正方形纸片折成开式纸盒的体积优化问题

GeoGebra 命令及参数

1. Polygon((0, 0), (k, 0), 4) → poly1
2. Intersect(xAxis, yAxis) → B
3. Line(E, G) → b
4. Line(F, H) → c
5. Line(E, F) → d
6. Line(G, H) → e
7. Intersect(d, poly1) → I, J
8. Intersect(e, poly1) → K, L
9. Intersect(b, poly1) → M, N
10. Intersect(c, poly1) → O, P
11. Segment(K, L) → g
12. Segment(M, N) → h
13. Segment(O, P) → i
14. Polygon(I, E, G, K) → poly2, i_1, e_1, g_1, k_3
15. Polygon(E, F, H, G) → poly3, e_2, f_1, h_1, g_2
16. Polygon(M, O, F, E) → poly4, m, o, f_2, e_3
17. Polygon(F, J, L, H) → poly5, f_3, j, l_3, h_2
18. Polygon(G, H, P, N) → poly6, g_3, h_3, p, n
19. Segment(A, C) → q
20. Segment(A, B) → r
21. Segment(C, D) → s
22. Segment(B, D) → t
23. Segment(I, E) → a_1
24. Segment(K, G) → b_1
25. Segment(G, N) → c_1
26. Segment(H, P) → d_1
27. Segment(H, L) → j_1
28. Segment(F, J) → k_1
29. Segment(F, O) → l_1
30. Segment(M, E) → m_1
31. Polygon(A, I, E, M) → poly7, a_2, i_2, e_4, m_2
32. Polygon(K, G, N, C) → poly8, k_2, g_4, n_1, c_2
33. Polygon(H, L, D, P) → poly9, h_4, l_2, d_2, p_1
34. Polygon(O, F, J, B) → poly10, o_1, f_4, j_2, b_2
35. Polygon(E, F, H, G) → poly11, q_1, r_1, s_1, t_1
36. Prism(poly11, a) → u, Q, edgeBQ, edgeAR, edgeCS, edgeDT, edgeQR, edgeRS, edgeST, edgeQT, R, S, T, faceABQR, faceACSR, faceCDTS, faceBDTQ, faceQRST
37. Net(u, fold) → v, U, F_1, G_1, H_1, I_1, J_1, faceUVWZ, face1, face3, face4, face2, V, face5, edgeUV, edgeVW, edgeWZ, edgeUZ, edge1, edge9, edge3, edge4, edge12, W, edge5, edge6, edge13, edge7, edge8, edge14, edge2, edge11, edge15, edge10, Z, A_1, B_1, C_1, D_1, E_1
38. Segment(O, B) → n_2
39. Segment(B, J) → p_2
40. Volume(u) → w
41. Segment(E, F) → q_2
42. Textfield(f) → inputBox1
43. If(k ≟ 12, Text[k, S_1], Text["k", S_1]) → text5
44. If(k ≟ 12, Text[k, T_1], Text["k", T_1]) → text6