Dodecahedron Sphere Construction

GeoGebra Commands & Parameters

1. Point(xAxis) → A
2. Point(xAxis) → B
3. Point(Circle[((A * (1 - sqrt(5))) + (B * (3 + sqrt(5)))) / 4, (Distance[A, B] * sqrt(10 + (2 * sqrt(5))) / 4), Segment[A, B]]) → C
4. Dodecahedron(A, B, C) → a, D, M, N, O, P, Q, R, S, T, faceABCDE, faceAEIOJ, E, faceABFKJ, faceBCGLF, faceCDHMG, faceDEINH, faceINSTO, faceJKPTO, faceFKPQL, faceGLQRM, faceHMRSN, facePQRST, F, edgeAE, edgeAB, edgeBC, edgeCD, edgeDE, edgeAJ, edgeEI, edgeIO, edgeJO, edgeJK, G, edgeFK, edgeBF, edgeFL, edgeGL, edgeCG, edgeGM, edgeHM, edgeDH, edgeHN, edgeIN, H, edgeNS, edgeST, edgeOT, edgePT, edgeKP, edgePQ, edgeLQ, edgeQR, edgeMR, edgeRS, I, J, K, L
5. Midpoint(O, G) → U
6. Sphere(U, A) → b
7. CircleArc(U, P, Q) → c
8. CircleArc(U, P, T) → d
9. CircleArc(U, T, S) → e
10. CircleArc(U, S, R) → f
11. CircleArc(U, R, Q) → g
12. OrthogonalLine(U, facePQRST) → h
13. Sequence(Rotate[{c, d, e, f, g}, a, h], a, 0, (2 * π / 5), (2 * π / 50)) → L_1
14. Line(U, T) → i
15. Sequence(Rotate[L_1, ((a * 2) * π / 3), i], a, 1, 2) → L_2
16. Sequence(Rotate[L_2, ((a * 2) * π / 5), h], a, 2, 2) → L_3
17. Line(U, P) → j
18. Rotate(L_1, (-2 * π / 3), j) → L_4
19. Mirror(L_1, U) → L_5
20. Mirror(L_2, U) → L_6
21. Mirror(L_3, U) → L_7
22. Mirror(L_4, U) → L_8
23. CircleArc(U, S, Q) → k
24. CircleArc(U, T, R) → p
25. CircleArc(U, P, S) → q
26. CircleArc(U, R, P) → r
27. CircleArc(U, T, Q) → s
28. Sequence(Rotate[{k, p, q, r, s}, a, h], a, 0, (2 * π / 5), (2 * π / 50)) → L_9
29. Sequence(Rotate[L_9, ((a * 2) * π / 3), i], a, 1, 2) → L_{10}
30. Sequence(Rotate[L_{10}, ((a * 2) * π / 5), h], a, 2, 2) → L_{11}
31. Rotate(L_9, (-2 * π / 3), j) → L_{12}
32. Mirror(L_9, U) → L_{13}
33. Mirror(L_{10}, U) → L_{14}
34. Mirror(L_{11}, U) → L_{15}
35. Mirror(L_{12}, U) → L_{16}