → Z_6
30. Polygon(Z_6, J_1, I_1, W_6) → q9, z_6, l_3, n_3, w_6
31. Line(M_6, N_6) → r_3
32. Circle(M_6, 1, r_3) → e_3
33. Circle(N_6, 1, r_3) → s_3
34. Ray(D, M_6) → k_4
35. Ray(C, N_6) → m_4
36. Intersect(k_4, e_3) → A_7, B_7
37. Intersect(m_4, s_3) → C_7, D_7
38. Rotate(A_7, rt, r_3) → E_7
39. Rotate(C_7, rt, r_3) → F_7
40. Polygon(E_7, M_6, N_6, F_7) → q10, e_7, p_4, s_4, f_7
41. Line(Z_6, W_6) → i_5
42. Circle(Z_6, 1, i_5) → p_5
43. Circle(W_6, 1, i_5) → q_5
44. Ray(J_1, Z_6) → j_5
45. Ray(I_1, W_6) → l_5
46. Intersect(j_5, p_5) → E_2, F_2
47. Intersect(l_5, q_5) → G_7, H_7
48. Rotate(G_7, rt, i_5) → I_7
49. Rotate(E_2, rt, i_5) → J_7
50. Polygon(J_7, Z_6, W_6, I_7) → q11, j_7, r_5, s_5, i_7
51. Line(J_7, I_7) → t_5
52. Circle(J_7, 1, t_5) → e_6
53. Circle(I_7, 1, t_5) → g_6
54. Ray(W_6, I_7) → a_5
55. Ray(Z_6, J_7) → g_7
56. Intersect(a_5, g_6) → S_5, T_5
57. Intersect(g_7, e_6) → U_5, Z_5
58. Rotate(U_5, rt, t_5) → K_7
59. Rotate(S_5, rt, t_5) → L_7
60. Polygon(J_7, I_7, L_7, K_7) → q12, h_7, k_7, l_7, m_7
61. Polygon(K, L, I, J) → q13, k, l, i, j
62. Rotate(J_5, (-rt), g) → M_7
63. Rotate(I_5, (-rt), g) → N_7
64. Polygon(T_1, Q_1, R_1, S_1) → q14, t_1, r_1, s_1, f_4
65. Polygon(N_7, S_1, R_1, M_7) → q15, n_7, g_4, h_4, a_4
66. Ray(R_1, M_7) → b_4
67. Ray(S_1, N_7) → c_4
68. Circle(N_7, 1, i_5) → d_4
69. Circle(M_7, 1, i_5) → e_4
70. Intersect(c_4, d_4) → G_5, H_5
71. Intersect(b_4, e_4) → O_7, P_7
72. Rotate(G_5, rt, i_5) → Q_7
73. Rotate(O_7, rt, i_5) → R_7
74. Polygon(Q_7, N_7, M_7, R_7) → q16, q_7, f_5, g_5, r_7
75. Line(Q_1, R_1) → h_5
76. Line(T_1, S_1) → k_5
77. Rotate(F_5, (-rt), h_5) → S_7
78. Rotate(E_5, (-rt), h_5) → T_7
79. Polygon(R_1, Q_1, S_7, T_7) → q17, m_5, n_5, s_7, t_7
80. Rotate(K_5, rt, k_5) → U_7
81. Rotate(L_5, rt, k_5) → V_7
82. Polygon(V_7, T_1, S_1, U_7) → q18, v_7, e_5, p_7, u_7
83. Rotate(N_5, rt, k_5) → W_7
84. Rotate(W_7, (-rt), v_7) → Z_7
85. Rotate(M_5, (-rt), v_7) → A_8
86. Polygon(V_7, T_1, A_8, Z_7) → q19, a_7, b_7, a_8, z_7
87. Rotate(C_4, (-rt), k) → B_8
88. Rotate(D_4, (-rt), k) → C_8
89. Polygon(C_8, B_8, L, K) → q20, c_8, b_8, l_8, k_8
90. Line(K, L) → d_7
91. Rotate(H_4, (-rt), d_7) → D_8
92. Rotate(D_8, (-rt), k_8) → E_8
