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Hexahedron as Planar Graph

Hexahedron as Planar Graph
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2017-11-16 17:58
PolygonSolid GeometryGeometric Construction
This example demonstrates how a hexahedron (cube) can be represented as a planar graph. Key mathematical concepts include planar graphs, polygons, and vertex connection relationships. Construction involves using commands like Segment and Polygon with objects such as H, C, D, E, K, L, M, N, O, T, h, i, j, k, i_1, k_1, o, pic1, F, J, pic2, a, b, c, d, e, f, G, I, veelhoek1, g, l, m, n, P, Q, R, S, veelhoek2, p. It is suitable for high school mathematics and discrete mathematics students to understand the transformation between spatial geometry and planar graphs, useful for teaching demonstrations or geometric construction practice.

GeoGebra Commands & Parameters

  1. Segment(L, M) → h
  2. Segment(M, N) → i
  3. Segment(N, E) → j
  4. Segment(T, M) → k
  5. Segment(K, L) → i_1
  6. Segment(O, N) → k_1
  7. Segment(T, K) → a
  8. Segment(L, E) → b
  9. Segment(K, H) → c
  10. Segment(T, O) → d
  11. Segment(O, H) → e
  12. Segment(H, E) → f
  13. Polygon(G, I, 4) → veelhoek1, g, l, m, n, P, Q
  14. Polygon(R, S, 4) → veelhoek2, p, q, r, s, U, V
  15. Segment(G, R) → t
  16. Segment(S, I) → g_1
  17. Segment(I, G) → h_1
  18. Segment(Q, V) → f_1
  19. Segment(U, P) → j_1