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Partition of a Cube into Three Pyramids

Partition of a Cube into Three Pyramids
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2014-10-15 00:56
Solid GeometryGeometric Construction
In collections Area and Volume (III) S.3 Ch.5 Area and Volume (III)-1
This example demonstrates how to partition a cube into three pyramids with square bases, all having the same volume. Key mathematical concepts include solid geometry volume calculation and geometric construction. Using GeoGebra commands such as Segment, Polygon, and Pyramid, the construction process of the pyramids is visually illustrated. Suitable for middle school and above students to learn solid geometry and geometric construction.

GeoGebra Commands & Parameters

  1. Segment(A, B) → AB
  2. Segment(B, C) → BC
  3. Segment(C, D) → CD
  4. Segment(D, A) → DA
  5. Segment(A, E) → AE
  6. Segment(B, F) → BF
  7. Segment(C, G) → CG
  8. Segment(D, H) → DH
  9. Segment(E, F) → EF
  10. Segment(F, G) → FG
  11. Segment(G, H) → GH
  12. Segment(H, E) → EH
  13. Polygon(A, B, C, D) → ABCD, b, c, e, f
  14. Pyramid(ABCD, E) → ABCDE, faceABE, faceBCE_1, faceCEI, faceAEI, arêteAE, arêteBE_1, arêteCE_1, arêteEI
  15. Polygon(B, C, G, F) → BCGF, d, g, h, i
  16. Polygon(C, D, H, G) → CDHG, c_1, d_1, h_1, g_1
  17. Pyramid(BCGF, E) → BCGFE, faceBCE, faceCEG_1, faceEFG, faceBEF, arêteBE, arêteCE_2, arêteEG_1, arêteEF
  18. Pyramid(CDHG, E) → CDHGE, faceCDE, faceDEH, faceEGH, faceCEG, arêteCE, arêteDE, arêteEH, arêteEG

AI Drawing Prompt Reference

Draw a cube and partition it into three pyramids with equal volumes. Start by drawing the four vertices A, B, C, and D of the cube, then connect these vertices to form the base ABCD. Next, draw lines from vertices A, B, and C to the centers E, F, and G of the opposite faces, forming the pyramids ABCE, BCDF, and CDGH. Finally, connect E, F, G, and H to form the bases BCGF and CDHG, completing the construction of the three pyramids.
The prompt above was compiled from the original drawing commands and is for reference only.