Dissection of Cube into Six Bie'nao (Right Triangular Pyramids)

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