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Divide a Cube into Pyramids

Divide a Cube into Pyramids
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2017-02-12 21:33
Solid Geometry
This example demonstrates how to divide a cube into multiple pyramids. Key mathematical concepts include solid geometry and volume calculation. Using GeoGebra commands such as If, Cube, Pyramid, Rotate, etc., the construction of the cube and its divided pyramids is shown. Suitable for high school mathematics education and students learning solid geometry.

GeoGebra Commands & Parameters

  1. If(t < 0.5, (2 * t), 1) → t1
  2. Cube(A, B, xOyPlane) → a, C, faceBCGF, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH_1, edgeEH_1, D, edgeEF, edgeBF, edgeFG, edgeCG, edgeGH_1, E, F, G, H, faceABCD, faceADHE, faceABFE
  3. Pyramid(faceABCD, H) → b, faceADH, faceABH_1, faceBCH_1, faceCDH, edgeDH, edgeAH_1, edgeBH_1, edgeCH_1
  4. Pyramid(faceBCGF, H) → c, faceBCH, faceBFH_1, faceFGH, faceCGH, edgeCH, edgeBH_2, edgeFH_1, edgeGH
  5. Pyramid(faceABFE, H) → d, faceABH, faceAEH, faceEFH, faceBFH, edgeBH, edgeAH, edgeEH, edgeFH
  6. Rotate(E, (90° * t1), edgeAB) → E'
  7. Midpoint(E', B) → I
  8. OrthogonalLine(I, Polygon[A, I, B]) → e
  9. Rotate(G, (90° * t1), edgeBC) → G'
  10. Midpoint(B, G') → J
  11. OrthogonalLine(J, Polygon[B, C, G']) → f
  12. Rotate(Pyramid[faceABCD, H], 0°, edgeDH) → b'
  13. If(t ≥ 0.5, (2 * (t - 0.5)), 0) → t2
  14. Rotate(Rotate[c, (90° * t1), edgeBC], (-((90° * t2))), f) → c'
  15. Rotate(Rotate[d, (90° * t1), edgeAB], (-90° * t2), e) → d'
  16. Segment(A, B) → g
  17. Segment(B, C) → h
  18. Segment(C, D) → i
  19. Segment(D, A) → j
  20. Segment(A, E) → k
  21. Segment(B, F) → l
  22. Segment(C, G) → m
  23. Segment(D, H) → n
  24. Segment(E, F) → p
  25. Segment(F, G) → q
  26. Segment(G, H) → r
  27. Segment(H, E) → s