固定对顶点的多面体（立方体、旋三角柱、十二面体）顶点的极值分布

GeoGebra 命令及参数

1. Text("" + Um1) → txt_p
2. LaTeX(Um1) → lll1_1
3. LaTeX(Um0) → lll0
4. Sphere(O, R) → p1
5. Textfield(n) → InputBox1
6. Textfield(i0) → InputBox2
7. Text(r) → Txtr
8. Textfield(k_1) → InputBox4
9. UnicodeToLetter(34) → u34
10. Textfield(k_2) → InputBox5
11. TableText(ltxt0, ltxt1, "v") → textltxt01
12. PointIn(p1) → A
13. Append(A, Sequence[((random(), random(), random()) * R), i, 2, n]) → l2s
14. Text(("(up\; to\; 10^{-15})\;\\ accuracy= " * ScientificText[cc, 3]), C, true, true) → text5r
15. Zip(Vector[a, a + UnitVector[a]], a, lP') → lVector1
16. Textfield(scale) → InputBox6
17. TableText(Append["i", 1…n], Append[" \fgcolor{orange}{GM :Δφ_i}, rad", l1], Append["\fgcolor{magenta}{GC :Δφ_i} , rad", l1c], "v") → text23
18. If(bu, "Animation", "Stop") → bue0
19. Zip(Vector[a, a + (1.5 * UnitVector[b])], a, lP', b, Wi_P) → lVector3
20. Zip(Vector[a, a + (1.5 * UnitVector[b])], a, lP', b, Wi_Pc) → lVector2
21. TableText({Join[{{"n"}, Sequence[i, i, 4, 69 + 3]}], Join[{{" p_n=P_n/[R*n*(n-1)/2]"}, lp}]}, "vl") → txt_lp
22. Sum(Flatten[Sequence[Append[Sequence[Element[txt_p, i], i, m1(k), m2(k)], " "], k, 1, 5]]) → txtUm1
23. Textfield(n1) → InputBox3
24. Text("\;\;\;\;\;\;\;\;\;\;\;\;\;\fgcolor{" + (If[c', "orange", "brown"]) + "} \boxed{ " + c' + ("}\;\;\;\; \;\;\;\;\; \\\;\; ( accuracy- up\; to\;\; 2.*10^{" - k_2) + ("\;})\;\\\;\; ➤➤➤\;\;\;\scalebox{1.3}{ " + (ScientificText[cc, 3])) + "}\;█ ", C, true, true) → text9
25. Zip(Segment[Element[lP', y(a)], Element[lP', z(a)]], a, ll1bb(1)) → ll1
26. Zip(Segment[Element[lP', y(a)], Element[lP', z(a)]], a, ll1bb(2)) → ll2
27. Zip(Segment[Element[lP', y(a)], Element[lP', z(a)]], a, ll1bb(3)) → ll3
28. Zip(Segment[Element[lP', y(a)], Element[lP', z(a)]], a, ll1bb(4)) → ll4
29. Zip(Segment[Element[lP', y(a)], Element[lP', z(a)]], a, ll1bb(5)) → ll5
30. Zip(Segment[Element[lP', y(a)], Element[lP', z(a)]], a, ll1bb(6)) → ll6