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Cube and Prism Construction: Demonstrating geometric concepts

Cube and Prism Construction: Demonstrating geometric concepts
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2018-06-27 16:40
PolygonSolid GeometryGeometric Construction
This example demonstrates the construction of a cube (Würfel) and a prism (Quader), involving concepts such as polygons, edges, and faces. The GeoGebra commands used include Point, Cube, Segment, Circle, Line, Intersect, Polygon, Prism, and objects like r, G, A, W, B, C, D, E, F. The construction involves determining vertices, edges, and faces of the cube and prism. Suitable for middle or high school mathematics to understand solid geometry and geometric construction. Key concepts include geometric construction, solid geometry, polygons, edges, and faces.

GeoGebra Commands & Parameters

  1. Point(Circle[(1, -1, -1), Distance[(-1, -1, -1), (1, -1, -1)], Segment[(-1, -1, -1), (1, -1, -1)]]) → A
  2. Cube((-1, -1, -1), (1, -1, -1), A) → W, B, FlächeABFE, FlächeCDEF, Kante2, Kante1, Kante4, KanteAB, Kante3, KanteBF, KanteCF, KanteCD, C, Kante5, KanteDE, KanteAE, KanteEF, D, E, F, Fläche1, Fläche3, Fläche2, Fläche4
  3. Segment(G, F) → g
  4. Segment(G, C) → f
  5. Segment(G, D) → h
  6. Circle(F, r, g) → c
  7. Segment(G, E) → i
  8. Circle(E, r, i) → d
  9. Circle(D, r, h) → e
  10. Circle(C, r, f) → k
  11. Circle(B, r, h) → p
  12. Circle(A, r, f) → q
  13. Circle(H, r, i) → r_1
  14. Circle(I, r, g) → s
  15. Point(c) → P_1
  16. Line(P_1, KanteCF) → j
  17. Intersect(j, k, 1) → J
  18. Line(P_1, KanteEF) → l
  19. Intersect(l, d, 1) → K
  20. Line(P_1, KanteBF) → m
  21. Intersect(m, p, 1) → L
  22. Line(J, Kante3) → n
  23. Intersect(n, r_1, 1) → M
  24. Line(K, KanteDE) → t
  25. Intersect(t, e, 1) → N
  26. Line(N, Kante5) → a
  27. Line(K, KanteAE) → b
  28. Intersect(a, s, 1) → O
  29. Intersect(b, q, 1) → P
  30. Polygon(P_1, J, N, K) → v1, p_1, j_1, n_1, k_1
  31. Prism(v1, L) → o, Q, KanteJQ, KanteNR, KanteKS, KanteLQ, KanteQR, KanteRS, KanteLS, R, S, Fläche5, FlächeJNRQ, FlächeKNRS, Fläche6, FlächeLQRS, Kante6
  32. Intersect(KanteBF, v1) → T
  33. Intersect(Kante3, v1) → U
  34. Intersect(Kante5, v1) → V
  35. Intersect(Kante3, FlächeLQRS) → Z
  36. Intersect(KanteBF, FlächeLQRS) → A_1
  37. Intersect(Kante5, FlächeLQRS) → B_1
  38. Intersect(KanteAE, FlächeLQRS) → C_1
  39. Intersect(KanteAE, v1) → D_1
  40. Segment(B_1, C_1) → f_1
  41. Segment(C_1, A_1) → g_1
  42. Segment(A_1, Z) → h_1
  43. Segment(Z, B_1) → i_1
  44. Segment(U, V) → l_1
  45. Segment(T, U) → m_1
  46. Segment(V, D_1) → q_1
  47. Segment(D_1, T) → s_1
  48. Intersect(k_1, Fläche3) → E_1
  49. Intersect(j_1, Fläche3) → F_1
  50. Segment(E_1, F_1) → t_1
