球面上的弦线网络：正二十面体与球体的几何构造

GeoGebra 命令及参数

1. Point(Circle[Midpoint[A, B], (Distance[A, B] * sqrt(3) / 2), Segment[A, B]]) → C
2. Icosahedron(A, B, C) → a, D, faceABC, faceACF, faceAFG, faceADG, faceABD, faceBDH, faceBEH, faceBCE, faceCEI, faceCFI, E, faceEHK, faceEIK, faceIKL, faceFIL, faceHJK, faceJKL, faceGJL, faceFGL, faceDHJ, faceDGJ, F, areteAC, areteAB, areteBC, areteAF, areteCF, areteAG, areteFG, areteAD, areteDG, areteBD, G, areteBH, areteDH, areteBE, areteEH, areteCE, areteCI, areteEI, areteFI, areteEK, areteHK, H, areteIK, areteIL, areteKL, areteFL, areteJK, areteHJ, areteJL, areteGL, areteGJ, areteDJ, I, J, K, L
3. Midpoint(D, I) → M
4. Sphere(M, A) → b
5. PointIn(b) → P
6. OrthogonalLine(M, xOyPlane) → f
7. Plane(J, f) → c
8. OrthogonalLine(M, c) → g
9. Intersect(f, b) → N, O
10. Angle(P, M, O) → α
11. Sequence(Rotate[Rotate[J, (-a), g], (3 * a), f], a, 0, α, α / 9) → L_1
12. Rotate(L_1, (2 * π / 3), f) → L_2
13. Sequence(Polygon[M, Element[L_1, i], Element[L_2, i]], i, 1, Length[L_1], n) → L_3
14. Rotate(L_3, (2 * π / 3), f) → L_4
15. Rotate(L_3, (-2 * π / 3), f) → L_5
16. Sequence(Rotate[{L_3, L_4, L_5}, ((a * 2) * π / 5), Line[M, J]], a, 1, 4) → L_6
17. Sequence(Rotate[{L_3, L_4, L_5}, ((a * 2) * π / 5), Line[M, K]], a, 2, 4) → L_7
18. Mirror(L_6, M) → L_8
19. Sequence(Rotate[{L_3, L_4, L_5}, ((a * 2) * π / 5), Line[M, L]], a, 2, 3) → L_9
20. Mirror(L_9, M) → L_{10}
21. Rotate({L_3, L_4, L_5}, (4 * π / 5), Line[M, J]) → L_{11}
22. Rotate(L_{11}, (4 * π / 5), Line[M, D]) → L_{12}
23. Rotate(L_{11}, (2 * π / 5), Line[M, D]) → L_{13}
24. Rotate(L_{11}, (6 * π / 5), Line[M, G]) → L_{14}
25. Rotate(L_{12}, (-2 * π / 5), Line[M, A]) → L_{15}