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Symmetry in Sphere and Dodecahedron

Symmetry in Sphere and Dodecahedron
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2019-05-12 05:21
Solid GeometryTransformationGeometric Construction
This example demonstrates the symmetry in sphere and dodecahedron. Key mathematical concepts include geometric transformations, symmetry, and polyhedra. It uses GeoGebra commands such as Intersect, Circle, Sphere, Point, Segment, Rotate, Polygon, and Dodecahedron for geometric construction. Suitable for high school and above students or teachers.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → STAR
  2. Circle(STAR, a) → c
  3. Sphere(STAR, a) → b
  4. Point(c) → planet
  5. Circle(STAR, d) → e
  6. Point(e) → F
  7. Segment(STAR, F) → f
  8. Rotate(F, 72°, STAR) → G
  9. Segment(STAR, G) → g
  10. Rotate(G, 72°, STAR) → H
  11. Segment(STAR, H) → h
  12. Rotate(H, 72°, STAR) → C
  13. Segment(STAR, C) → i
  14. Rotate(C, 72°, STAR) → B
  15. Segment(B, STAR) → j
  16. Polygon(F, G, 5) → poly1, k, m, n, p, q, C_1, E, F_1
  17. Dodecahedron(poly1, true) → l, A, P, Q, R, S, T, U, face1, faceAGFKL, face2, face3, D, face4, faceJOTUP, faceKLQUP, faceALQRM, faceDMRSN, faceINSTO, faceQRSTU, edgeFK, edge2, edgeJP, I, edgeKP, edgeKL, edgeAL, edgeAG, edgeAM, edgeDM, edge1, edgeDN, edgeIN, edgeEI, J, edgeIO, edgeJO, edgeOT, edgeTU, edgePU, edgeQU, edgeLQ, edgeQR, edgeMR, edgeRS, K, edgeNS, edgeST, L, M, N, O
  18. Segment(H, planet) → r
  19. Segment(C, planet) → s
  20. Segment(B, planet) → t
  21. Segment(G, planet) → f_1
  22. Segment(F, planet) → g_1
  23. Segment(S, planet) → h_1
  24. Segment(T, planet) → i_1
  25. Segment(Q, planet) → j_1
  26. Segment(R, planet) → k_1
  27. Segment(U, planet) → l_1
  28. Segment(N, planet) → m_1
  29. Segment(D, planet) → n_1
  30. Segment(O, planet) → p_1
  31. Segment(J, planet) → q_1
  32. Segment(M, planet) → r_1
  33. Segment(P, planet) → s_1
  34. Segment(A, planet) → t_1
  35. Segment(L, planet) → a_1
  36. Segment(K, planet) → b_1
  37. Segment(I, planet) → c_1

AI Drawing Prompt Reference

Draw a sphere and a dodecahedron with the sphere's center at the origin. Use rotations to demonstrate the symmetry of the dodecahedron. Start by drawing the sphere and a circle, then create the dodecahedron and rotate its vertices. Finally, connect the sphere's center to the dodecahedron's vertices to show the symmetry.
The prompt above was compiled from the original drawing commands and is for reference only.