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Hexaederstern Construction

Hexaederstern Construction
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2018-10-25 00:52
PolygonSolid GeometryGeometric Construction
In collections surface 3D /3D-Oberflächen 1
This example demonstrates the construction of a hexahedron star by creating a cube and generating its star polyhedron. Key math concepts include solid geometry, polygon construction, linear optimization, ellipse, power functions, histogram, and geometric mean. GeoGebra commands used are: cube construction, intersection calculation, midpoint determination, and polygon drawing. Suitable for high school and above students to learn complex geometric shape construction methods, ideal for teaching solid geometry and geometric constructions.

GeoGebra Commands & Parameters

  1. Cube((1, 0, 0), (0, 1, 0), zAxis) → a_1, A, Fläche4, FlächeABFE, FlächeCDEF, Kante2, Kante1, Kante4, KanteAB, Kante3, KanteBF, KanteCF, B, KanteCD, Kante5, KanteDE, KanteAE, KanteEF, C, D, E, F, Fläche1, Fläche3, Fläche2
  2. Intersect(Kante2, xAxis) → G
  3. Intersect(Kante1, yAxis) → H
  4. Midpoint(B, C) → S3
  5. Midpoint(E, C) → S6
  6. Midpoint(A, D) → S5
  7. Midpoint(D, G) → S4
  8. Midpoint(A, G) → S1
  9. Midpoint(E, B) → S2
  10. Polygon(A, P1, B) → d1, b, a_2, p1
  11. Polygon(P1, G, B) → d2, b_1, f, g
  12. Polygon(P1, H, G) → d3, g_1, h, h_1
  13. Polygon(P1, A, H) → d4, h_2, i, a_3
  14. Polygon(E, P2, F) → d5, f_1, e, p2
  15. Polygon(P2, B, F) → d6, f_2, j, b_2
  16. Polygon(P2, A, B) → d7, b_3, k, a_4
  17. Polygon(P2, E, A) → d8, a_5, l, e_1
  18. Polygon(F, P3, C) → d9, c, f_3, p3
  19. Polygon(F, B, P3) → d10, m, f_4, b_4
  20. Polygon(B, G, P3) → d11, n, b_5, g_2
  21. Polygon(G, C, P3) → d12, p, g_3, c_1
  22. Polygon(C, P4, D) → d13, d, c_2, p4
  23. Polygon(C, G, P4) → d14, q, c_3, g_4
  24. Polygon(P4, G, H) → d15, h_3, r, g_5
  25. Polygon(P4, H, D) → d16, d_1, s, h_4
  26. Polygon(D, P5, E) → d17, e_2, d_2, p5
  27. Polygon(D, H, P5) → d18, t, d_3, h_5
  28. Polygon(P5, H, A) → d19, a_6, i_1, h_6
  29. Polygon(P5, A, E) → d20, e_3, j_1, a_7
  30. Polygon(C, P6, D) → d21, d_4, c_4, p6
  31. Polygon(D, P6, E) → d22, e_4, d_5, k_1
  32. Polygon(F, P6, E) → d23, e_5, f_5, l_1
  33. Polygon(F, C, P6) → d24, m_1, f_6, c_5