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Beginners Metatron's Cube

Beginners Metatron's Cube
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2014-09-15 04:49
CircleSolid GeometryGeometric Construction
This example demonstrates how to create Metatron's Cube, a geometric figure consisting of 13 circles and lines connecting their centers, showcasing symmetry and spatial relationships. Core math concepts include circles, centroids, line segments, geometric construction, and symmetry. It uses GeoGebra commands like Intersect, Circle, Point, Segment, and Ellipse. Suitable for beginners learning geometric construction, spatial visualization, and symmetry concepts, serving as a foundational tool for geometry education or exploratory learning.

GeoGebra Commands & Parameters

  1. Intersect(a, b) → A
  2. Circle(A, B) → c
  3. Point(yAxis) → G
  4. Intersect(c, yAxis, 2) → H
  5. Circle(G, H) → f
  6. Point(yAxis) → I
  7. Intersect(f, yAxis, 2) → J
  8. Circle(I, J) → g
  9. Intersect(c, b, 2) → D
  10. Circle(D, A) → d
  11. Intersect(d, b, 2) → F
  12. Circle(F, D) → e
  13. Intersect(c, a, 2) → K
  14. Circle(K, A) → h
  15. Intersect(h, a, 2) → L
  16. Circle(L, K) → k
  17. Intersect(k, a, 2) → M
  18. Circle(M, L) → p
  19. Intersect(p, a, 2) → N
  20. Circle(N, M) → q
  21. Intersect(c, b, 1) → O
  22. Circle(O, A) → r
  23. Intersect(r, b, 2) → P
  24. Circle(P, O) → s
  25. Intersect(s, b, 2) → Q
  26. Circle(Q, P) → t
  27. Intersect(t, b, 2) → R
  28. Circle(R, Q) → c_1
  29. Intersect(c_1, b, 2) → S
  30. Circle(S, R) → d_1
  31. Circle(D, A) → e_1
  32. Intersect(e_1, b, 2) → T
  33. Circle(T, D) → f_1
  34. Intersect(f_1, b, 2) → U
  35. Circle(U, T) → g_1
  36. Intersect(g_1, b, 2) → V
  37. Circle(V, U) → h_1
  38. Intersect(c, r, 1) → W
  39. Circle(W, A) → k_1
  40. Intersect(k_1, a, 2) → Z
  41. Circle(Z, W) → p_1
  42. Intersect(p_1, a, 1) → A_1
  43. Circle(A_1, Z) → q_1
  44. Intersect(q_1, a, 2) → B_1
  45. Circle(B_1, A_1) → r_1
  46. Circle(R, Q) → s_1
  47. Point(yAxis) → C
  48. Intersect(c, yAxis, 1) → E
  49. Circle(C, E) → t_1
  50. Point(yAxis) → C_1
  51. Intersect(t_1, yAxis, 2) → D_1
  52. Circle(C_1, D_1) → c_2
  53. Segment(P, Z) → i
  54. Segment(P, G) → j
  55. Segment(G, L) → l
  56. Segment(L, T) → m
  57. Segment(Z, C) → n
  58. Segment(C, T) → a_1
  59. Segment(B_1, C_1) → b_1
  60. Segment(B_1, R) → i_1
  61. Segment(R, I) → j_1
  62. Segment(I, N) → l_1
  63. Segment(N, V) → m_1
  64. Segment(C_1, V) → n_1
  65. Segment(I, V) → a_2
  66. Segment(I, B_1) → b_2
  67. Segment(B_1, V) → d_2
  68. Segment(N, R) → e_2
  69. Segment(R, C_1) → f_2
  70. Segment(C_1, N) → g_2
  71. Segment(P, A) → h_2
  72. Segment(A, L) → i_2
  73. Segment(A, C) → j_2
  74. Segment(I, G) → k_2
  75. Segment(N, L) → l_2
  76. Segment(T, V) → m_2
  77. Segment(C, C_1) → n_2
  78. Segment(B_1, Z) → p_2
  79. Segment(R, P) → q_2
  80. Segment(A, Z) → r_2
  81. Segment(A, T) → s_2
  82. Segment(G, A) → t_2
  83. Segment(L, C) → a_3
  84. Segment(L, P) → b_3
  85. Segment(P, C) → c_3
  86. Segment(G, Z) → d_3
  87. Segment(G, T) → e_3
  88. Segment(Z, T) → f_3
  89. Intersect(j_1, l_1) → E_1
  90. Intersect(b_1, n_1) → F_1
  91. Intersect(m_1, a_2) → G_1
  92. Ellipse(E_1, F_1, G_1) → g_3
  93. Intersect(g_3, i_1, 1) → H_1
  94. Ellipse(H_1, G_1, F_1) → h_3
  95. Intersect(g_3, h_3, 1) → I_1
  96. Intersect(g_3, h_3, 4) → J_1
  97. Ellipse(I_1, J_1, F_1) → k_3
  98. Intersect(h_3, k_3, 3) → K_1
  99. Intersect(h_3, k_3, 2) → L_1
  100. Segment(K_1, L_1) → i_3
  101. Intersect(g_3, h_3, 2) → M_1
  102. Intersect(g_3, h_3, 3) → N_1
  103. Segment(M_1, N_1) → j_3
  104. Intersect(g_3, k_3, 1) → O_1
  105. Intersect(g_3, k_3, 4) → P_1
  106. Segment(O_1, P_1) → l_3

AI Drawing Prompt Reference

Draw a geometric figure consisting of 13 circles and lines connecting their centers, showcasing symmetry and spatial relationships. Start by drawing a large circle, then draw 12 concentric circles inside it, each with its center connected to the center of the large circle. Next, connect these circle centers to form a hexagonal structure. Finally, draw a circle inscribed in the hexagon to complete the figure.
The prompt above was compiled from the original drawing commands and is for reference only.