Tessellations and Volumes

GeoGebra Commands & Parameters

1. Sequence(Mat * Element[cube, k], k, 1, 8) → cube'
2. Sequence(I + (Element[cube', k, 1, 1], Element[cube', k, 2, 1]), k, 1, 8) → listepoints
3. Element(listepoints, 7) → F
4. Element(listepoints, 6) → B_3
5. Element(listepoints, 1) → E
6. Element(listepoints, 2) → A
7. Element(Element[AE, 3], 1) → droite
8. Element(listepoints, 4) → C_1
9. Element(listepoints, 3) → D
10. Polygon(A, E, C_1, D) → poly1, a_1, b, c_1, d
11. Element(listepoints, 8) → G
12. Element(listepoints, 5) → H
13. Polygon(B_3, F, G, H) → poly2, e, f, g, h
14. Element(listepoints, 3) → C
15. Polygon(F, C, A, B_3) → poly3, f_1, i, a_2, b_1
16. Element(AB, 3, 1) → avant
17. Polygon(C_1, G, H, E) → poly4, c_2, g_1, h_1, e_1
18. Element(AC, 3, 1) → dessus
19. Polygon(F, C, C_1, G) → poly5, f_2, c_3, c_4, g_2
20. Polygon(A, B_3, H, E) → poly6, a_3, b_2, h_2, e_2
21. Segment(E, A) → c
22. Segment(A, C) → j
23. Segment(A, B_3) → k
24. Segment(C, C_1) → l
25. Segment(C_1, E) → m
26. Segment(A, B_3) → p
27. Segment(B_3, H) → q
28. Segment(H, E) → r
29. Segment(H, G) → s
30. Segment(B_3, F) → t
31. Segment(G, C_1) → d_1
32. Segment(F, G) → i_1
33. Segment(F, C) → j_1
34. Polygon(A, B_3, F', D') → poly7, a_4, b_3, f', d'
35. Polygon(E, A, D'', C') → poly8, e_3, a_5, d'', c'
36. Polygon(B_3, F'', G', H) → poly9, b_4, f'', g', h_3
37. Polygon(H, G'', C''', E) → poly10, h_4, g'', c''', e_4
38. Polygon(A_2, B_2, G'', C''') → poly11, a_6, b_5, g''_1, c'''_1
39. Sequence(E + (A - E) * k / m_1, k, 0, m_1) → l_2
40. Sequence(A + (B_3 - A) * k / k_1, k, 0, k_1) → l_1
41. Sequence(H + (E - H) * k / k_1, k, 0, k_1) → l_4
42. Sequence(B_3 + (H - B_3) * k / m_1, k, 0, m_1) → l_5
43. Sequence(Segment[Element[l_1, k], Element[l_4, k_1 - k + 2]], k, 0, k_1) → s_1
44. Sequence(G + (C_1 - G) * k / k_1, k, 0, k_1) → l_6
45. Sequence(H + (G - H) * k / n_1, k, 0, n_1) → l_7
46. Sequence(E + (C_1 - E) * k / n_1, k, 0, n_1) → l_8
47. Sequence(Segment[Element[l_4, k], Element[l_6, k]], k, 0, k_1) → s_4
48. Sequence(D + (C_1 - D) * k / m_1, k, 0, m_1) → l_9
49. Sequence(D + (A - D) * k / n_1, k, 0, n_1) → l_{10}
50. Sequence(B_3 + (F - B_3) * k / n_1, k, 0, n_1) → l_{12}
51. Sequence(D + (F - D) * k / k_1, k, 0, k_1) → l_{11}
52. Sequence(Segment[Element[l_{11}, k], Element[l_6, k_1 - k + 2]], k, 0, k_1) → s_7
53. Sequence(Segment[Element[l_{11}, k], Element[l_1, k]], k, 0, k_1) → s_8
54. Sequence(G + (F - G) * k / m_1, k, 0, m_1) → l_{13}
55. Sequence(Segment[Element[l_2, k], Element[l_5, m_1 - k + 2]], k, 0, m_1) → s_2
56. Sequence(Segment[Element[l_9, k], Element[l_2, m_1 - k + 2]], k, 0, m_1) → s_6
57. Sequence(Segment[Element[l_{13}, k], Element[l_9, m_1 - k + 2]], k, 0, m_1) → s_{12}
58. Sequence(Segment[Element[l_{13}, k], Element[l_5, m_1 - k + 2]], k, 0, m_1) → s_{11}
59. Sequence(Segment[Element[l_{12}, k], Element[l_{10}, n_1 - k + 2]], k, 0, n_1) → s_9
60. Sequence(Segment[Element[l_{12}, k], Element[l_7, k]], k, 0, n_1) → s_{10}
61. Sequence(Segment[Element[l_7, k], Element[l_8, k]], k, 0, n_1) → s_3
62. Sequence(Segment[Element[l_8, k], Element[l_{10}, n_1 - k + 2]], k, 0, n_1) → s_5
63. Translate(A, Vector[A, J]) → U_A
64. Translate(U_A, Vector[1 / n_1 * Vector[A, C]]) → U_C
65. Translate(U_A, Vector[1 / k_1 * Vector[A, B_3]]) → U_B
66. Translate(U_B, Vector[1 / n_1 * Vector[A, C]]) → U_F
67. Polygon(J, U_C, U_F, U_B) → poly12, j_2, u_c, u_f, u_b
68. Translate(U_A, Vector[1 / m_1 * Vector[A, E]]) → U_E
69. Translate(U_E, Vector[1 / n_1 * Vector[E, C_1]]) → U_C1
70. Polygon(U_C, J, U_E, U_C1) → poly13, u_1, j_3, u_e, u_c1
71. Translate(U_C1, Vector[1 / k_1 * Vector[C_1, G]]) → U_G
72. Polygon(U_C, U_C1, U_G, U_F) → poly14, u_2, u_3, u_g, u_4
73. Translate(U_E, Vector[1 / k_1 * Vector[E, H]]) → U_H
74. Polygon(U_C1, U_G, U_H, U_E) → poly15, u_5, u_6, u_h, u_7
75. Polygon(U_H, U_G, U_F, U_B) → poly16, u_8, u_9, u_{10}, u_{11}
76. Polygon(U_H, U_B, U_A, U_E) → poly17, u_{12}, u_{13}, u_a, u_{14}