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Two Parts of a Cube by Renáta Vágová (3)

Two Parts of a Cube by Renáta Vágová (3)
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2019-04-30 04:41
VectorSolid GeometryGeometric Construction
In collections TWO PARTS OF A CUBE
This example demonstrates two parts of a cube. It involves concepts such as cube, secant line, and quadratic functions. Using GeoGebra commands like Point, Cube, Midpoint, Line, Vector, Translate, Rotate, etc., the various faces and edges of the cube can be constructed. Suitable for middle or high school students learning solid geometry.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  4. Cube(A, B, C) → c, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  5. Point(xAxis) → L
  6. Point(xAxis) → M
  7. Point(Circle[M, Distance[L, M], Segment[L, M]]) → N
  8. Cube(L, M, N) → k, O, faceNOSR, facePQRS, edgeLO, edgeLM, edgeMN, edgeNO, edgeLP, edgeOS, edgePS, edgePQ, P, edgeMQ, edgeQR, edgeNR, edgeRS, Q, R, S, faceLMNO, faceLOSP, faceLMQP, faceMNRQ
  9. Midpoint(H, B) → S_2
  10. Midpoint(S, M) → S_1
  11. Line(S_1, S_2) → p_1
  12. Line(S_2, yAxis) → f
  13. Line(S_1, yAxis) → g
  14. Line(S_2, zAxis) → h
  15. Line(S_1, zAxis) → i
  16. Point(p_1) → I
  17. Point(p_1) → J
  18. Vector(I, J) → u
  19. Translate(i, Vector[(p * u)]) → i'
  20. Translate(g, Vector[(p * u)]) → g'
  21. Rotate(A, α, p_1) → A'
  22. Rotate(B, α, p_1) → B'
  23. Rotate(C, α, p_1) → C'
  24. Rotate(D, α, p_1) → D'
  25. Rotate(E, α, p_1) → E'
  26. Rotate(F, α, p_1) → F'
  27. Rotate(G, α, p_1) → G'
  28. Rotate(H, α, p_1) → H'
  29. Rotate(A', β, f) → A''
  30. Rotate(B', β, f) → B''
  31. Rotate(C', β, f) → C''
  32. Rotate(D', β, f) → D''
  33. Rotate(E', β, f) → E''
  34. Rotate(F', β, f) → F''
  35. Rotate(G', β, f) → G''
  36. Rotate(H', β, f) → H''
  37. Translate(k, Vector[(p * u)]) → k'
  38. Translate(L, Vector[(p * u)]) → L'
  39. Translate(M, Vector[(p * u)]) → M'
  40. Translate(N, Vector[(p * u)]) → N'
  41. Translate(O, Vector[(p * u)]) → O'
  42. Translate(P, Vector[(p * u)]) → P'
  43. Translate(Q, Vector[(p * u)]) → Q'
  44. Translate(R, Vector[(p * u)]) → R'
  45. Translate(S, Vector[(p * u)]) → S'
  46. Rotate(c, α, p_1) → c'
  47. Rotate(c', β, f) → c''
  48. Rotate(G'', γ, h) → G'''
  49. Rotate(H'', γ, h) → H'''
  50. Rotate(E'', γ, h) → E'''
  51. Rotate(F'', γ, h) → F'''
  52. Rotate(D'', γ, h) → D'''
  53. Rotate(C'', γ, h) → C'''
  54. Rotate(A'', γ, h) → A'''
  55. Rotate(B'', γ, h) → B'''
  56. Rotate(c'', γ, h) → c'''
  57. Rotate(k', δ, p_1) → k''
  58. Rotate(L', δ, p_1) → L''
  59. Rotate(M', δ, p_1) → M''
  60. Rotate(N', δ, p_1) → N''
  61. Rotate(O', δ, p_1) → O''
  62. Rotate(P', δ, p_1) → P''
  63. Rotate(Q', δ, p_1) → Q''
  64. Rotate(R', δ, p_1) → R''
  65. Rotate(S', δ, p_1) → S''
  66. Rotate(k'', ε, g') → k'''
  67. Rotate(L'', ε, g') → L'''
  68. Rotate(M'', ε, g') → M'''
  69. Rotate(N'', ε, g') → N'''
  70. Rotate(O'', ε, g') → O'''
  71. Rotate(P'', ε, g') → P'''
  72. Rotate(Q'', ε, g') → Q'''
  73. Rotate(R'', ε, g') → R'''
  74. Rotate(S'', ε, g') → S'''
  75. Rotate(k''', ζ, i') → a
  76. Rotate(L''', ζ, i') → K
  77. Rotate(M''', ζ, i') → T
  78. Rotate(N''', ζ, i') → U
  79. Rotate(O''', ζ, i') → V
  80. Rotate(P''', ζ, i') → W
  81. Rotate(Q''', ζ, i') → Z
  82. Rotate(R''', ζ, i') → A_1
  83. Rotate(S''', ζ, i') → B_1
  84. Midpoint(H''', G''') → C_1
  85. Midpoint(E''', F''') → D_1
  86. Midpoint(D''', C''') → E_1
  87. Midpoint(A''', B''') → F_1
  88. Midpoint(A''', D''') → G_1
  89. Midpoint(E''', H''') → H_1
  90. Midpoint(F''', G''') → I_1
  91. Midpoint(B''', C''') → J_1
  92. Midpoint(C_1, D_1) → K_1
  93. Midpoint(C_1, E_1) → L_1
  94. Midpoint(G_1, H_1) → M_1
  95. Midpoint(D_1, F_1) → N_1
  96. Midpoint(J_1, I_1) → O_1
  97. Midpoint(G_1, J_1) → P_1
  98. Midpoint(V, T) → Q_1
  99. Midpoint(B_1, Z) → R_1
  100. Midpoint(A_1, T) → T_1
  101. Midpoint(B_1, U) → U_1
  102. Midpoint(B_1, K) → V_1
  103. Midpoint(Z, K) → W_1
  104. Midpoint(B_1, A_1) → Z_1
  105. Midpoint(A_1, Z) → A_2
