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Cube Layer Problem

Cube Layer Problem
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2019-02-16 01:43
Solid GeometryTransformationGeometric Construction
In collections SPATIAL VISUALISATION TASKS
This example demonstrates the layering of a cube. Key mathematical concepts include solid geometry and geometric construction. Using GeoGebra commands such as Line, Polygon, Cube, and Intersect, the example constructs the various faces and edges of the cube. Suitable for high school or university-level solid geometry studies.

GeoGebra Commands & Parameters

  1. Line(A, zAxis) → f
  2. Polygon(B, C, 4) → mnohouholník1, g, h, i, j, D, E
  3. Point(Circle[E, Distance[D, E], Segment[D, E]]) → F
  4. Cube(D, E, F) → a, G, stenaFGKJ, stenaHIJK, hranaDG, hranaDE, hranaEF, hranaFG, hranaDH, hranaGK, hranaHK, hranaHI, H, hranaEI, hranaIJ, hranaFJ, hranaJK, I, J, K, stenaDEFG, stenaDGKH, stenaDEIH, stenaEFJI
  5. Line(A, xAxis) → k
  6. Circle(A, r, k) → c
  7. Circle(A, r) → d
  8. Intersect(d, k, 2) → L
  9. Vector(A, L) → u
  10. Intersect(f, c, 1) → M
  11. Vector(A, M) → v
  12. Intersect(d, c, 2) → N
  13. Vector(A, N) → w
  14. Intersect(d, k, 2) → O
  15. Vector(A, O) → b
  16. Intersect(d, c, 2) → P
  17. Vector(A, P) → e
  18. Rotate(L, 45°, A) → L'
  19. Vector(A, L') → m
  20. Translate(a, v) → a'
  21. Translate(a, Vector[(2 * v)]) → a'_1
  22. Translate(a, w) → a'_4
  23. Translate(a, Vector[(2 * w)]) → a'_5
  24. Angle(P, A, M) → α
  25. Intersect(f, c) → Q, R
  26. Circle(Q, L', R) → p
  27. Translate(a, Vector[e + v]) → a'_8
  28. Translate(a, Vector[(2 * e) + v]) → a'_9
  29. Translate(a, Vector[e + (2 * v)]) → a'_{12}
  30. Translate(a, Vector[(2 * e) + (2 * v)]) → a'_{13}
  31. Intersect(d, c, 1) → S
  32. Vector(A, S) → l
  33. Vector(A, R) → n
  34. Intersect(d, k, 1) → T
  35. Vector(A, T) → q
  36. Translate(a, Vector[(-v)]) → a'_2
  37. Translate(a, Vector[(-2 * v)]) → a'_3
  38. Translate(a, Vector[b - v]) → a'_{16}
  39. Translate(a, Vector[e - v]) → a'_{17}
  40. Translate(a, Vector[(2 * e) - v]) → a'_{18}
  41. Translate(a, Vector[e - (2 * v)]) → a'_6
  42. Translate(a, Vector[(2 * e) - (2 * v)]) → a'_7
  43. Translate(a, l) → a'_{10}
  44. Translate(a, Vector[(2 * l)]) → a'_{11}
  45. Translate(a, b) → a'_{14}
  46. Translate(a, Vector[(2 * b)]) → a'_{15}
  47. Translate(a, Vector[e + b]) → a'_{19}
  48. Translate(a, Vector[e + (2 * b)]) → a'_{20}
  49. Translate(a, Vector[(2 * e) + b]) → a'_{21}
  50. Translate(a, Vector[(2 * e) + (2 * b)]) → a'_{22}
  51. Translate(a, Vector[l + (2 * b)]) → a'_{24}
  52. Translate(a, Vector[(2 * l) + b]) → a'_{25}
  53. Translate(a, Vector[(2 * l) + (2 * b)]) → a'_{26}
  54. Translate(a, Vector[l + b]) → a'_{27}
  55. Translate(a, Vector[(2 * v) + b]) → a'_{30}
  56. Translate(a, Vector[(2 * v) + (2 * b)]) → a'_{31}
  57. Translate(a, Vector[v + l]) → a'_{32}
  58. Translate(a, Vector[v + b + l]) → a'_{33}
  59. Translate(a, Vector[v + (2 * b) + l]) → a'_{34}
