星形十二面体

星形十二面体
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2014-12-25 00:32
所属专题 My 3D Collection
①本范例演示了如何通过 GeoGebra 构造星形十二面体,一种由正十二面体的顶点向外延伸形成的复杂多面体;②涉及的核心数学概念包括立体几何、三角函数、矩阵运算及方差计算;③作图要点提炼自构造摘要,使用了 Point(点)、Dodecahedron(正十二面体)、Line(线)、Intersect(交点)、Pyramid(金字塔)等命令及对象;④适合高中及以上数学学习者,用于理解多面体构造与空间几何关系。

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. Line(K, P) → b
  4. Line(P, Q) → c
  5. Line(Q, L) → d
  6. Line(L, F) → e
  7. Line(F, K) → f
  8. Line(B, F) → g
  9. Line(B, C) → h
  10. Line(C, G) → i
  11. Line(G, L) → j
  12. Line(Q, R) → k
  13. Line(R, M) → l
  14. Line(M, G) → m
  15. Line(R, S) → n
  16. Line(S, T) → p
  17. Line(T, P) → q
  18. Line(T, O) → r
  19. Line(O, J) → s
  20. Line(J, K) → t
  21. Line(B, A) → a_1
  22. Line(A, J) → b_1
  23. Line(M, H) → c_1
  24. Line(H, N) → d_1
  25. Line(N, S) → e_1
  26. Line(N, I) → f_1
  27. Line(I, O) → g_1
  28. Line(I, E) → h_1
  29. Line(E, D) → i_1
  30. Line(D, C) → j_1
  31. Line(D, H) → k_1
  32. Intersect(j, h) → U
  33. Intersect(h_1, k_1) → V
  34. Line(A, E) → l_1
  35. Intersect(j_1, l_1) → W
  36. Intersect(a_1, t) → Z
  37. Intersect(l_1, s) → A_1
  38. Intersect(f, c) → B_1
  39. Intersect(q, t) → C_1
  40. Intersect(n, c_1) → D_1
  41. Intersect(k, m) → E_1
  42. Intersect(d, a_1) → F_1
  43. Intersect(d, b) → G_1
  44. Intersect(s, h_1) → H_1
  45. Pyramid(facePQRST, G_1) → o, face5, edge1, face4, face3, face1, face2, edge5, edge4, edge3, edge2
  46. Pyramid(faceINSTO, H_1) → u, face7, edge10, face6, face8, face10, face9, edge8, edge6, edge7, edge9
  47. Pyramid(faceHMRSN, E_1) → v, face11, edge13, face13, face15, face14, face12, edge11, edge12, edge14, edge15
  48. Pyramid(faceDEINH, W) → w, faceDEW, edgeIW, faceDHW, faceHNW, faceINW, faceEIW, edgeEW, edgeDW, edgeHW, edgeNW
  49. Pyramid(faceGLQRM, D_1) → m_1, face16, edge18, face18, face20, face19, face17, edge16, edge17, edge19, edge20
  50. Pyramid(faceCDHMG, U) → n_1, faceCDU, edgeHU, faceCGU, faceGMU, faceHMU, faceDHU, edgeDU, edgeCU, edgeGU, edgeMU
  51. Pyramid(faceBCGLF, F_1) → o_1, face21, edge24, face22, face24, face25, face23, edge22, edge21, edge23, edge25
  52. Pyramid(faceFKPQL, C_1) → p_1, face26, edge28, face28, face30, face29, face27, edge26, edge27, edge29, edge30
  53. Pyramid(faceJKPTO, B_1) → q_1, face32, edge32, face34, face35, face33, face31, edge31, edge33, edge35, edge34
  54. Pyramid(faceAEIOJ, Z) → r_1, faceAJZ, edgeOZ, faceAEZ, faceEIZ, faceIOZ, faceJOZ, edgeJZ, edgeAZ, edgeEZ, edgeIZ
  55. Pyramid(faceABCDE, V) → s_1, faceAEV, edgeDV, faceABV, faceBCV, faceCDV, faceDEV, edgeEV, edgeAV, edgeBV, edgeCV
  56. Pyramid(faceABFKJ, A_1) → t_1, face36, edge38, face37, face40, face39, face38, edge37, edge36, edge39, edge40

AI 绘图提示语参考

绘制一个星形十二面体,通过将正十二面体的顶点向外延伸形成复杂的多面体。首先画出正十二面体的基本结构,然后从每个顶点向外延伸线条,形成星状突起。注意线条的交点和形成的面,最终构成一个由多个三棱锥和五边形面组成的星形多面体。
以上提示语为根据原始绘图命令整理而来,仅供参考。