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Cube Dissected into Six Bie'nao: Geometric Construction

Cube Dissected into Six Bie'nao: Geometric Construction
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2017-03-01 06:20
Solid GeometryGeometric ConstructionSlider Animation
This example demonstrates how a cube is divided into six bie'nao, a common problem in solid geometry. The key mathematical concepts involve geometric construction, solid geometry, and spatial division. Construction points include using GeoGebra commands such as Intersect, Point, Cube, Pyramid, etc., to create the cube and its faces and edges. Suitable for middle or high school students learning geometric construction and spatial visualization.

GeoGebra Commands & Parameters

  1. Intersect(zAxis, xOyPlane) → 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_1, edgeAB_1, edgeBC_1, edgeCD_1, edgeAE_1, edgeDH_1, edgeEH_1, edgeEF_1, E, edgeBF_1, edgeFG_1, edgeCG_1, edgeGH_1, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  5. Pyramid(H, D, G, F) → b, faceDGH, edgeFG_2, faceDFH_1, faceDFG_1, faceFGH, edgeDH_2, edgeDG_1, edgeGH, edgeFH_1, edgeDF_1
  6. Pyramid(G, D, C, F) → c, faceCDG, edgeCF_1, faceDFG, faceCDF_1, faceCFG, edgeDG, edgeCD_2, edgeCG, edgeFG, edgeDF_2
  7. Pyramid(B, C, D, F) → d, faceBCD, edgeDF_3, faceBCF, faceCDF, faceBDF_1, edgeBC, edgeCD, edgeBD_1, edgeBF_2, edgeCF
  8. Pyramid(A, D, B, F) → e, faceABD, edgeBF, faceADF_1, faceBDF, faceABF, edgeAD_2, edgeBD, edgeAB, edgeAF_1, edgeDF_4
  9. Pyramid(H, E, D, F) → f, faceDEH, edgeDF_5, faceEFH, faceDEF_1, faceDFH, edgeEH, edgeDE_1, edgeDH, edgeFH, edgeEF_2
  10. Pyramid(E, D, A, F) → g, faceADE, edgeAF, faceDEF, faceADF, faceAEF, edgeDE, edgeAD, edgeAE, edgeEF, edgeDF

AI Drawing Prompt Reference

Draw a cube and divide it into six bie'nao. First, create a cube, then construct the six bie'nao using the cube's vertices and edges, including their faces and edges.
The prompt above was compiled from the original drawing commands and is for reference only.