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Two Parts of a Cube by Renáta Vágová

Two Parts of a Cube by Renáta Vágová
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2019-04-30 00:57
VectorSolid GeometryGeometric Construction
In collections TWO PARTS OF A CUBE
This example demonstrates two parts of a cube. It involves basic concepts in solid geometry, such as points, lines, faces, and polyhedra. Using GeoGebra commands like Point, Cube, Midpoint, Line, Vector, Translate, and Rotate, the two parts of the cube can be constructed. Suitable for middle school and above students to learn 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(D''', B''') → C_1
  85. Midpoint(D''', A''') → D_1
  86. Midpoint(A''', B''') → E_1
  87. Midpoint(D''', C''') → F_1
  88. Midpoint(C''', B''') → G_1
  89. Pyramid(D_1, C_1, F_1, D''', H''') → b, face5, edge2, edge1, edge3, edgeD'''H''', face3, face4, face2, face1, edge6, edge7, edge5, edge4
  90. Pyramid(C''', F_1, C_1, G_1, G''') → d, face10, edgeC'''G''', edge9, edge8, edge10, face6, face8, face9, face7, edge11, edge13, edge14, edge12
  91. Pyramid(D_1, C_1, E_1, A''', E''') → e, face15, edge16, edge15, edge17, edgeA'''E''', face13, face14, face12, face11, edge20, edge21, edge19, edge18
  92. Pyramid(C_1, E_1, B''', G_1, F''') → j, face20, edge22, edge23, edgeB'''F''', edge24, face18, face16, face17, face19, edge27, edge25, edge26, edge28
  93. Midpoint(B_1, A_1) → H_1
  94. Midpoint(A_1, U) → I_1
  95. Midpoint(U, V) → J_1
  96. Midpoint(V, B_1) → K_1
  97. Midpoint(B_1, W) → L_1
  98. Midpoint(W, K) → M_1
  99. Midpoint(K, T) → N_1
  100. Midpoint(T, U) → O_1
  101. Midpoint(Z, T) → P_1
  102. Midpoint(Z, A_1) → Q_1
  103. Midpoint(M_1, P_1) → R_1
  104. Midpoint(H_1, J_1) → T_1
  105. Midpoint(Q_1, O_1) → U_1
  106. Midpoint(K, V) → V_1
  107. Midpoint(V_1, L_1) → W_1
  108. Prism(K_1, A_1, U, M_1) → l, Z_1, edge30, edge34, edge33, edge31, edge35, edge37, edge36, A_2, face21, face25, face23, face24, face22, edge32, edge29
  109. Prism(Z_1, A_1, L_1, A_2) → m, B_2, edge41, edge43, edge40, edge42, edge44, edge46, edge45, C_2, face26, face29, face28, face30, face27, edge39, edge38
  110. Midpoint(V, T) → D_2
  111. Pyramid(B_1, W, Z, A_1, D_2) → o, face35, edge53, edge48, edge50, edge52, face32, face31, face33, face34, edge47, edgeWZ_1, edge49, edge51
  112. Pyramid(V_1, K, T, O_1, Z) → r, face39, edge57, edgeKZ, edgeTZ, edge56, face36, faceKTZ, face37, face38, edge54, edgeKT_1, edge55, edge58
  113. Pyramid(O_1, T, K, V_1, W) → s, face43, edge61, edgeTW, edgeKW, edge62, face41, faceKTW, face40, face42, edge60, edgeKT, edge59, edge63
  114. Pyramid(V_1, V, U, O_1, B_1) → t, face48, edge69, edge66, edge64, edge68, face46, face44, face45, face47, edge67, edgeUV_1, edge65, edge70
  115. Pyramid(V_1, V, U, O_1, A_1) → v, face53, edge76, edge73, edge71, edge75, face51, face49, face50, face52, edge74, edgeUV, edge72, edge77
  116. Pyramid(B_1, A_1, J_1, D_2) → a_1, face54, edge83, face55, face56, face57, edge78, edge79, edge81, edge82, edge80
  117. Pyramid(W, B_1, V_1, D_2) → b_1, face58, edge89, face59, face61, face60, edge84, edge87, edge85, edge86, edge88
  118. Pyramid(W, Z, N_1, D_2) → c_1, face62, edge94, face63, face65, face64, edgeWZ, edge92, edge90, edge91, edge93
  119. Pyramid(A_1, Z, O_1, D_2) → d_1, face66, edge100, face67, face68, face69, edge95, edge96, edge98, edge99, edge97