柏拉图立体展开图：探索立体几何的平面表示

GeoGebra 命令及参数

1. Polygon(A, B, 3, xOyPlane) → poly1, f, g, h, C
2. Icosahedron(poly1, true) → a, D, faceACF, faceAFG, faceADG, faceABD, faceBDH, faceBEH, faceBCE, faceCEI, faceCFI, faceEHK, E, faceEIK, faceIKL, faceFIL, faceHJK, faceJKL, faceGJL, faceFGL, faceDHJ, faceDGJ, edgeAF, F, edgeCF, edgeAG, edgeFG, edgeAD, edgeDG, edgeBD, edgeBH, edgeDH, edgeBE, edgeEH, G, edgeCE, edgeCI, edgeEI, edgeFI, edgeEK, edgeHK, edgeIK, edgeIL, edgeKL, edgeFL, H, edgeJK, edgeHJ, edgeJL, edgeGL, edgeGJ, edgeDJ, I, J, K, L
3. Polygon(M, N, 4) → poly2, i, j, k, l, O, P
4. Cube(poly2, true) → b, Q, edgeMQ, edgePT, edgeQT, edgeQR, edgeNR, edgeRS, edgeOS, edgeST, R, S, T, faceMPTQ, faceMNRQ, faceNOSR, faceOPTS, faceQRST
5. Polygon(U, V, 3, xOyPlane) → poly3, m, n, p, W
6. Tetrahedron(poly3, true) → c, Z, faceUWZ, faceUVZ, faceVWZ, edgeUZ, edgeWZ, edgeVZ
7. Polygon(A_1, B_1, 3) → poly4, q, r, s, C_1
8. Octahedron(poly4, true) → d, D_1, face7, edge2, edge6, edge1, edge8, edge3, edge4, edge7, edge5, edge9, E_1, F_1, face2, face3, face1, face5, face4, face6
9. Polygon(G_1, H_1, 5) → poly5, t, e, f_1, g_1, h_1, I_1, J_1, K_1
10. Dodecahedron(poly5, true) → o, L_1, U_1, V_1, W_1, Z_1, A_2, B_2, face9, face8, face10, face11, M_1, face12, face16, face17, face13, face14, face15, face18, edge10, edge14, edge22, N_1, edge24, edge23, edge15, edge11, edge16, edge17, edge12, edge18, edge19, edge13, O_1, edge20, edge21, edge28, edge34, edge29, edge31, edge25, edge30, edge26, edge32, P_1, edge27, edge33, Q_1, R_1, S_1, T_1
11. Net(b, u) → v, C_2, L_2, M_2, N_2, O_2, P_2, face19, face23, face21, face20, face22, D_2, face24, edge36, edge35, edge39, edge42, edge44, edge50, edge46, edge45, edge47, E_2, edge37, edge38, edge48, edge40, edge41, edge49, edge43, edge52, edge53, edge51, F_2, G_2, H_2, I_2, J_2, K_2
12. Net(a, u) → w, Q_2, B_3, C_3, D_3, E_3, F_3, G_3, H_3, I_3, J_3, K_3, R_2, L_3, M_3, N_3, face25, face30, face34, face33, face27, face28, face29, S_2, face26, face31, face32, face37, face38, face40, face43, face39, face41, face44, T_2, face42, face36, face35, edge55, edge54, edge60, edge63, edge67, edge87, edge68, U_2, edge65, edge66, edge69, edge56, edge71, edge57, edge58, edge59, edge75, edge61, V_2, edge77, edge62, edge64, edge89, edge79, edge76, edge78, edge82, edge84, edge83, W_2, edge94, edge90, edge80, edge81, edge85, edge86, edge91, edge93, edge92, edge88, Z_2, edge72, edge74, edge73, edge70, A_3
13. Net(o, u) → a_1, O_3, Z_3, A_4, B_4, C_4, D_4, E_4, F_4, G_4, H_4, I_4, P_3, J_4, K_4, L_4, M_4, N_4, O_4, P_4, Q_4, R_4, S_4, Q_3, T_4, U_4, V_4, W_4, Z_4, A_5, B_5, C_5, D_5, face45, R_3, face50, face47, face46, face48, face49, face55, face54, face51, face52, face53, S_3, face56, edge96, edge95, edge99, edge102, edge105, edge107, edge132, edge130, edge109, T_3, edge108, edge110, edge111, edge97, edge98, edge116, edge117, edge100, edge101, edge122, U_3, edge123, edge103, edge104, edge128, edge129, edge106, edge133, edge136, edge137, edge134, V_3, edge135, edge142, edge143, edge131, edge112, edge114, edge115, edge113, edge118, edge120, W_3, edge121, edge119, edge124, edge126, edge127, edge125, edge138, edge140, edge141, edge139
14. Net(c, u) → b_1, E_5, face58, edge145, edge144, edge148, edge150, edge152, edge151, edge146, edge147, edge149, F_5, G_5, H_5, I_5, J_5, face57, face60, face59
15. Net(d, u) → c_1, Q_5, B_6, face61, face65, face67, face63, face64, face62, face66, face68, edge154, R_5, edge153, edge158, edge160, edge163, edge166, edge164, edge162, edge155, edge165, edge156, S_5, edge157, edge159, edge161, edge168, edge167, edge169, T_5, U_5, V_5, W_5, Z_5, A_6