用两个立方体拼成菱形十二面体的几何构造

GeoGebra 命令及参数

1. Intersect(yAxis, zAxis) → A
2. Point(xAxis) → B
3. Mirror(B, A) → B'
4. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
5. 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
6. Point(Circle[A, Distance[B', A], Segment[B', A]]) → I
7. Cube(B', A, I) → b, J, faceIJNM_1, faceKLMN_1, edgeB'J_1, edgeAB'_1, edgeAI_1, edgeIJ_1, edgeB'K_1, edgeJN_1, edgeKN_1, edgeKL_1, K, edgeAL_1, edgeLM_1, edgeIM_1, edgeMN_1, L, M, N, faceAB'JI_1, faceB'JNK_1, faceAB'KL_1, faceAIML_1
8. Midpoint(J, L) → O
9. Pyramid(J, N, M, I, O) → c, faceIJNM, edgeJO_1, edgeNO_1, edgeMO_1, edgeIO_1, faceJNO_1, faceMNO_1, faceIMO_1, faceIJO_1, edgeJN_2, edgeMN_2, edgeIM_2, edgeIJ_2
10. Pyramid(I, J, B', A, O) → d, faceAB'JI, edgeIO_2, edgeJO_2, edgeB'O_1, edgeAO_1, faceIJO, faceB'JO_1, faceAB'O_1, faceAIO_1, edgeIJ, edgeB'J_2, edgeAB'_2, edgeAI_2
11. Pyramid(I, A, L, M, O) → e, faceAIML, edgeIO, edgeAO_2, edgeLO_1, edgeMO_2, faceAIO, faceALO_1, faceLMO_1, faceIMO, edgeAI, edgeAL_2, edgeLM_2, edgeIM
12. Pyramid(J, N, K, B', O) → f, faceB'JNK, edgeJO, edgeNO_2, edgeKO_1, edgeB'O_2, faceJNO, faceKNO_1, faceB'KO_1, faceB'JO, edgeJN, edgeKN_2, edgeB'K_2, edgeB'J
13. Pyramid(B', A, L, K, O) → g, faceAB'KL, edgeB'O, edgeAO, edgeLO_2, edgeKO_2, faceAB'O, faceALO, faceKLO_1, faceB'KO, edgeAB', edgeAL, edgeKL_2, edgeB'K
14. Pyramid(N, M, L, K, O) → h, faceKLMN, edgeNO, edgeMO, edgeLO, edgeKO, faceMNO, faceLMO, faceKLO, faceKNO, edgeMN, edgeLM, edgeKL, edgeKN
15. Rotate(h, ((-n) * π), Segment[H, E]) → h'
16. Rotate(N, ((-n) * π), Segment[H, E]) → N'
17. Rotate(K, ((-n) * π), Segment[H, E]) → K'
18. Rotate(f, ((-n) * π), Segment[H, E]) → f'
19. Rotate(f', ((-n) * π), Segment[N', K']) → f''
20. Rotate(d, ((-n) * π), Segment[A, D]) → d'
21. Rotate(c, (n * π), Segment[H, D]) → c'
22. Rotate(g, (n * π), Segment[A, E]) → g'