  106. Midpoint(Z, W) → B_2
  107. Midpoint(V, U) → C_2
  108. Midpoint(K, T) → D_2
  109. Midpoint(T, U) → E_2
  110. Midpoint(V, K) → F_2
  111. Midpoint(B_1, W) → G_2
  112. Midpoint(Z, T) → H_2
  113. Midpoint(K, W) → I_2
  114. Midpoint(B_1, V) → J_2
  115. Midpoint(U, A_1) → K_2
  116. Midpoint(G''', C''') → L_2
  117. Midpoint(D''', H''') → M_2
  118. Midpoint(A''', E''') → N_2
  119. Midpoint(F''', B''') → O_2
  120. Prism(H''', C_1, L_2, C''', E_1, M_2, H_1) → b, P_2, face3, face6, face2, face8, edge1, edge7, edge5, edge4, edge9, edge3, Q_2, edge2, edge8, edge13, edge6, edge10, edge14, edge11, edge15, edge16, edge17, R_2, edge18, edge12, T_2, U_2, face7, face1, face5, face4
  121. Prism(P_2, U_2, H_1, D_1) → d, V_2, edge22, edge19, edge26, edge24, edge20, edge27, edge21, W_2, face10, face12, face13, face11, face9, edge25, edge23
  122. Prism(Q_2, R_2, T_2, O_2) → e, Z_2, edge32, edge28, edge34, edge35, edge29, edge36, edge30, A_3, face15, face16, face18, face17, face14, edge31, edge33
  123. Prism(U, V, F_2, D_2, T, K_2) → j, B_3, face19, face25, edgeUV, edge40, edge42, edge37, edgeTU_1, edge39, edge41, edge44, C_3, edge43, edge38, edge45, edge47, edge48, edge49, edge46, D_3, E_3, face24, face21, face22, face23, face20
  124. Prism(K_2, T_1, U_1, A_1) → l, F_3, edge56, edge50, edge55, edge57, edge51, edge58, edge52, G_3, face27, face28, face30, face29, face26, edge54, edge53
  125. Prism(Z, T, U, A_1, B_2) → n, H_3, edgeTZ, edgeTU, edge60, edge62, edge63, edge59, edge61, edge64, edge65, edge67, I_3, edge68, edge66, J_3, face31, face33, face32, face34, face35, face36
  126. Prism(U_1, I_3, Q_1, J_2) → o, K_3, edge69, edge72, edge76, edge71, edge74, edge77, edge75, L_3, face37, face41, face40, face39, face38, edge73, edge70
  127. Prism(R_1, W_1, B_2, G_2) → q, M_3, edge79, edge80, edge82, edge83, edge84, edge86, edge85, N_3, face42, face44, face46, face45, face43, edge78, edge81
  128. Prism(A_2, A_1, K_2, E_2, T, H_2, R_1) → s, O_3, face47, face48, face51, face54, edge90, edge91, edge97, edge87, edge88, edge96, P_3, edge93, edge92, edge100, edge98, edge89, edge99, edge94, edge101, edge102, edge103, Q_3, edge104, edge95, R_3, S_3, face53, face49, face50, face52
  129. Prism(S_3, R_3, Q_3, I_2) → t, T_3, edge109, edge105, edge112, edge110, edge106, edge113, edge107, U_3, face56, face58, face59, face57, face55, edge111, edge108
  130. Prism(R_1, P_3, O_3, G_2) → v, V_3, edge115, edge114, edge121, edge120, edge117, edge122, edge118, W_3, face60, face62, face64, face63, face61, edge116, edge119
  131. Prism(F_2, C_2, U, E_2, D_2, K, V_1) → a_1, Z_3, face70, face65, face66, face72, edge132, edge126, edge127, edge134, edge123, edge124, A_4, edge129, edge133, edge128, edge136, edge135, edge125, edge130, edge137, edge138, edge139, B_4, edge140, edge131, C_4, D_4, face71, face69, face67, face68
  132. Prism(V_1, Z_3, J_2, G_2) → b_1, E_4, edge142, edge141, edge148, edge147, edge144, edge149, edge145, F_4, face73, face75, face77, face76, face74, edge143, edge146
  133. Prism(B_4, H_2, C_4, A_2) → c_1, G_4, edge156, edge150, edge155, edge157, edge151, edge158, edge152, H_4, face79, face80, face82, face81, face78, edge153, edge154

AI Drawing Prompt Reference

Draw two parts of a cube, one with vertices at points A, B, and C, and the other with vertices at points L, M, and N. Construct a cube using points A, B, and C, and another cube using points L, M, and N. Find the midpoint S₂ of H and B, and the midpoint S₁ of S and M. Draw a line p₁ through S₁ and S₂, and draw lines f, g, h, and i from S₂, S₁, S₂, and S₁ respectively. Take points I and J on line p₁ and draw vector u from I to J. Translate lines i, g, h, and i along vector u, rotate points A, B, C, D, E, F, G, and H around line p₁ by α degrees, then rotate points A, B, C, D, E, F, G, and H around line f by β degrees. Finally, rotate cube c around line p₁ by α degrees, then around line f by β degrees, and rotate point G around line h by γ degrees.
The prompt above was compiled from the original drawing commands and is for reference only.