十二面体半金字塔展开图

GeoGebra 命令及参数

1. Point(Circle[(((1 - sqrt(5)) * A) + ((3 + sqrt(5)) * B)) / 4, (Distance[A, B] * sqrt(10 + (2 * sqrt(5))) / 4), Segment[A, B]]) → C
2. Dodecahedron(A, B, C) → a, D, M, N, O, P, Q, R, S, T, faceABCDE, faceAEIOJ, E, faceABFKJ, faceBCGLF, faceCDHMG, faceDEINH, faceINSTO, faceJKPTO, faceFKPQL, faceGLQRM, faceHMRSN, facePQRST, F, edgeAE, edgeAB, edgeBC, edgeCD, edgeDE, edgeAJ, edgeEI, edgeIO, edgeJO, edgeJK, G, edgeFK, edgeBF, edgeFL, edgeGL, edgeCG, edgeGM, edgeHM, edgeDH, edgeHN, edgeIN, H, edgeNS, edgeST, edgeOT, edgePT, edgeKP, edgePQ, edgeLQ, edgeQR, edgeMR, edgeRS, I, J, K, L
3. Segment(U, U + (0, 0, 2)) → b
4. Point(b) → V
5. Rotate(Polygon[A, B, F, K, J], (α * t), Segment[A, B]) → poly1
6. Rotate(Polygon[F, K, P, Q, L], (α * t), Segment[K, F]) → poly2
7. Rotate(Polygon[P, Q, R, S, T], (α * t), Segment[P, Q]) → poly3
8. Rotate(poly2, (α * t), Segment[A, B]) → poly2'
9. Rotate(poly3, (α * t), Segment[K, F]) → poly3'
10. Rotate(poly3', (α * t), Segment[A, B]) → poly3''
11. Circle(A, B, D) → c
12. Center(c) → W
13. OrthogonalLine(W, Plane[A, B, D]) → d
14. Rotate(poly1, 72*°, d) → poly1'
15. Rotate(poly1', 72*°, d) → poly1''
16. Rotate(poly1'', 72*°, d) → poly1'''
17. Rotate(poly1''', 72*°, d) → poly4
18. Rotate(poly2', 72*°, d) → poly2''
19. Rotate(poly2'', 72*°, d) → poly2'''
20. Rotate(poly2''', 72*°, d) → poly5
21. Rotate(poly5, 72*°, d) → poly5'
22. Polygon(A, B, C, D, E) → poly6, a_1, b_1, c_1, d_1, e
23. TableText({{LaTeX[A, true, true]}, {LaTeX[B, true, true]}, {LaTeX[C, true, true]}, {LaTeX[D, true, true]}, {LaTeX[E, true, true]}, {LaTeX[F, true, true]}, {LaTeX[G, true, true]}, {LaTeX[H, true, true]}, {LaTeX[I, true, true]}, {LaTeX[J, true, true]}, {LaTeX[K, true, true]}, {LaTeX[L, true, true]}, {LaTeX[M, true, true]}, {LaTeX[N, true, true]}, {LaTeX[O, true, true]}, {LaTeX[P, true, true]}, {LaTeX[Q, true, true]}, {LaTeX[R, true, true]}, {LaTeX[S, true, true]}, {LaTeX[T, true, true]}, {LaTeX[U, true, true]}, {LaTeX[V, true, true]}, {LaTeX[W, true, true]}}) → text1
24. Rotate(poly2''', 72*°, d) → poly7
25. Rotate(poly1'', 72*°, d) → poly1'''_1
26. Polygon(A, B, C, D, E) → poly8, a_2, b_2, c_2, d_2, e_1
27. Rotate(poly1''', 72*°, d) → poly9
28. Rotate(poly5, 72*°, d) → poly5'_1
29. Rotate(Polygon[A, B, F, K, J], (α * t), Segment[A, B]) → poly10
30. Rotate(poly2, (α * t), Segment[A, B]) → poly2'_1
31. Rotate(poly3', (α * t), Segment[A, B]) → poly3''_1
32. Rotate(poly1, 72*°, d) → poly1'_1
33. Rotate(poly2', 72*°, d) → poly2''_1
34. Rotate(poly1', 72*°, d) → poly1''_1
35. Rotate(poly2'', 72*°, d) → poly2'''_1