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Cube Parts Demonstration by Renáta Vágová (5)

Cube Parts Demonstration by Renáta Vágová (5)
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2019-04-24 14:19
PolygonSolid GeometryOptimization
In collections TWO PARTS OF A CUBE
This example demonstrates different parts of a cube and their geometric relationships. It involves core math concepts like solid geometry, polygons, linear programming, and logarithms. The construction uses GeoGebra commands and objects such as Point, Cube, Intersect, Line, Rotate, Polygon, and Pyramid. Suitable for high school and above students to understand spatial geometry and optimization problems.

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) → a, 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) → I
  6. Point(xAxis) → J
  7. Point(Circle[J, Distance[I, J], Segment[I, J]]) → K
  8. Cube(I, J, K) → b, L, faceKLPO, faceMNOP, edgeIL_1, edgeIJ_1, edgeJK_1, edgeKL_1, edgeIM_1, edgeLP_1, edgeMP_1, edgeMN_1, M, edgeJN_1, edgeNO, edgeKO, edgeOP, N, O, P, faceIJKL, faceILPM_1, faceIJNM_1, faceJKON
  9. Intersect(yAxis, xAxis) → Q
  10. Point(xAxis) → R
  11. Point(Circle[R, Distance[Q, R], Segment[Q, R]]) → S
  12. Cube(Q, R, S) → c, T, faceSTZW, faceUVWZ, edgeQT_1, edgeQR, edgeRS_1, edgeST_1, edgeQU, edgeTZ, edgeUZ, edgeUV, U, edgeRV_1, edgeVW_1, edgeSW_1, edgeWZ, V, W, Z, faceQRST, faceQTZU, faceQRVU, faceRSWV
  13. Point(xAxis) → A_1
  14. Point(xAxis) → B_1
  15. Point(Circle[B_1, Distance[A_1, B_1], Segment[A_1, B_1]]) → C_1
  16. Cube(A_1, B_1, C_1) → d, D_1, face5, face6, edge2, edge1, edge4, edge6, edge3, edge8, edge10, edge9, E_1, edge5, edge11, edge7, edge12, F_1, G_1, H_1, face1, face3, face2, face4
  17. Point(xAxis) → I_1
  18. Point(xAxis) → J_1
  19. Point(Circle[J_1, Distance[I_1, J_1], Segment[I_1, J_1]]) → K_1
  20. Cube(I_1, J_1, K_1) → e, L_1, face11, face12, edge14, edge13, edge16, edge18, edge15, edge20, edge22, edge21, M_1, edge17, edge23, edge19, edge24, N_1, O_1, P_1, face7, face9, face8, face10
  21. Line(A, yAxis) → f
  22. Line(I, yAxis) → g
  23. Line(A_1, yAxis) → h
  24. Line(I_1, yAxis) → i
  25. Line(A, zAxis) → j
  26. Line(I, zAxis) → k
  27. Line(A_1, zAxis) → l
  28. Line(I_1, zAxis) → m
  29. Rotate(a, α, f) → a'
  30. Rotate(a', β, xAxis) → a''
  31. Rotate(a'', γ, j) → a'''
  32. Rotate(b, δ, g) → b'
  33. Rotate(b', ε, xAxis) → b''
  34. Rotate(b'', ζ, k) → b'''
  35. Rotate(c, (-η), yAxis) → c'
  36. Rotate(c', θ, xAxis) → c''
  37. Rotate(c'', ι, zAxis) → c'''
  38. Rotate(d, κ, h) → d'
  39. Rotate(d', λ, xAxis) → d''
  40. Rotate(d'', μ, l) → d'''
  41. Rotate(e, ν, i) → e'
  42. Rotate(e', ξ, xAxis) → e''
  43. Rotate(e'', ο, m) → e'''
  44. Polygon(B, G, E) → t1, e_1, b_1, g_1
  45. Polygon(E, B, F) → t2, f_1, e_2, b_2
  46. Polygon(E, F, G) → t3, g_2, e_3, f_2