93. Rotate(G_4, (-rt), k_8) → F_8
94. Polygon(E_8, C_8, K, F_8) → q21, e_8, f_8, k_9, g_8
95. Line(B_8, C_8) → h_8
96. Circle(B_8, 1, h_8) → d_8
97. Circle(C_8, 1, h_8) → p_8
98. Ray(L, B_8) → i_8
99. Intersect(i_8, d_8) → G_8, H_8
100. Ray(K, C_8) → j_8
101. Intersect(j_8, p_8) → I_8, J_8
102. Rotate(G_8, rt, h_8) → E_4
103. Rotate(I_8, rt, h_8) → F_4
104. Polygon(E_4, B_8, C_8, F_4) → q22, m_8, n_8, q_8, r_8
105. Line(I, L) → s_8
106. Rotate(Z_3, rt, s_8) → K_8
107. Rotate(W_3, rt, s_8) → L_8
108. Polygon(I, L_8, K_8, L) → q23, i_9, t_8, f_9, l_9
109. Rotate(A_4, rt, s_8) → M_8
110. Rotate(M_8, rt, i_9) → N_8
111. Rotate(B_4, rt, i_9) → O_8
112. Polygon(O_8, I, L_8, N_8) → q24, o_8, i_{10}, g_9, h_9
113. Line(O, P) → j_9
114. Line(N, M) → m_9
115. Polygon(N, O, P, M) → q25, n, o, p, m
116. Rotate(I_4, rt, s_8) → P_8
117. Rotate(K_4, rt, s_8) → Q_8
118. Rotate(L_4, rt, s_8) → R_8
119. Polygon(Q_8, M, P, R_8) → q26, i_4, m_{10}, p_9, j_4
120. Rotate(P_8, (-rt), i_4) → S_8
121. Rotate(J_4, (-rt), i_4) → T_8
122. Polygon(S_8, T_8, M, Q_8) → q27, l_4, n_4, m_{11}, q_4
123. Rotate(M_4, (-rt), j_9) → U_8
124. Rotate(N_4, (-rt), j_9) → V_8
125. Polygon(P, O, V_8, U_8) → q28, p_{10}, o_2, v_8, u_8
126. Line(U_8, V_8) → r_4
127. Circle(U_8, 1, r_4) → c_9
128. Circle(V_8, 1, r_4) → d_9
129. Ray(P, U_8) → n_9
130. Ray(O, V_8) → q_9
131. Intersect(n_9, c_9) → W_8, Z_8
132. Intersect(q_9, d_9) → A_9, B_9
133. Rotate(W_8, rt, r_4) → C_9
134. Rotate(A_9, rt, r_4) → D_9
135. Polygon(C_9, U_8, V_8, D_9) → q29, r_9, s_9, t_9, a_9
136. Rotate(Q_4, (-rt), j_9) → E_9
137. Circle(E_9, 1, r_4) → e_9
138. Line(E_9, t_9) → b_9
139. Intersect(b_9, e_9, 1) → F_9
140. Rotate(F_9, (-rt), t_9) → O_4
141. Rotate(E_9, (-rt), t_9) → P_4
142. Polygon(O_4, P_4, V_8, D_9) → q30, o_4, f_{10}, g_{10}, h_{10}
143. Polygon(E, F, G, H) → q31, e, f, g_2, h
144. Rotate(N_2, (-rt), j_9) → R_4
145. Rotate(O_2, (-rt), j_9) → G_9
146. Polygon(R_4, H, G, G_9) → q32, h_2, h_{11}, g_{11}, i_2
147. Circle(R_4, 1, r_4) → p_2
148. Circle(G_9, 1, r_4) → c_{10}
149. Ray(G, G_9) → j_2
150. Ray(H, R_4) → l_2
151. Intersect(l_2, p_2) → M_2, P_2
152. Intersect(j_2, c_{10}) → H_9, I_9
153. Rotate(M_2, rt, r_4) → J_9
