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Metatron's Cube

Metatron's Cube
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2017-09-25 05:27
CirclePolygonSolid GeometryGeometric Construction
This example demonstrates the construction of Metatron's Cube and its connection to the Zodiac. It involves core mathematical concepts such as geometric construction, circles, polygons, and solid geometry. Key GeoGebra commands/objects used in the construction include Intersect, Point, Segment, Circle, Line, Polygon, Distance, Pyramid, Tetrahedron, Plane, and Mirror. It is suitable for high school students and math enthusiasts studying geometric construction and solid geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Segment(A, B) → f
  4. Circle(A, Segment[A, B]) → c
  5. Point(yAxis) → C
  6. Circle(C, f) → d
  7. Point(yAxis) → D
  8. Circle(D, f) → e
  9. Point(yAxis) → E
  10. Circle(E, f) → g
  11. Point(yAxis) → F
  12. Circle(F, f) → h
  13. Circle(G, f) → k
  14. Circle(H, f) → p
  15. Circle(I, f) → q
  16. Circle(J, f) → r
  17. Line(J, G) → i
  18. Line(I, H) → j
  19. Point(j) → K
  20. Circle(K, f) → s
  21. Point(j) → L
  22. Circle(L, f) → t
  23. Point(i) → M
  24. Circle(M, f) → c_1
  25. Point(i) → N
  26. Circle(N, f) → d_1
  27. Polygon(L, F, N, K, E, M) → poly1, l, f_1, n, k_1, e_1, m
  28. Polygon(M, F, K) → t1, k_2, m_1, f_2
  29. Polygon(L, E, N) → t2, n_1, l_1, e_2
  30. Intersect(d, f_2, 2) → O
  31. Intersect(f_2, n_1) → P
  32. Intersect(k_2, n_1) → Q
  33. Intersect(k_2, e_2) → R
  34. Intersect(m_1, e_2) → S
  35. Intersect(m_1, l_1) → T
  36. Intersect(f_2, l_1) → U
  37. Polygon(P, Q, R, S, T, U) → poly2, p_1, q_1, r_1, s_1, t_1, u
  38. Distance(M, F) → distanceMF
  39. Distance(S, K) → distanceSK
  40. Distance(M, F) → MF
  41. Distance(S, K) → SK
  42. Pyramid(t2, 0) → o, V, faceELV, faceENV, faceLNV, edgeLV, edgeEV, edgeNV
  43. Tetrahedron(L, E, faceLNV) → v, W, edgeLZ, edgeWZ, edgeEZ, Z, faceELW, faceLWZ, faceELZ, faceEWZ, edgeLW, edgeEL, edgeEW
  44. Plane(Z, xOyPlane) → w
  45. Mirror(faceLWZ, w) → faceLWZ'
  46. Mirror(faceELZ, w) → faceELZ'
  47. Mirror(faceEWZ, w) → faceEWZ'