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二十面体三角柱

二十面体三角柱
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2018-06-02 01:37
立体几何变换几何作图
该范例展示了二十面体三角柱的构造。涉及的核心数学概念包括立体几何中的多面体和柱体。通过使用GeoGebra命令如Point, Rotate, Icosahedron, Prism等，可以直观地理解多面体的旋转和构造过程。适合高中及以上学生或教师用于教学和学习立体几何。

GeoGebra 命令及参数

  1. Point(xAxis) → A
  2. Rotate(A, (2 * π / 3)) → A'
  3. Point(Circle[Midpoint[A, A'], (Distance[A, A'] * sqrt(3) / 2), Segment[A, A']]) → B
  4. Icosahedron(A, A', B) → a_1, C, d, f, h, g, e, b, c, a, i, j, D, m, n, s, p, r, t, q, o, l, k, E, edgeAB, edgeAA', edgeA'B, edgeAE, edgeBE, edgeAF, edgeEF, edgeAC, edgeCF, edgeA'C, F, edgeA'G, edgeCG, edgeA'D, edgeDG, edgeBD, edgeBH, edgeDH, edgeEH, edgeDJ, edgeGJ, G, edgeHJ, edgeHK, edgeJK, edgeEK, edgeIJ, edgeGI, edgeIK, edgeFK, edgeFI, edgeCI, H, I, J, K
  5. Prism(a, u) → v, L, edgeDN, edgeLM, edgeMN, edgeLN, M, N, faceA'BLM, faceA'DNM, faceBDNL, faceLMN, edgeBL, edgeA'M
  6. Prism(b, u) → w, O, edgeCQ, edgeOP, edgePQ, edgeOQ, P, Q, faceA'GOP, faceA'CQP, faceCGOQ, faceOPQ, edgeGO, edgeA'P
  7. Prism(c, u) → b_1, R, edgeGT, edgeRS, edgeST, edgeRT, S, T, faceA'DRS, faceA'GTS, faceDGTR, faceRST, edgeDR, edgeA'S
  8. Prism(d, u) → c_1, U, edgeA'W, edgeUV, edgeVW, edgeUW, V, W, faceABUV, faceAA'WV, faceA'BUW, faceUVW, edgeBU, edgeAV
  9. Prism(e, u) → d_1, Z, edge2, edge3, edge5, edge4, A_1, B_1, face2, face3, face4, face1, edgeA'Z, edge1
  10. Prism(f, u) → e_1, C_1, edge7, edge9, edge11, edge10, D_1, E_1, face7, face6, face8, face5, edge8, edge6
  11. Prism(g, u) → f_1, F_1, edge14, edge15, edge17, edge16, G_1, H_1, face10, face11, face12, face9, edge13, edge12
  12. Prism(h, u) → g_1, I_1, edge19, edge21, edge23, edge22, J_1, K_1, face15, face14, face16, face13, edge20, edge18
  13. Prism(i, u) → h_1, M_1, edge25, edge27, edge29, edge28, N_1, O_1, face19, face18, face20, face17, edge26, edge24
  14. Prism(j, u) → i_1, P_1, edge32, edge33, edge35, edge34, Q_1, R_1, face22, face23, face24, face21, edge31, edge30
  15. Prism(k, u) → j_1, S_1, edge36, edge39, edge41, edge40, T_1, U_1, face28, face27, face26, face25, edge37, edge38
  16. Prism(l, u) → k_1, V_1, edge43, edge45, edge47, edge46, W_1, Z_1, face31, face32, face30, face29, edge42, edge44
  17. Prism(m, u) → l_1, A_2, edge49, edge51, edge53, edge52, B_2, C_2, face35, face34, face36, face33, edge50, edge48
  18. Prism(n, u) → m_1, D_2, edge56, edge57, edge59, edge58, E_2, F_2, face38, face39, face40, face37, edge55, edge54
  19. Prism(o, u) → n_1, G_2, edge61, edge63, edge65, edge64, H_2, I_2, face43, face44, face42, face41, edge60, edge62
  20. Prism(p, u) → o_1, J_2, edge68, edge69, edge71, edge70, K_2, L_2, face46, face48, face47, face45, edge66, edge67
  21. Prism(q, u) → p_1, M_2, edge73, edge75, edge77, edge76, N_2, O_2, face51, face52, face50, face49, edge72, edge74
  22. Prism(r, u) → q_1, P_2, edge78, edge81, edge83, edge82, Q_2, R_2, face56, face55, face54, face53, edge79, edge80
  23. Prism(s, u) → r_1, S_2, edge85, edge87, edge89, edge88, T_2, U_2, face59, face58, face60, face57, edge86, edge84
  24. Prism(t, u) → s_1, V_2, edge90, edge93, edge95, edge94, W_2, Z_2, face64, face62, face63, face61, edge92, edge91