Cube Pattern on Sphere Construction

GeoGebra Commands & Parameters

1. Point(yAxis) → E
2. Polygon(B, C, D, A) → q1, b, c, d, a
3. Cube(q1, true) → e, F, edgeBF, edgeAI, edgeFI, edgeFG, edgeCG, edgeGH, edgeDH, edgeHI, G, H, I, faceABFI, faceBCGF, faceCDHG, faceADHI, faceFGHI
4. Centroid(faceCDHG) → J
5. Segment(C, H) → f
6. Segment(D, G) → g
7. Midpoint(C, D) → K
8. Midpoint(C, G) → L
9. Midpoint(G, H) → M
10. Midpoint(H, D) → N
11. Segment(K, M) → h
12. Segment(L, N) → i
13. Line(E, J) → j
14. Rotate(C, 22.5°, j) → C'
15. Rotate(H, 22.5°, j) → H'
16. Segment(C', H') → f'
17. Segment(C, D) → k
18. Segment(G, H) → l
19. Segment(K, L) → m
20. Intersect(m, f') → O
21. Segment(C, O) → n
22. Segment(O, J) → p
23. Mirror(O, f) → O'
24. Segment(C, O') → q
25. Segment(O', J) → r
26. Segment(O, K) → s
27. Segment(L, O') → t
28. Rotate(O', 90°, j) → O''
29. Rotate(J, 90°, j) → J'
30. Segment(O'', J') → r'
31. Rotate(O, 90°, j) → O'_{1}
32. Rotate(J, 90°, j) → J'_{1}
33. Segment(O'_{1}, J'_{1}) → p'
34. Rotate(C, 90°, j) → C'_{1}
35. Rotate(O', 90°, j) → O''_{1}
36. Segment(C'_{1}, O''_{1}) → q'
37. Rotate(C, 90°, j) → C'_{2}
38. Rotate(O, 90°, j) → O'_{2}
39. Segment(C'_{2}, O'_{2}) → n'
40. Rotate(L, 90°, j) → L'
41. Rotate(O', 90°, j) → O''_{2}
42. Segment(L', O''_{2}) → t'
43. Rotate(O, 90°, j) → O'_{3}
44. Rotate(K, 90°, j) → K'
45. Segment(O'_{3}, K') → s'
46. Mirror(O, J'_{1}) → O'_{4}
47. Mirror(O', J'_{1}) → O''_{3}
48. Mirror(O, J'_{1}) → O'_{5}
49. Mirror(J, J'_{1}) → J'_{2}
50. Segment(O'_{5}, J'_{2}) → p'_{1}
51. Mirror(O', J'_{2}) → O''_{4}
52. Mirror(J, J'_{2}) → J'_{3}
53. Segment(O''_{4}, J'_{3}) → r'_{1}
54. Mirror(C, J'_{3}) → C'_{3}
55. Mirror(O', J'_{3}) → O''_{5}
56. Segment(C'_{3}, O''_{5}) → q'_{1}
57. Mirror(C, J'_{3}) → C'_{4}
58. Mirror(O, J'_{3}) → O'_{6}
59. Segment(C'_{4}, O'_{6}) → n'_{1}
60. Mirror(L, J'_{3}) → L'_{1}
61. Mirror(O', J'_{3}) → O''_{6}
62. Segment(L'_{1}, O''_{6}) → t'_{1}
63. Mirror(O, J'_{3}) → O'_{7}
64. Mirror(K, J'_{3}) → K'_{1}
65. Segment(O'_{7}, K'_{1}) → s'_{1}
66. Mirror(O''_{2}, J'_{3}) → P
67. Mirror(L', J'_{3}) → L''
68. Mirror(O''_{2}, J'_{3}) → Q
69. Segment(L'', Q) → t''
70. Mirror(O'', J'_{3}) → O'''
71. Mirror(J', J'_{3}) → J''
72. Segment(O''', J'') → r''
73. Mirror(C'_{1}, J'') → R
74. Mirror(O''_{1}, J'') → S
75. Segment(R, S) → q''
76. Mirror(C'_{2}, J'') → T
77. Mirror(O'_{2}, J'') → U
78. Segment(T, U) → n''
79. Mirror(O'_{3}, J'') → V
80. Mirror(O'_{1}, J'') → W
81. Mirror(J'_{1}, J'') → Z
82. Segment(W, Z) → p''
83. Mirror(O'_{3}, Z) → A_1
84. Mirror(K', Z) → K''
85. Segment(A_1, K'') → s''
86. Segment(C'_{2}, C'_{4}) → f_1
87. Segment(C, T) → g_1
88. Ray(E, L') → h_1
89. Ray(E, O) → i_1
90. Ray(E, C) → j_1
91. Ray(E, O') → k_1
92. Ray(E, K'') → l_1
93. Sphere(E, C) → o
94. Intersect(k_1, o) → B_1,
95. Intersect(l_1, o) → C_1,
96. Intersect(i_1, o) → D_1,
97. Intersect(h_1, o) → E_1,
98. Intersect(j, o) → F_1, G_1
99. Polygon(C, G_1, D_1) → t1, d_1, c_1, m_1
100. Polygon(C, B_1, G_1) → t2, n_1, c_2, b_1
101. Polygon(C, D_1, E_1) → t3, e_1, c_3, p_1
102. Polygon(C, C_1, B_1) → t4, q_1, c_4, r_1
103. Intersect(j, p'_{1}) → H_1
104. Polygon(C_1, G_1, B_1) → t5, s_1, t_1, a_1
105. Polygon(G_1, E_1, D_1) → t6, f_2, g_2, h_2
106. Rotate(l1, 90°, j) → l1'
107. Rotate(l1, 180°, j) → l1'_{1}
108. Rotate(l1, 270°, j) → l1'_{2}
109. Rotate(l1, 0°, j) → l1'_{3}
110. Line(E, C) → i_2
111. Rotate(l2, 120°, i_2) → l2'
112. Rotate(l2, (-(120°)), i_2) → l2'_{1}
113. Rotate(l2, 0°, i_2) → l2'_{2}
114. Line(E, B) → j_2
115. Rotate(l2', 120°, j_2) → l2''
116. Rotate(l2'', (-(120°)), i_2) → l2'''
117. Rotate(l2'', 120°, i_2) → l2'''_{1}