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Hexastring Cube

Hexastring Cube
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2020-05-15 02:10
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the construction of a hexastring cube. It involves core concepts from combinatorics, algebra, and solid geometry. Using GeoGebra commands such as Translate, Mirror, and Midpoint, the cube's faces and edges can be dynamically constructed. Suitable for high school mathematics education and students learning solid geometry.

GeoGebra Commands & Parameters

  1. Translate(O, Vector[(R / sqrt(2) * v)]) → F
  2. Mirror(F, O) → H
  3. Translate(O, Vector[(R / sqrt(2) * u)]) → G
  4. Midpoint(F, G) → B
  5. Vector(O, B) → z
  6. Midpoint(H, G) → E
  7. Translate(E, Vector[(R / 2 * w)]) → E'
  8. Mirror(G, O) → A
  9. Midpoint(A, H) → D
  10. Vector(O, E) → d
  11. Translate(D, Vector[(R / 2 * w)]) → D'
  12. Midpoint(F, A) → C
  13. Translate(C, Vector[(R / 2 * w)]) → C'
  14. Translate(O, Vector[(R / 2 * w)]) → P
  15. Translate(P, z) → B'
  16. Translate(O, z) → O'
  17. Sequence(Translate[B', Vector[((-i) * d)]], i, 0, 1, n) → liste2
  18. Sequence(Translate[P, Vector[(i * z)]], i, 0, 1, n) → liste1
  19. Sequence(Translate[C', Vector[(i * z)]], i, 0, 1, n) → liste6
  20. Sequence(Translate[B', Vector[(i * d)]], i, 0, 1, n) → liste4
  21. Sequence(Translate[P, Vector[((-i) * d)]], i, 0, 1, n) → liste7
  22. Sequence(Segment[Element[liste7, i], Element[liste6, i]], i, 1, 1 / n) → liste8
  23. Sequence(Translate[C', Vector[((-i) * z)]], i, 0, 1, n) → liste9
  24. Sequence(Segment[Element[liste7, i], Element[liste9, i]], i, 1, 1 / n) → liste10
  25. Sequence(Translate[D', Vector[((-i) * d)]], i, 0, 1, n) → liste12
  26. Sequence(Translate[P, Vector[((-i) * z)]], i, 0, 1, n) → liste11
  27. Sequence(Segment[Element[liste12, i], Element[liste11, i]], i, 1, 1 / n) → liste13
  28. Sequence(Translate[E', Vector[((-i) * z)]], i, 0, 1, n) → liste15
  29. Sequence(Translate[D', Vector[(i * d)]], i, 0, 1, n) → liste14
  30. Sequence(Segment[Element[liste14, i], Element[liste11, i]], i, 1, 1 / n) → liste16
  31. Sequence(Translate[P, Vector[(i * d)]], i, 0, 1, n) → liste17
  32. Sequence(Segment[Element[liste15, i], Element[liste17, i]], i, 1, 1 / n) → liste18
  33. Sequence(Translate[E', Vector[(i * z)]], i, 0, 1, n) → liste19
  34. Sequence(Segment[Element[liste19, i], Element[liste17, i]], i, 1, 1 / n) → liste20
  35. Mirror(O', O) → O''
  36. Sequence(Segment[Element[liste1, i], Element[liste2, i]], i, 1, 1 / n) → liste3
  37. Sequence(Segment[Element[liste1, i], Element[liste4, i]], i, 1, 1 / n) → liste5
  38. Translate(O, Vector[(R / 2 * w)]) → E4
  39. Translate(O, Vector[(((-R)) / 2 * w)]) → Q
  40. Translate(A, Vector[(((-R)) / 2 * w)]) → AA
  41. Translate(C, Vector[(((-R)) / 2 * w)]) → CC
  42. Translate(E, Vector[(((-R)) / 2 * w)]) → EE
  43. Translate(D, Vector[(((-R)) / 2 * w)]) → DD
  44. Translate(B, Vector[(((-R)) / 2 * w)]) → BB
  45. Translate(F, Vector[(((-R)) / 2 * w)]) → FF
  46. Translate(G, Vector[(((-R)) / 2 * w)]) → GG
  47. Translate(G, Vector[(R / 2 * w)]) → G'
  48. Translate(F, Vector[(R / 2 * w)]) → F'
  49. Translate(A, Vector[(R / 2 * w)]) → A'
  50. Translate(H, Vector[(R / 2 * w)]) → H'