  47. Polygon(B, G, F) → t4, f_3, b_3, g_3
  48. Rotate(t1, α, f) → t1'
  49. Rotate(t1', β, xAxis) → t1''
  50. Rotate(t1'', γ, j) → t1'''
  51. Rotate(t3, α, f) → t3'
  52. Rotate(t3', β, xAxis) → t3''
  53. Rotate(t3'', γ, j) → t3'''
  54. Rotate(t4, α, f) → t4'
  55. Rotate(t4', β, xAxis) → t4''
  56. Rotate(t4'', γ, j) → t4'''
  57. Rotate(t2, α, f) → t2'
  58. Rotate(t2', β, xAxis) → t2''
  59. Rotate(t2'', γ, j) → t2'''
  60. Pyramid(L, I, M, P, K) → n, faceILPM, edgeKL, edgeIK_1, edgeKM_1, edgeKP, faceIKL, faceIKM_1, faceKMP, faceKLP, edgeIL, edgeIM_2, edgeMP, edgeLP
  61. Pyramid(M, I, J, N, K) → o, faceIJNM, edgeKM, edgeIK, edgeJK, edgeKN, faceIKM, faceIJK, faceJKN, faceKMN, edgeIM, edgeIJ, edgeJN, edgeMN
  62. Rotate(n, δ, g) → n'
  63. Rotate(n', ε, xAxis) → n''
  64. Rotate(n'', ζ, k) → n'''
  65. Rotate(o, δ, g) → o'
  66. Rotate(o', ε, xAxis) → o''
  67. Rotate(o'', ζ, k) → o'''
  68. Point(c''') → Q_1
  69. Pyramid(Q, Q_1, R, S, T, W) → p, face15, edgeST, edgeQT, edgeQW, edge27, edgeRW_1, edgeSW, edgeTW, face13, face14, faceRSW, faceSTW, faceQTW, edge25, edge26, edgeRS
  70. Pyramid(Q_1, R, W, V) → q, face17, edgeVW, face16, faceRVW, face18, edge28, edgeRW, edge30, edge29, edgeRV
  71. Rotate(p, (-η), yAxis) → p'
  72. Rotate(p', θ, xAxis) → p''
  73. Rotate(p'', ι, zAxis) → p'''
  74. Rotate(q, (-η), yAxis) → q'
  75. Rotate(q', θ, xAxis) → q''
  76. Rotate(q'', ι, zAxis) → q'''
  77. Pyramid(A_1, B_1, C_1, D_1, F_1) → r, face23, edge33, edge35, edge37, edge38, face19, face21, face22, face20, edge31, edge34, edge36, edge32
  78. Pyramid(D_1, A_1, E_1, H_1, F_1) → s, face28, edge42, edge41, edge44, edge46, face24, face25, face27, face26, edge39, edge40, edge45, edge43
  79. Pyramid(C_1, D_1, H_1, F_1) → t, face30, edge52, face29, face32, face31, edge47, edge51, edge49, edge48, edge50
  80. Rotate(r, κ, h) → r'
  81. Rotate(r', λ, xAxis) → r''
  82. Rotate(r'', μ, l) → r'''
  83. Rotate(s, κ, h) → s'
  84. Rotate(s', λ, xAxis) → s''
  85. Rotate(s'', μ, l) → s'''
  86. Rotate(t, κ, h) → t'
  87. Rotate(t', λ, xAxis) → t''
  88. Rotate(t'', μ, l) → t'''
  89. Pyramid(L_1, I_1, J_1, M_1) → u, face33, edge57, face35, face34, face36, edge54, edge53, edge56, edge58, edge55
  90. Rotate(u, ν, i) → u'
  91. Rotate(u', ξ, xAxis) → u''
  92. Rotate(u'', ο, m) → u'''

AI Drawing Prompt Reference

Draw a cube to demonstrate its different parts and geometric relationships. First, create three cubes, each defined by three points on the x-axis spaced equally. Then, draw three lines along the y-axis and z-axis, and rotate each cube around these lines to show different perspectives. Finally, connect the vertices of the cubes to form multiple polygonal faces, highlighting the structure and spatial relationships of the cube.
The prompt above was compiled from the original drawing commands and is for reference only.