  51. Intersect(KanteQR, Fläche3) → G_1
  52. Intersect(KanteLS, Fläche3) → H_1
  53. Intersect(k_1, Fläche4) → I_1
  54. Intersect(j_1, Fläche4) → J_1
  55. Intersect(KanteQR, Fläche4) → K_1
  56. Intersect(KanteLS, Fläche4) → L_1
  57. Segment(I_1, L_1) → a_1
  58. Segment(L_1, K_1) → b_1
  59. Segment(J_1, K_1) → c_1
  60. Intersect(k_1, a_1) → M_1
  61. Segment(J_1, M_1) → d_1
  62. Segment(H_1, G_1) → f_2
  63. Segment(E_1, H_1) → g_2
  64. Intersect(Kante2, FlächeJNRQ) → O_1
  65. Intersect(KanteCF, FlächeJNRQ) → Q_1
  66. Intersect(KanteDE, FlächeJNRQ) → R_1
  67. Intersect(Kante4, FlächeJNRQ) → S_1
  68. Segment(R_1, S_1) → h_2
  69. Segment(Q_1, R_1) → i_2
  70. Segment(Q_1, O_1) → j_2
  71. Segment(O_1, S_1) → k_2
  72. Intersect(KanteCF, Fläche6) → T_1
  73. Intersect(Kante2, Fläche6) → U_1
  74. Intersect(KanteDE, Fläche6) → V_1
  75. Intersect(Kante4, Fläche6) → W_1
  76. Segment(V_1, T_1) → l_2
  77. Segment(V_1, W_1) → m_2
  78. Segment(T_1, U_1) → n_2
  79. Segment(W_1, U_1) → p_2
  80. Intersect(Kante6, FlächeCDEF) → Z_1
  81. Intersect(KanteJQ, FlächeCDEF) → A_2
  82. Intersect(KanteNR, FlächeCDEF) → B_2
  83. Segment(Z_1, A_2) → q_2
  84. Segment(A_2, B_2) → r_2
  85. Intersect(KanteKS, FlächeCDEF) → C_2
  86. Segment(B_2, C_2) → s_2
  87. Segment(Z_1, C_2) → t_2
  88. Intersect(KanteKS, Fläche1) → D_2
  89. Intersect(KanteNR, Fläche1) → E_2
  90. Intersect(Kante6, Fläche1) → F_2
  91. Intersect(KanteJQ, Fläche1) → G_2
  92. Segment(D_2, F_2) → a_2
  93. Segment(F_2, G_2) → b_2
  94. Segment(E_2, D_2) → c_2
  95. Segment(G_2, E_2) → d_2
  96. Intersect(KanteEF, Fläche5) → H_2
  97. Intersect(KanteCD, Fläche5) → I_2
  98. Intersect(KanteAB, Fläche5) → J_2
  99. Intersect(Kante1, Fläche5) → K_2
  100. Intersect(KanteCD, FlächeKNRS) → L_2
  101. Intersect(Kante1, FlächeKNRS) → M_2
  102. Intersect(KanteEF, FlächeKNRS) → N_2
  103. Intersect(KanteAB, FlächeKNRS) → O_2
  104. Segment(L_2, N_2) → e_2
  105. Segment(N_2, O_2) → f_3
  106. Segment(L_2, M_2) → g_3
  107. Segment(M_2, O_2) → h_3
  108. Segment(H_2, I_2) → i_3
  109. Segment(I_2, K_2) → j_3
  110. Segment(J_2, K_2) → k_3
  111. Segment(H_2, J_2) → l_3
  112. Intersect(p_1, Fläche2) → N_1
  113. Intersect(n_1, Fläche2) → P_2
  114. Intersect(KanteLQ, Fläche2) → Q_2
  115. Intersect(KanteRS, Fläche2) → R_2
  116. Segment(N_1, P_2) → e_1
  117. Segment(P_2, R_2) → m_3
  118. Segment(N_1, Q_2) → n_3
  119. Segment(Q_2, R_2) → p_3
  120. Intersect(n_1, FlächeABFE) → S_2
  121. Intersect(KanteRS, FlächeABFE) → T_2
  122. Intersect(p_1, FlächeABFE) → U_2
  123. Intersect(KanteLQ, FlächeABFE) → V_2
  124. Segment(S_2, U_2) → q_3
  125. Segment(U_2, V_2) → r_3
  126. Segment(S_2, T_2) → s_3
  127. Segment(T_2, V_2) → t_3
  128. Segment(F_1, G_1) → a_3