  51. Translate(H, Vector[(((-R)) / 2 * w)]) → HH
  52. Polygon(H', G', F', A') → poly2, h', g', f', a'
  53. Sequence(Translate[Q, Vector[(i * z)]], i, 0, 1, n) → liste21
  54. Sequence(Translate[Q, Vector[((-i) * z)]], i, 0, 1, n) → liste22
  55. Sequence(Translate[DD, Vector[(i * d)]], i, 0, 1, n) → liste23
  56. Sequence(Translate[EE, Vector[((-i) * z)]], i, 0, 1, n) → liste24
  57. Sequence(Translate[Q, Vector[(i * d)]], i, 0, 1, n) → liste25
  58. Sequence(Translate[EE, Vector[(i * z)]], i, 0, 1, n) → liste26
  59. Sequence(Translate[BB, Vector[((-i) * d)]], i, 0, 1, n) → liste27
  60. Sequence(Translate[BB, Vector[(i * d)]], i, 0, 1, n) → liste28
  61. Sequence(Translate[CC, Vector[(i * z)]], i, 0, 1, n) → liste29
  62. Sequence(Translate[Q, Vector[((-i) * d)]], i, 0, 1, n) → liste30
  63. Sequence(Translate[CC, Vector[((-i) * z)]], i, 0, 1, n) → liste31
  64. Sequence(Translate[DD, Vector[((-i) * d)]], i, 0, 1, n) → liste32
  65. Vector(O, E4) → f
  66. Sequence(Segment[Element[liste25, i], Element[liste24, i]], i, 1, 1 / n) → liste33
  67. Sequence(Segment[Element[liste26, i], Element[liste25, i]], i, 1, 1 / n) → liste34
  68. Sequence(Segment[Element[liste21, i], Element[liste28, i]], i, 1, 1 / n) → liste35
  69. Sequence(Segment[Element[liste21, i], Element[liste27, i]], i, 1, 1 / n) → liste36
  70. Sequence(Segment[Element[liste22, i], Element[liste23, i]], i, 1, 1 / n) → liste37
  71. Sequence(Segment[Element[liste22, i], Element[liste32, i]], i, 1, 1 / n) → liste38
  72. Sequence(Segment[Element[liste31, i], Element[liste30, i]], i, 1, 1 / n) → liste39
  73. Sequence(Segment[Element[liste30, i], Element[liste29, i]], i, 1, 1 / n) → liste40
  74. Sequence(Translate[D, Vector[((-i) * f)]], i, 0, 1, n) → liste41
  75. Sequence(Translate[D, Vector[(i * f)]], i, 0, 1, n) → liste42
  76. Sequence(Translate[B, Vector[((-i) * f)]], i, 0, 1, n) → liste43
  77. Sequence(Translate[B, Vector[(i * f)]], i, 0, 1, n) → liste44
  78. Sequence(Translate[H, Vector[((-i) * f)]], i, 0, 1, n) → liste45
  79. Sequence(Translate[H, Vector[(i * f)]], i, 0, 1, n) → liste46
  80. Sequence(Translate[A, Vector[((-i) * f)]], i, 0, 1, n) → liste47
  81. Sequence(Translate[A, Vector[(i * f)]], i, 0, 1, n) → liste48
  82. Sequence(Translate[C, Vector[((-i) * f)]], i, 0, 1, n) → liste49
  83. Sequence(Translate[C, Vector[(i * f)]], i, 0, 1, n) → liste50
  84. Sequence(Translate[G, Vector[((-i) * f)]], i, 0, 1, n) → liste51
  85. Vector(O, D) → k
  86. Sequence(Translate[G, Vector[(i * f)]], i, 0, 1, n) → liste52
  87. Sequence(Translate[D, Vector[((-i) * d)]], i, 0, 1, n) → liste53
  88. Sequence(Translate[D, Vector[(i * d)]], i, 0, 1, n) → liste54
  89. Sequence(Translate[B, Vector[((-i) * d)]], i, 0, 1, n) → liste55
  90. Sequence(Translate[B, Vector[(i * d)]], i, 0, 1, n) → liste56
  91. Sequence(Translate[E, Vector[((-i) * k)]], i, 0, 1, n) → liste57
  92. Sequence(Translate[C, Vector[((-i) * k)]], i, 0, 1, n) → liste58
  93. Sequence(Translate[E, Vector[(i * k)]], i, 0, 1, n) → liste59
  94. Sequence(Translate[C, Vector[(i * k)]], i, 0, 1, n) → liste60
  95. Sequence(Translate[F, Vector[((-i) * f)]], i, 0, 1, n) → liste61
  96. Sequence(Translate[F, Vector[(i * f)]], i, 0, 1, n) → liste62
  97. Sequence(Translate[E, Vector[((-i) * f)]], i, 0, 1, n) → liste63