154. Rotate(H_9, rt, r_4) → K_9
155. Polygon(J_9, R_4, G_9, K_9) → q33, m_2, j_{10}, k_{10}, l_{10}
156. Line(H, E) → n_{10}
157. Rotate(H_2, (-rt), n_{10}) → L_9
158. Rotate(G_2, (-rt), n_{10}) → M_9
159. Polygon(M_9, E, H, L_9) → q34, q_{10}, e_{10}, h_{12}, r_{10}
160. Rotate(L_2, rt, m_9) → N_9
161. Rotate(K_2, rt, m_9) → O_9
162. Rotate(I_2, rt, m_9) → P_9
163. Polygon(F, E, N_9, O_9) → q35, f_{11}, e_{11}, s_{10}, o_9
164. Rotate(P_9, (-rt), o_9) → Q_9
165. Rotate(J_2, (-rt), o_9) → R_9
166. Polygon(R_9, F, O_9, Q_9) → q36, t_{10}, f_{12}, a_{10}, b_{10}
167. Polygon(P_1, M_1, N_1, O_1) → q37, p_1, m_1, n_1, o_1
168. Rotate(H_6, (-rt), j_1) → S_9
169. Rotate(G_6, (-rt), j_1) → T_9
170. Rotate(F_6, (-rt), j_1) → U_9
171. Polygon(T_9, O_1, N_1, U_9) → q38, f_6, h_6, i_6, u_9
172. Rotate(S_9, (-rt), f_6) → V_9
173. Rotate(I_6, (-rt), f_6) → W_9
174. Polygon(V_9, W_9, O_1, T_9) → q39, v_9, w_9, j_6, a_6
175. Rotate(A_6, rt, m_9) → Z_9
176. Rotate(E_6, rt, m_9) → A_{10}
177. Rotate(B_6, rt, m_9) → B_{10}
178. Polygon(N_1, B_{10}, Z_9, M_1) → q40, b_6, c_6, z_9, d_6
179. Rotate(D_6, rt, m_9) → C_{10}
180. Rotate(C_6, rt, m_9) → D_{10}
181. Line(Z_9, M_1) → d_{10}
182. Rotate(D_{10}, rt, d_{10}) → E_{10}
183. Rotate(A_{10}, rt, d_{10}) → F_{10}
184. Rotate(J_6, rt, d_{10}) → G_{10}
185. Polygon(F_{10}, G_{10}, M_1, Z_9) → q41, i_{11}, j_{11}, k_{11}, l_{11}
186. Line(Z_9, F_{10}) → n_{11}
187. Rotate(E_{10}, rt, n_{11}) → H_{10}
188. Rotate(C_{10}, rt, n_{11}) → I_{10}
189. Polygon(Z_9, F_{10}, H_{10}, I_{10}) → q42, p_{11}, q_{11}, r_{11}, s_{11}
190. Line(C_1, D_1) → t_{11}
191. Line(B_1, A_1) → a_{11}
192. Rotate(D_3, rt, t_{11}) → J_{10}
193. Rotate(E_3, rt, t_{11}) → K_{10}
194. Rotate(F_3, rt, t_{11}) → L_{10}
195. Polygon(D_1, C_1, A_1, B_1) → q43, b_1, c_1, f_3, g_3
196. Polygon(K_{10}, C_1, D_1, L_{10}) → q44, h_3, i_3, j_3, k_3
197. Line(K_{10}, C_1) → c_3
198. Rotate(J_{10}, (-rt), c_3) → M_{10}
199. Rotate(C_3, (-rt), c_3) → N_{10}
200. Polygon(M_{10}, N_{10}, C_1, K_{10}) → q45, d_3, b_{11}, c_{11}, d_{11}
201. Rotate(I_3, rt, a_{11}) → O_{10}
202. Rotate(L_3, rt, a_{11}) → P_{10}
203. Rotate(G_3, rt, a_{11}) → Q_{10}
204. Polygon(O_{10}, B_1, A_1, P_{10}) → q46, o_{10}, g_{12}, i_{12}, j_{12}
