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十二面体在立方体内的翻转

十二面体在立方体内的翻转
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2016-09-07 17:22
多边形立体几何
所属专题 My 3D Collection
①本范例演示十二面体在立方体内的翻转效果与空间关系；②涉及核心数学概念包括立体几何、多边形、变换与空间对称；③构造要点运用了点、十二面体、立方体、镜像、线段、多边形等 GeoGebra 命令与对象；④适合高中及以上学生及数学爱好者用于理解空间几何与多面体性质。

GeoGebra 命令及参数

  1. Point(Circle[(((0, 0) * (1 - sqrt(5))) + ((0, 1) * (3 + sqrt(5)))) / 4, (Distance[(0, 0), (0, 1)] * sqrt(10 + (2 * sqrt(5))) / 4), Segment[(0, 0), (0, 1)]]) → A
  2. Dodecahedron((0, 0), (0, 1), A) → a, B, K, L, M, N, O, P, Q, R, face1, face3, C, face2, face4, faceABFKE, faceBCGLF, faceGLQRM, faceHINRM, faceDINOJ, faceEJOPK, faceFKPQL, faceNOPQR, D, edge2, edge1, edge4, edgeAB, edgeBC, edge3, edgeCG, edgeGM, edgeHM, edgeHI, E, edgeDI, edge5, edgeDJ, edgeEJ, edgeAE, edgeEK, edgeFK, edgeBF, edgeFL, edgeGL, F, edgeLQ, edgeQR, edgeMR, edgeNR, edgeIN, edgeNO, edgeJO, edgeOP, edgeKP, edgePQ, G, H, I, J
  3. Point(edge4) → S
  4. Cube(E, O, Q) → b, T, faceQTZW, faceUVWZ, edgeET, edgeEO, edgeOQ, edgeQT, edgeEU, edgeTZ, edgeUZ, edgeUV, U, edgeOV, edgeVW, edgeQW, edgeWZ, V, W, Z, faceEOQT, faceETZU, faceEOVU, faceOQWV
  5. Mirror(N, faceOQWV) → N'
  6. Mirror(R, faceOQWV) → R'
  7. Mirror(J, faceEOVU) → J'
  8. Mirror(D, faceEOVU) → D'
  9. Mirror(A, faceETZU) → A'
  10. Mirror(B, faceETZU) → B'
  11. Mirror(H, faceUVWZ) → H'
  12. Mirror(A_1, faceUVWZ) → B_1
  13. Mirror(L, faceQTZW) → L'
  14. Mirror(G, faceQTZW) → G'
  15. Mirror(K, faceEOQT) → K'
  16. Mirror(P, faceEOQT) → P'
  17. Mirror(K, faceEOQT) → K'_1
  18. Segment(J', O) → h
  19. Segment(J', E) → i
  20. Segment(A', E) → k
  21. Segment(A', S) → l
  22. Segment(B', T) → m
  23. Segment(B', Z) → n
  24. Segment(B', A') → p
  25. Segment(B_1, S) → q
  26. Segment(B_1, Z) → r
  27. Segment(D', V) → f
  28. Segment(D', S) → g
  29. Segment(D', J') → j
  30. Segment(H', V) → s
  31. Segment(H', W) → t
  32. Segment(H', B_1) → c
  33. Segment(W, G') → d
  34. Segment(G', Z) → e
  35. Segment(Q, L') → f_1
  36. Segment(L', T) → g_1
  37. Segment(Q, R') → i_1
  38. Segment(R', W) → j_1
  39. Segment(N', O) → k_1
  40. Segment(N', V) → l_1
  41. Segment(O, P') → m_1
  42. Segment(Q, P') → n_1
  43. Segment(R', N') → q_1
  44. Segment(L', G') → p_1
  45. Polygon(O, N', R', Q) → poly1, o, n', r', q_2
  46. Polygon(N', V, W, R') → poly2, n'_1, v, w, r'_1
  47. Polygon(O, J', D', V) → poly3, o_1, j', d', v_1
  48. Polygon(E, J', D', S) → poly5, e_1, j'_1, d'_1, s_1
  49. Polygon(G', L', Q, W) → poly4, g', l'_2, q_3, w_1
  50. Polygon(Z, G', L', T) → poly8, z_1, g'_1, l'_3, t_2
  51. Polygon(Q, P', K', T) → poly6, q_4, p', k', t_1
  52. Polygon(P', O, E, K') → poly7, p'_1, o_2, e_2, k'_1
  53. Polygon(T, E, A', B') → poly9, t_3, e_3, a', b'
  54. Polygon(Z, B', A', S) → poly10, z_2, b'_1, a'_1, s_2
  55. Polygon(H', W, Z, B_1) → poly11, h', w_2, z_3, b_1
  56. Polygon(V, H', B_1, S) → poly12, v_2, h'_1, b_2, s_3