  98. Sequence(Translate[E, Vector[(i * f)]], i, 0, 1, n) → liste64
  99. Sequence(Segment[Element[liste12, i], Element[liste42, i]], i, 1, 1 / n) → liste65
  100. Sequence(Segment[Element[liste14, i], Element[liste42, i]], i, 1, 1 / n) → liste66
  101. Sequence(Segment[Element[liste15, i], Element[liste64, i]], i, 1, 1 / n) → liste67
  102. Sequence(Segment[Element[liste64, i], Element[liste19, i]], i, 1, 1 / n) → liste68
  103. Sequence(Segment[Element[liste4, i], Element[liste44, i]], i, 1, 1 / n) → liste69
  104. Sequence(Segment[Element[liste2, i], Element[liste44, i]], i, 1, 1 / n) → liste70
  105. Sequence(Segment[Element[liste50, i], Element[liste6, i]], i, 1, 1 / n) → liste71
  106. Sequence(Segment[Element[liste50, i], Element[liste9, i]], i, 1, 1 / n) → liste72
  107. Sequence(Segment[Element[liste52, i], Element[liste56, i]], i, 1, 1 / n) → liste73
  108. Sequence(Segment[Element[liste62, i], Element[liste55, i]], i, 1, 1 / n) → liste74
  109. Sequence(Segment[Element[liste62, i], Element[liste58, i]], i, 1, 1 / n) → liste75
  110. Sequence(Segment[Element[liste48, i], Element[liste60, i]], i, 1, 1 / n) → liste76
  111. Sequence(Segment[Element[liste53, i], Element[liste48, i]], i, 1, 1 / n) → liste77
  112. Sequence(Segment[Element[liste54, i], Element[liste46, i]], i, 1, 1 / n) → liste78
  113. Sequence(Segment[Element[liste56, i], Element[liste51, i]], i, 1, 1 / n) → liste79
  114. Sequence(Segment[Element[liste43, i], Element[liste28, i]], i, 1, 1 / n) → liste80
  115. Sequence(Segment[Element[liste43, i], Element[liste27, i]], i, 1, 1 / n) → liste81
  116. Sequence(Segment[Element[liste61, i], Element[liste55, i]], i, 1, 1 / n) → liste82
  117. Sequence(Segment[Element[liste61, i], Element[liste58, i]], i, 1, 1 / n) → liste83
  118. Sequence(Segment[Element[liste49, i], Element[liste29, i]], i, 1, 1 / n) → liste84
  119. Sequence(Segment[Element[liste49, i], Element[liste31, i]], i, 1, 1 / n) → liste85
  120. Sequence(Segment[Element[liste60, i], Element[liste47, i]], i, 1, 1 / n) → liste86
  121. Sequence(Segment[Element[liste53, i], Element[liste47, i]], i, 1, 1 / n) → liste87
  122. Sequence(Segment[Element[liste57, i], Element[liste52, i]], i, 1, 1 / n) → liste88
  123. Sequence(Segment[Element[liste57, i], Element[liste51, i]], i, 1, 1 / n) → liste89
  124. Sequence(Segment[Element[liste63, i], Element[liste26, i]], i, 1, 1 / n) → liste90
  125. Sequence(Segment[Element[liste63, i], Element[liste24, i]], i, 1, 1 / n) → liste91
  126. Sequence(Segment[Element[liste59, i], Element[liste46, i]], i, 1, 1 / n) → liste92
  127. Sequence(Segment[Element[liste59, i], Element[liste45, i]], i, 1, 1 / n) → liste93
  128. Sequence(Segment[Element[liste45, i], Element[liste54, i]], i, 1, 1 / n) → liste94
  129. Sequence(Segment[Element[liste32, i], Element[liste41, i]], i, 1, 1 / n) → liste95
  130. Sequence(Segment[Element[liste41, i], Element[liste23, i]], i, 1, 1 / n) → liste96
  131. Polygon(G', F', FF, GG) → poly1, g'_1, f'_1, ff, gg
  132. Polygon(F', A', AA, FF) → poly3, f'_2, a'_1, aa, ff_1
  133. Polygon(H', A', AA, HH) → poly4, h'_1, a'_2, aa_1, hh
  134. Polygon(H', G', GG, HH) → poly5, h'_2, g'_2, gg_1, hh_1
  135. Polygon(HH, AA, FF, GG) → poly6, hh_2, aa_2, ff_2, gg_2