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Unfolding a Cube

Unfolding a Cube
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2020-01-27 01:21
Solid GeometryTransformationGeometric Construction
This example demonstrates how to cut a cube into 6 congruent pyramids to explore the volume of each pyramid. Using GeoGebra commands such as Point, Cube, Midpoint, Pyramid, etc., students can visually understand the concept of volume in solid geometry. Suitable for middle school and above students.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(yAxis) → 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. Midpoint(D, F) → I
  6. Pyramid(faceABCD, I) → b, faceADI, faceABI_1, faceBCI, faceCDI, edgeDI, edgeAI_1, edgeBI_1, edgeCI
  7. Circle(edgeAB, F) → c
  8. Point(c) → J
  9. Angle(F, B, J) → α
  10. Pyramid(faceABFE, I) → d, faceABI, faceAEI, faceEFI, faceBFI, edgeBI, edgeAI, edgeEI, edgeFI
  11. Rotate(d, α, edgeAB) → d'
  12. Rotate(d', 90*°, zAxis) → d''
  13. Rotate(d'', 90*°, zAxis) → d'''
  14. Rotate(d''', 90*°, zAxis) → e
  15. Line(B, J) → f
  16. Midpoint(B, J) → K
  17. OrthogonalPlane(K, f) → g
  18. Mirror(b, g) → b'