Symmetries of Napoleon's Tessellation

GeoGebra Commands & Parameters

1. Polygon(A, B, C) → poly1, c_1, a_1, b_1
2. Polygon(A, C, 3) → poly2, d, e, f, D
3. Polygon(C, B, 3) → poly3, g, h, i, E
4. Polygon(B, A, 3) → poly4, j, k, l, F
5. Circle(F, A, B) → p
6. Circle(A, D, C) → q
7. Circle(C, E, B) → r
8. Center(p) → G
9. Center(q) → H
10. Center(r) → I
11. Vector(B, D) → u
12. Vector(A, E) → v
13. Vector(C, F) → w
14. Sequence(Polygon[Translate[A, Vector[(n * u)]], Translate[B, Vector[(n * u)]], Translate[C, Vector[(n * u)]]], n, -10, 10) → list1
15. Sequence(Translate[list1, Vector[(n * v)]], n, -10, 10) → list2
16. Rotate(list2, 120°, I) → list3
17. Rotate(list2, 240°, I) → list4
18. Rotate(Translate[list2, Vector[(a * u) + (b * v) + (c * w)]], α, J) → triangles1
19. Rotate(Translate[list3, Vector[(a * u) + (b * v) + (c * w)]], α, J) → triangles2
20. Rotate(Translate[list4, Vector[(a * u) + (b * v) + (c * w)]], α, J) → triangles3
21. Polygon(B, G, A, H, C, I) → poly5, b_2, g_1, a_2, h_1, c_2, i_1
22. Sequence(Polygon[Translate[B, Vector[(n * u)]], Translate[G, Vector[(n * u)]], Translate[A, Vector[(n * u)]], Translate[H, Vector[(n * u)]], Translate[C, Vector[(n * u)]], Translate[I, Vector[(n * u)]]], n, -10, 10) → list5
23. Sequence(Translate[list5, Vector[(n * v)]], n, -10, 10) → list6
24. Rotate(list6, 120°, I) → list7
25. Rotate(list6, 240°, I) → list8
26. Rotate(Translate[list6, Vector[(a * u) + (b * v) + (c * w)]], α, J) → hexagons1
27. Rotate(Translate[list7, Vector[(a * u) + (b * v) + (c * w)]], α, J) → hexagons2
28. Rotate(Translate[list8, Vector[(a * u) + (b * v) + (c * w)]], α, J) → hexagons3
29. Polygon(K, L, M, N, O, P) → poly6, k_1, l_1, m_1, n_1, o_1, p_1
30. Rotate(K, 120°, J) → K'
31. Rotate(L, 120°, J) → L'
32. Rotate(M, 120°, J) → M'
33. Rotate(N, 120°, J) → N'
34. Rotate(O, 120°, J) → O'
35. Rotate(P, 120°, J) → P'
36. Polygon(K', L', M', N', O', P') → poly6', k', l', m', n', o', p'
37. Rotate(K', 120°, J) → K''
38. Rotate(L', 120°, J) → L''
39. Rotate(M', 120°, J) → M''
40. Rotate(N', 120°, J) → N''
41. Rotate(O', 120°, J) → O''
42. Rotate(P', 120°, J) → P''
43. Polygon(K'', L'', M'', N'', O'', P'') → poly6'', k'', l'', m'', n'', o'', p''