Octonion Multiplication Chart and Fano Plane

GeoGebra Commands & Parameters

1. Polygon(e3, e5, 3) → poly1, f, g, h, e6
2. Incircle(e3, e5, e6) → c
3. Center(c) → e7
4. Intersect(c, f) → e2, H
5. Intersect(c, g) → e1,
6. Intersect(c, h) → e4,
7. Segment(e5, e7) → i
8. Segment(e7, e4) → j
9. Segment(e6, e7) → k
10. Segment(e7, e2) → l
11. Segment(e3, e7) → m
12. Segment(e7, e1) → n
13. Segment(e4, e6) → p
14. CircumcircleArc(e6, A, e3) → d
15. CircleArc(e7, e1, e4) → e
16. CircleArc(e7, e4, e2) → q
17. CircleArc(e7, e2, e1) → r
18. Segment(e6, e1) → s
19. Segment(e1, e5) → t
20. Segment(e5, e2) → a
21. Segment(e2, e3) → b
22. Point(e) → B
23. Point(r) → C
24. Point(q) → D
25. Tangent(D, q) → f_1,
26. UnitVector(f_1) → u
27. Segment(D, D + (0.1 * u)) → g_1
28. Tangent(B, e) → h_1,
29. UnitVector(h_1) → v
30. Segment(B, B + (0.1 * v)) → i_1
31. Tangent(C, r) → j_1,
32. UnitVector(j_1) → w
33. Segment(C, C + (0.1 * w)) → k_1
34. Dilate(e5, 0.6, e7) → e5'
35. Dilate(e7, 0.6, e7) → e7'
36. Segment(e5', e7') → i'
37. Dilate(e6, 0.6, e7) → e6'
38. Dilate(e7, 0.6, e7) → e7'_1
39. Segment(e6', e7'_1) → k'
40. Dilate(e3, 0.6, e7) → e3'
41. Dilate(e7, 0.6, e7) → e7'_2
42. Segment(e3', e7'_2) → m'
43. Tangent(A, d) → l_1,
44. UnitVector(l_1) → u_1
45. Segment(A, A - (0.1 * u_1)) → m_1
46. Segment(e3, e4) → n_1
47. TableText({R0, R1, R2, R3, R4, R5, R6, R7}, "c_|h") → text1
48. Sequence(G + (w * (F - G)), w, 0, 1, 1 / 6) → L_1
49. Point(L_1) → I
50. Sequence(M + (w * (N - M)), w, 0, 1, 1 / 6) → L_2
51. Point(L_2) → O
52. Polygon((x(O), y(I)), (x(O), y(K)), (x(R), y(K)), (x(R), y(I))) → q1, r_1, s_1, t_1, a_1
53. Polygon({I, J, K, L}) → p_1
54. Polygon({O, P, Q, R}) → q_1
55. IndexOf(O, L_2) → o
56. IndexOf(I, L_1) → b_1
57. Element(Element[L3, b_1], o) → text2