  60. Translate(a, Vector[v + (2 * l)]) → a'_{35}
  61. Translate(a, Vector[v + (2 * l) + b]) → a'_{36}
  62. Translate(a, Vector[v + (2 * l) + (2 * b)]) → a'_{38}
  63. Translate(a, Vector[(2 * v) + l]) → a'_{39}
  64. Translate(a, Vector[(2 * v) + (2 * l)]) → a'_{40}
  65. Translate(a, Vector[(2 * v) + l + b]) → a'_{41}
  66. Translate(a, Vector[(2 * v) + (2 * l) + b]) → a'_{42}
  67. Translate(a, Vector[(2 * v) + (2 * l) + (2 * b)]) → a'_{43}
  68. Translate(a, Vector[(2 * v) + l + (2 * b)]) → a'_{44}
  69. Translate(a, Vector[b + v]) → a'_{45}
  70. Translate(a, Vector[(2 * b) + v]) → a'_{46}
  71. Translate(a, Vector[b + e + v]) → a'_{47}
  72. Translate(a, Vector[(2 * b) + e + v]) → a'_{48}
  73. Translate(a, Vector[b + (2 * e) + v]) → a'_{49}
  74. Translate(a, Vector[(2 * b) + (2 * e) + v]) → a'_{50}
  75. Translate(a, Vector[b + e + (2 * v)]) → a'_{51}
  76. Translate(a, Vector[(2 * b) + e + (2 * v)]) → a'_{52}
  77. Translate(a, Vector[(2 * b) + (2 * e) + (2 * v)]) → a'_{53}
  78. Translate(a, Vector[(2 * v) + (2 * e) + b]) → a'_{54}
  79. Translate(a, Vector[(-v) + (2 * b)]) → a'_{55}
  80. Translate(a, Vector[(-v) + e + b]) → a'_{56}
  81. Translate(a, Vector[(-v) + e + (2 * b)]) → a'_{57}
  82. Translate(a, Vector[(-v) + (2 * e) + b]) → a'_{58}
  83. Translate(a, Vector[(-v) + (2 * e) + (2 * b)]) → a'_{59}
  84. Translate(a, Vector[(-2 * v) + e + b]) → a'_{60}
  85. Translate(a, Vector[(-2 * v) + (2 * e) + b]) → a'_{61}
  86. Translate(a, Vector[(-2 * v) + (2 * e) + (2 * b)]) → a'_{62}
  87. Translate(a, Vector[(-2 * v) + e + (2 * b)]) → a'_{63}
  88. Translate(a, Vector[(-2 * v) + b]) → a'_{64}
  89. Translate(a, Vector[(-2 * v) + (2 * b)]) → a'_{65}
  90. Translate(a, Vector[(-2 * v) + (-2 * b)]) → a'_{66}
  91. Translate(a, Vector[(-2 * v) + (-b)]) → a'_{67}
  92. Translate(a, Vector[(-v) + q]) → a'_{68}
  93. Translate(a, Vector[(-v) + (2 * q)]) → a'_{69}
  94. Translate(a, Vector[(-v) + q + e]) → a'_{70}
  95. Translate(a, Vector[(-v) + q + (2 * e)]) → a'_{71}
  96. Translate(a, Vector[(-v) + (2 * q) + e]) → a'_{72}
  97. Translate(a, Vector[(-v) + (2 * q) + (2 * e)]) → a'_{73}
  98. Translate(a, Vector[(-2 * v) + q + e]) → a'_{74}
  99. Translate(a, Vector[(-2 * v) + (2 * q) + e]) → a'_{75}
  100. Translate(a, Vector[(-2 * v) + q + (2 * e)]) → a'_{76}
  101. Translate(a, Vector[(-2 * v) + (2 * q) + (2 * e)]) → a'_{77}
  102. Translate(a, Vector[(-2 * v) + q + e]) → a'_{78}
  103. Translate(a, Vector[q + (2 * e)]) → a'_{79}
  104. Translate(a, Vector[q + e]) → a'_{80}
  105. Translate(a, q) → a'_{81}
  106. Translate(a, Vector[(2 * q) + (2 * e)]) → a'_{82}
  107. Translate(a, Vector[(2 * q) + e]) → a'_{83}
  108. Translate(a, Vector[(2 * q)]) → a'_{84}
  109. Translate(a, Vector[v + (2 * e) + q]) → a'_{85}
  110. Translate(a, Vector[v + (2 * e) + (2 * q)]) → a'_{86}
  111. Translate(a, Vector[v + e + q]) → a'_{87}
  112. Translate(a, Vector[v + e + (2 * q)]) → a'_{88}
  113. Translate(a, Vector[v + q]) → a'_{89}
  114. Translate(a, Vector[v + (2 * q)]) → a'_{90}
