Equilateral Triangle Transformations

GeoGebra Commands & Parameters

1. Polygon(A, B, 3) → poly1, f, g, h, C
2. Polygon(D, E, 3) → poly2, i, j, k, F
3. Dilate(A, If[0 < a ≤ 1, 1 - a, 0], B) → A'
4. Dilate(D, If[0 < a ≤ 1, 1 - a, 0], E) → D'
5. Segment(A, A') → l
6. Segment(D, D') → m
7. Rotate(B, If[1 < a ≤ 2, ((a - 1) * pi / 3), pi / 3], A) → B'
8. Rotate(E, If[1 < a ≤ 2, ((a - 1) * pi / 3), pi / 3], D) → E'
9. Segment(A, B') → n
10. Segment(D, E') → p
11. Rotate(A, If[2 < a ≤ 3, ((a - 2) * pi / 3), pi / 3], C) → A'_{1}
12. Rotate(D, If[2 < a ≤ 3, ((a - 2) * pi / 3), pi / 3], F) → D'_{1}
13. Segment(C, A'_{1}) → q
14. Segment(F, D'_{1}) → r
15. Midpoint(A, D) → G
16. Midpoint(B, E) → H
17. Midpoint(C, F) → I
18. Dilate(C, If[4 < a ≤ 5, 5 - a, 0], I) → C'
19. Segment(C, C') → s
20. Dilate(I, If[5 < a ≤ 6, 6 - a, 0], F) → I'
21. Segment(I, I') → t
22. Rotate(C, If[6 < a ≤ 7, ((a - 6) * pi), pi], I) → C'_{1}
23. Segment(I, C'_{1}) → b
24. Polygon(G, H, I) → t1, i_1, g_1, h_1
25. Dilate(A, If[7 < a ≤ 8, 8 - a, 0], G) → A'_{2}
26. Segment(A, A'_{2}) → c
27. Dilate(G, If[8 < a ≤ 9, 9 - a, 0], D) → G'
28. Segment(G, G') → d
29. Rotate(A, If[9 < a ≤ 10, ((a - 9) * pi), pi], G) → A'_{3}
30. Segment(G, A'_{3}) → e
31. Dilate(B, If[10 < a ≤ 11, 11 - a, 0], H) → B'_{1}
32. Segment(B, B'_{1}) → f_1
33. Dilate(H, If[11 < a ≤ 12, 12 - a, 0], E) → H'
34. Segment(H, H') → j_1
35. Rotate(B, If[12 < a ≤ 13, ((a - 12) * pi), pi], H) → B'_{2}
36. Segment(H, B'_{2}) → k_1
37. Dilate(G, If[14 < a ≤ 15, 15 - a, 0], H) → G'_{1}
38. Segment(G, G'_{1}) → l_1
39. Rotate(H, If[15 < a ≤ 16, ((a - 15) * pi / 3), pi / 3], G) → H'_{1}
40. Segment(G, H'_{1}) → m_1
41. Rotate(G, If[16 < a ≤ 17, ((a - 16) * pi / 3), pi / 3], I) → G'_{2}
42. Segment(I, G'_{2}) → n_1