205. Rotate(H_3, (-rt), o_{10}) → R_{10}
206. Rotate(Q_{10}, (-rt), o_{10}) → S_{10}
207. Polygon(R_{10}, B_1, O_{10}, S_{10}) → q47, k_{12}, l_{12}, m_{12}, n_{12}
208. Line(O_{10}, P_{10}) → p_{12}
209. Circle(P_{10}, 1, p_{12}) → c_{12}
210. Circle(O_{10}, 1, p_{12}) → d_{12}
211. Ray(A_1, P_{10}) → q_{12}
212. Ray(B_1, O_{10}) → r_{12}
213. Intersect(r_{12}, d_{12}) → J_3, K_3
214. Intersect(q_{12}, c_{12}) → T_{10}, U_{10}
215. Rotate(J_3, rt, p_{12}) → V_{10}
216. Rotate(T_{10}, rt, p_{12}) → W_{10}
217. Polygon(W_{10}, P_{10}, O_{10}, V_{10}) → q48, w_{10}, s_{12}, t_{12}, v_{10}
218. Rotate(P_3, rt, s_8) → Z_{10}
219. Rotate(O_3, rt, s_8) → A_{11}
220. Rotate(N_3, rt, s_8) → B_{11}
221. Rotate(M_3, rt, s_8) → C_{11}
222. Polygon(W, Z, U, V) → q49, w, z_1, u, v
223. Polygon(B_{11}, V, U, C_{11}) → q50, m_3, v_1, u_1, p_3
224. Rotate(V_3, rt, t_{11}) → D_{11}
225. Rotate(S_3, rt, t_{11}) → E_{11}
226. Polygon(E_{11}, U, Z, D_{11}) → q51, q_3, u_3, z_3, t_3
227. Circle(E_{11}, 1, t_3) → e_{12}
228. Circle(D_{11}, 1, t_3) → c_{13}
229. Ray(Z, D_{11}) → a_{12}
230. Ray(U, E_{11}) → b_{12}
231. Intersect(b_{12}, e_{12}) → F_{11}, G_{11}
232. Intersect(a_{12}, c_{13}) → H_{11}, I_{11}
233. Rotate(H_{11}, (-rt), t_3) → J_{11}
234. Rotate(F_{11}, (-rt), t_3) → K_{11}
235. Polygon(J_{11}, D_{11}, E_{11}, K_{11}) → q52, f_{13}, g_{13}, h_{13}, i_{13}
236. Rotate(A_{11}, (-rt), m_3) → L_{11}
237. Rotate(R_3, (-rt), m_3) → M_{11}
238. Polygon(B_{11}, L_{11}, M_{11}, V) → q53, j_{13}, k_{13}, l_{13}, v_3
239. Circle(L_{11}, 1, k_{13}) → d_{13}
240. Circle(M_{11}, 1, k_{13}) → e_{13}
241. Ray(B_{11}, L_{11}) → m_{13}
242. Ray(V, M_{11}) → n_{13}
243. Intersect(m_{13}, d_{13}) → N_{11}, O_{11}
244. Intersect(n_{13}, e_{13}) → P_{11}, Q_{11}
245. Rotate(N_{11}, (-rt), k_{13}) → R_{11}
246. Rotate(P_{11}, (-rt), k_{13}) → S_{11}
247. Polygon(R_{11}, S_{11}, M_{11}, L_{11}) → q54, p_{13}, q_{13}, r_{13}, s_{13}
248. Line(G_1, H_1) → t_{13}
249. Line(F_1, E_1) → a_{13}
250. Rotate(R_2, rt, a_{13}) → T_{11}
251. Rotate(Q_2, rt, a_{13}) → U_{11}
252. Rotate(T_2, (-rt), r) → V_{11}
253. Rotate(S_2, (-rt), r) → W_{11}
254. Polygon(G_1, H_1, E_1, F_1) → q55, g_1, h_1, f_1, q_2