  115. Translate(a, Vector[(2 * v) + q + (2 * e)]) → a'_{91}
  116. Translate(a, Vector[(2 * v) + (2 * q) + (2 * e)]) → a'_{92}
  117. Translate(a, Vector[(2 * v) + q + e]) → a'_{93}
  118. Translate(a, Vector[(2 * v) + (2 * q) + e]) → a'_{94}
  119. Translate(a, Vector[(2 * v) + q]) → a'_{95}
  120. Translate(a, Vector[(-v) + b + l]) → a'_{96}
  121. Translate(a, Vector[(-v) + b + (2 * l)]) → a'_{97}
  122. Translate(a, Vector[(-v) + (2 * b) + l]) → a'_{98}
  123. Translate(a, Vector[(-v) + (2 * b) + (2 * l)]) → a'_{99}
  124. Translate(a, Vector[(-2 * v) + b + l]) → a'_{100}
  125. Translate(a, Vector[(-2 * v) + (2 * b) + l]) → a'_{101}
  126. Translate(a, Vector[(-2 * v) + (2 * b) + (2 * l)]) → a'_{102}
  127. Translate(a, Vector[(-2 * v) + b + (2 * l)]) → a'_{103}
  128. Translate(a, Vector[(-2 * v) + (2 * l)]) → a'_{104}
  129. Translate(a, Vector[(-2 * v) + l]) → a'_{105}
  130. Translate(a, Vector[(-2 * v) - (2 * b) + l]) → a'_{106}
  131. Translate(a, Vector[(-2 * v) - b + l]) → a'_{107}
  132. Translate(a, Vector[(-2 * v) - b + (2 * l)]) → a'_{108}
  133. Translate(a, Vector[(-2 * v) - (2 * b) + (2 * l)]) → a'_{109}
  134. Translate(a, Vector[(-v) - (2 * b) + l]) → a'_{110}
  135. Translate(a, Vector[(-v) - b + l]) → a'_{111}
  136. Translate(a, Vector[(2 * v) + (2 * q)]) → a'_{112}
  137. Translate(a, Vector[(-v) + l]) → a'_{113}
  138. Translate(a, Vector[(-v) + (2 * l)]) → a'_{114}
  139. Translate(a, Vector[(-v) + (2 * l) + q]) → a'_{115}
  140. Translate(a, Vector[(-v) + (2 * l) + (2 * q)]) → a'_{116}
  141. Translate(a, Vector[l + q]) → a'_{117}
  142. Translate(a, Vector[(2 * l) + q]) → a'_{118}
  143. Translate(a, Vector[l + (2 * q)]) → a'_{119}
  144. Translate(a, Vector[(2 * l) + (2 * q)]) → a'_{120}
  145. Translate(a, Vector[v + l + q]) → a'_{121}
  146. Translate(a, Vector[v + (2 * l) + q]) → a'_{122}
  147. Translate(a, Vector[v + l + (2 * q)]) → a'_{123}
  148. Translate(a, Vector[v + (2 * l) + (2 * q)]) → a'_{124}
  149. Translate(a, Vector[(2 * v) + (2 * l) + q]) → a'_{126}
  150. Translate(a, Vector[(2 * v) + l + q]) → a'_{127}
  151. Translate(a, Vector[(2 * v) + l + (2 * q)]) → a'_{128}
  152. Translate(a, Vector[(2 * v) + (2 * l) + (2 * q)]) → a'_{129}

AI Drawing Prompt Reference

Draw a cube, first draw a line f through point A and the z-axis, then draw a quadrilateral mnohouholník1 with points B and C, construct point F, and draw a cube a with points D, E, and F. Then draw a line k through point A and the x-axis, construct circles c and d, find points L, M, N, O, P, construct vectors u, v, w, b, e, and m, rotate point L to get L', and translate cube a to get a', a'_1, a'_4, a'_5. Construct angle α, find points Q, R, S, T, construct circle p, translate cube a to get a'_8, a'_9, a'_{12}, a'_{13}, construct vectors l, n, q, and translate cube a to get a'_2, a'_3, a'_{16}, a'_{17}, a'_{18}, a'_6, a'_7, a'_{10}, a'_{11}, a'_{14}, a'_{15}, a'_{19}, a'_{20}.
The prompt above was compiled from the original drawing commands and is for reference only.