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Two Parts of a Cube

Two Parts of a Cube
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2019-04-30 03:52
AngleSolid GeometryGeometric Construction
In collections TWO PARTS OF A CUBE
This example demonstrates two parts of a cube. It involves key concepts such as angles, straight lines, quadratic functions, and symmetry. Using GeoGebra commands like Point, Cube, Midpoint, Line, etc., the construction of the cube's faces and edges is illustrated. Suitable for high school geometry education to help students understand basic concepts of 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, G''', L_2, C''', E_1, M_2, H_1) → b, P_2, face2, face6, face5, face7, face4, face9, edge4, edge1, edge2, edge8, Q_2, edge7, edge11, edge6, edge5, edge10, edge3, edge15, edge9, edge12, edge16, R_2, edge13, edge17, edge18, edge19, edge20, edge21, edge14, T_2, U_2, V_2, face8, face3, face1
  121. Prism(P_2, Q_2, R_2, D_1) → d, W_2, edge26, edge22, edge28, edge29, edge23, edge30, edge24, Z_2, face11, face12, face14, face13, face10, edge25, edge27
  122. Prism(T, D_2, F_2, V, U, H_2) → e, A_3, face15, face21, edge31, edge36, edge34, edgeUV_1, edgeTU_1, edge32, edge37, edge38, B_3, edge35, edge33, edge39, edge41, edge42, edge43, edge40, C_3, D_3, face20, face16, face19, face18, face17
  123. Midpoint(T_1, B_3) → E_3
  124. Prism(T_1, E_3, U_1, D_3, A_2) → j, F_3, edge46, edge48, edge47, edge45, edge44, edge53, edge49, edge52, edge50, edge54, G_3, edge55, edge51, H_3, face24, face22, face26, face25, face23, face27
  125. Prism(A_1, U, T, Z, Z_1) → m, I_3, edge57, edgeTU_2, edgeTZ, edge59, edge61, edge58, edge56, edge60, edge62, edge64, J_3, edge65, edge63, K_3, face28, face31, face29, face30, face32, face33
  126. Prism(R_1, W_1, K_3, G_2) → n, L_3, edge68, edge67, edge70, edge73, edge71, edge74, edge72, M_3, face34, face36, face38, face37, face35, edge66, edge69
  127. Prism(Z_1, J_2, B_1, R_1) → q, N_3, edge75, edge78, edge82, edge77, edge79, edge83, edge80, O_3, face39, face43, face42, face41, face40, edge81, edge76
  128. Prism(O_3, A_2, T_1, Q_1, F_2, W) → r, P_3, face45, face49, edge92, edge90, edge87, edge88, edge94, edge84, edge93, edge91, Q_3, edge89, edge95, edge85, edge96, edge97, edge98, edge86, R_3, S_3, face50, face44, face48, face46, face47
  129. Prism(U, T, K, V, K_2) → t, T_3, edgeTU, edgeKT, edgeKV, edgeUV, edge101, edge100, edge99, edge102, edge103, edge105, U_3, edge106, edge104, V_3, faceKTUV, face53, face51, face52, face54, face55
  130. Prism(T_1, W_1, T_3, A_2) → v, W_3, edge109, edge108, edge111, edge114, edge112, edge115, edge113, Z_3, face56, face58, face60, face59, face57, edge107, edge110