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Cube Geometry: Shortest Paths Between Opposite Vertices

Cube Geometry: Shortest Paths Between Opposite Vertices
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2015-07-14 02:31
VectorSolid GeometryGeometric Construction
In collections Cube Geometry
This example demonstrates the 6 shortest paths connecting opposite vertices in a cube. Core math concepts include solid geometry, path optimization, and spatial visualization. It is constructed using GeoGebra commands like Intersect, Point, Cube, Midpoint, and Segment, highlighting key geometric principles. Ideal for high school geometry education and spatial reasoning development.

GeoGebra Commands & Parameters

  1. Intersect(yAxis, zAxis) → A
  2. Point(xAxis) → B
  3. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  4. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  5. Intersect
  6. Midpoint(edgeAE) → I
  7. Midpoint(edgeEH) → J
  8. Midpoint(edgeGH) → K
  9. Midpoint(edgeCG) → L
  10. Midpoint(edgeBC) → M
  11. Midpoint(edgeAB) → N
  12. Segment(F, J) → c
  13. Segment(F, I) → d
  14. Segment(F, N) → e
  15. Segment(F, M) → f
  16. Segment(F, L) → g
  17. Segment(F, K) → h
  18. Segment(K, D) → i
  19. Segment(J, D) → j
  20. Segment(I, D) → k
  21. Segment(N, D) → l
  22. Segment(M, D) → m
  23. Segment(L, D) → n