Order of Rotational Symmetry of Regular Polygons

GeoGebra Commands & Parameters

1. Line(A, B) → a
2. OrthogonalLine(A, a) → b
3. OrthogonalLine(B, a) → c
4. Circle(A, B) → d
5. Intersect(d, b, 2) → C
6. OrthogonalLine(C, b) → e
7. Intersect(e, c) → D
8. Polygon(A, B, D, C) → P, a_1, b_1, d_1, c_1
9. Midpoint(C, B) → E
10. Segment(F, G) → f
11. OrthogonalLine(G, f) → g
12. Circle(G, F) → h
13. Intersect(h, g, 1) → H
14. Circle(H, G) → k
15. Intersect(k, g, 2) → I
16. Segment(F, I) → i
17. Circle(F, I) → p
18. Line(G, F) → j
19. Intersect(p, j, 2) → J
20. Midpoint(J, G) → K
21. Segment(J, K) → l
22. Circle(F, l) → q
23. Circle(G, l) → r
24. Intersect(r, q, 1) → L
25. Segment(F, L) → m
26. Segment(L, G) → n
27. AngularBisector(F, G, L) → s
28. AngularBisector(L, F, G) → t
29. Intersect(r, s, 2) → M
30. Intersect(q, t, 1) → N
31. Polygon(M, L, N, G, F) → Q, m_1, l_1, n_1, g_1, f_1
32. Segment(O, R) → e_1
33. Circle(O, R) → h_1
34. Circle(R, O) → k_1
35. Ray(O, R) → i_1
36. Intersect(k_1, i_1, 2) → S
37. Circle(S, R) → p_1
38. Intersect(k_1, h_1, 2) → T
39. Intersect(p_1, k_1, 2) → U
40. Intersect(p_1, k_1, 1) → V
41. Intersect(k_1, h_1, 1) → W
42. Polygon(T, U, S, V, W, O) → Y, t_1, u, s_1, v, w, o
43. Midpoint(M, L) → Z
44. Midpoint(L, N) → A_1
45. Segment(F, A_1) → j_1
46. Segment(Z, G) → q_1
47. Intersect(q_1, j_1) → B_1
48. Rotate(A, α, E) → A'
49. Rotate(B, α, E) → B'
50. Rotate(D, α, E) → D'
51. Rotate(C, α, E) → C'
52. Polygon(A', B', D', C') → P', a', b', d', c'
53. Rotate(M, β, B_1) → M'
54. Rotate(L, β, B_1) → L'
55. Rotate(N, β, B_1) → N'
56. Rotate(G, β, B_1) → G'
57. Rotate(F, β, B_1) → F'
58. Polygon(M', L', N', G', F') → Q', m', l', n', g', f'
59. Rotate(T, γ, R) → T'
60. Rotate(U, γ, R) → U'
61. Rotate(S, γ, R) → S'
62. Rotate(V, γ, R) → V'
63. Rotate(W, γ, R) → W'
64. Rotate(O, γ, R) → O'
65. Polygon(T', U', S', V', W', O') → Y', t', u', s', v', w', o'