255. Polygon(T_{11}, F_1, E_1, U_{11}) → q56, r_2, s_2, t_2, u_{11}
256. Polygon(V_{11}, G_1, F_1, W_{11}) → q57, v_{11}, a_3, b_{13}, w_{11}
257. Rotate(V_2, (-rt), t_{13}) → Z_{11}
258. Rotate(W_2, (-rt), t_{13}) → A_{12}
259. Rotate(B_3, (-rt), t_{13}) → B_{12}
260. Polygon(A_{12}, H_1, G_1, B_{12}) → q58, f_{14}, g_{14}, h_{14}, i_{14}
261. Circle(A_{12}, 1, i_{14}) → c_{14}
262. Circle(B_{12}, 1, i_{14}) → d_{14}
263. Ray(H_1, A_{12}) → j_{14}
264. Ray(G_1, B_{12}) → k_{14}
265. Intersect(j_{14}, c_{14}) → Z_2, A_3
266. Intersect(k_{14}, d_{14}) → C_{12}, D_{12}
267. Rotate(Z_2, (-rt), i_{14}) → E_{12}
268. Rotate(C_{12}, (-rt), i_{14}) → F_{12}
269. Polygon(E_{12}, A_{12}, B_{12}, F_{12}) → q59, l_{14}, m_{14}, n_{14}, p_{14}
270. Rotate(Z_{11}, (-rt), f_{14}) → G_{12}
271. Rotate(U_2, (-rt), f_{14}) → H_{12}
272. Polygon(H_{12}, H_1, A_{12}, G_{12}) → q60, q_{14}, r_{14}, s_{14}, t_{14}
273. Rotate(U_4, rt, a_{13}) → I_{12}
274. Rotate(S_4, rt, a_{13}) → J_{12}
275. Rotate(T_4, rt, a_{13}) → K_{12}
276. Polygon(Q, R, S, T) → q61, q, r_{15}, s_{15}, t_4
277. Polygon(K_{12}, R, Q, J_{12}) → q62, b_5, r_{16}, q_{15}, c_5
278. Rotate(I_{12}, (-rt), q_{15}) → L_{12}
279. Rotate(V_4, (-rt), q_{15}) → M_{12}
280. Polygon(J_{12}, Q, M_{12}, L_{12}) → q63, d_5, q_{16}, a_{14}, b_{14}
281. Rotate(W_4, (-rt), t_{13}) → N_{12}
282. Rotate(B_5, (-rt), t_{13}) → O_{12}
283. Rotate(C_5, (-rt), t_{13}) → P_{12}
284. Polygon(N_{12}, T, S, O_{12}) → q64, e_{14}, t_{15}, s_{16}, o_{12}
285. Circle(O_{12}, 1, o_{12}) → c_{15}
286. Circle(N_{12}, 1, o_{12}) → d_{15}
287. Ray(T, N_{12}) → f_{15}
288. Ray(S, O_{12}) → g_{15}
289. Intersect(f_{15}, d_{15}) → Q_{12}, R_{12}
290. Intersect(g_{15}, c_{15}) → S_{12}, T_{12}
291. Rotate(Q_{12}, (-rt), o_{12}) → U_{12}
292. Rotate(S_{12}, (-rt), o_{12}) → V_{12}
293. Polygon(U_{12}, N_{12}, O_{12}, V_{12}) → q65, u_{12}, h_{15}, i_{15}, v_{12}
294. Circle(P_{12}, 1, h_{15}) → e_{15}
295. Line(P_{12}, i_{15}) → j_{15}
296. Intersect(j_{15}, e_{15}) → W_{12}, Z_{12}
297. Rotate(W_{12}, (-rt), i_{15}) → A_{13}
298. Rotate(P_{12}, (-rt), i_{15}) → B_{13}
299. Polygon(A_{13}, B_{13}, O_{12}, V_{12}) → q66, k_{15}, l_{15}, m_{15}, n_{15}