Divide a Cube into Three Parts

GeoGebra Commands & Parameters

1. Intersect(xAxis, yAxis) → 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, edgeDH, edgeEH, edgeEF, E, edgeBF_1, edgeFG, edgeCG_1, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
5. Pyramid(A, C, D, G) → d, faceACD, edgeDG, faceACG, faceCDG, faceADG, edgeAC, edgeCD, edgeAD, edgeAG, edgeCG
6. Pyramid(B, C, D, A, G) → b, face1, edge5, edge6, edge7, edge8, face2, face3, face4, face5, edge1, edge2, edge3, edge4
7. Rotate(b, (-(90°)), edgeGH) → b_1
8. Rotate(b_1, 90°, edgeCG) → b_2
9. Rotate(b, If[0 < c ≤ 1, (-(((c * 90))°))], edgeGH) → b_{01}
10. Rotate(b_2, If[2 < c ≤ 3, (((c - 2) * 90))°], edgeFG) → b_{23}
11. Rotate(b_2, 90°, edgeFG) → b_3
12. Rotate(b_3, (-(90°)), edgeGH) → b_4
13. Rotate(b_3, If[3 < c ≤ 4, (((-(c - 3)) * 90))°], edgeGH) → b_{34}
14. Rotate(d, (-(90°)), edgeGH) → d_1
15. Rotate(d_1, 90°, edgeCG) → d_2
16. Rotate(d_2, 90°, edgeFG) → d_3
17. Rotate(d_3, (-(90°)), edgeGH) → d_4
18. Rotate(d, If[4 < c ≤ 5, (-(((c * 90))°))], edgeGH) → d_{01}
19. Rotate(d_2, If[6 < c ≤ 7, (((c - 2) * 90))°], edgeFG) → d_{23}
20. Rotate(d_3, If[7 < c ≤ 8, (((-(c - 7)) * 90))°], edgeGH) → d_{34}
21. Line(G, H) → r_1
22. Line(C, G) → r_2
23. Line(F, G) → r_3
24. Line(G, H) → r_4
25. Rotate(b_1, If[1 < c ≤ 2, (((c - 1) * 90))°], edgeCG) → b_{12}