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Geometric Construction of Octahedron as Planar Graph

Geometric Construction of Octahedron as Planar Graph
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2017-11-17 14:20
PolygonSolid GeometryGeometric Construction
In collections Solids, graphs and paths
This example demonstrates representing an octahedron as a planar graph, illustrating the relationship between solid geometry and graph theory. Core concepts include polyhedra, planar graphs, and Euler's formula. Construction utilizes GeoGebra commands like Segment and Polygon to define vertices and edges precisely. Suitable for high school or college geometry classes to visualize 3D shapes in 2D.

GeoGebra Commands & Parameters

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