基本立体图形

基本立体图形
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2018-01-16 16:21
该范例演示了基本的立体图形,包括立方体、四面体、棱锥、棱柱等。涉及的核心数学概念包括立体几何中的基本图形和性质。通过使用GeoGebra命令如Point、Cube、Polygon、Pyramid等,可以直观地展示这些立体图形的构造过程。适合初中及以上学生或教师使用,用于教学或自我学习。

GeoGebra 命令及参数

  1. Point(Circle[B_2, Distance[A_2, B_2], Segment[A_2, B_2]]) → C
  2. Cube(A_2, B_2, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB_1, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  3. Polygon(I, J, 4) → poly1, f, g, h, i, K, L
  4. Polygon(M, N, 5) → poly2, j, k, l, m, n, O, P, Q
  5. Polygon(R, S, 6) → poly3, p, W, q, r, s, t, b, T, U, V
  6. Pyramid(poly1, 1) → c, Z, faceIJZ, faceJKZ, faceKLZ, faceILZ, edgeIZ, edgeJZ, edgeKZ, edgeLZ
  7. Pyramid(poly2, 1) → d, A_1, edge4, edge5, face1, face3, face4, face5, face2, edge1, edge2, edge3
  8. Pyramid(poly3, 1) → e, B_1, edge8, edge9, edge10, edge11, face6, face8, face9, face10, face11, face7, edge6, edge7
  9. Point(Circle[Midpoint[C_1, D_1], (Distance[C_1, D_1] * sqrt(3) / 2), Segment[C_1, D_1]]) → E_1
  10. Tetrahedron(C_1, D_1, E_1) → o, F_1, edge17, edge16, face12, face14, face13, face15, edge13, edge12, edge15, edge14
  11. Circle(G_1, 0.5) → c_1
  12. Circle(H_1, 0.5) → d_1
  13. Cone(d_1, 1) → u, e_1, v
  14. Cylinder(c_1, 1) → w, f_1, a_1
  15. Polygon(A_3, J_1, B_3, I_1) → poly4, a_2, j_1, b_1, i_1
  16. Prism(poly4, 1) → g_1, K_1, edge18, edge21, edge19, edge20, edge22, edge24, edge25, edge23, L_1, M_1, N_1, face17, face19, face18, face16, face20
  17. Sphere(A_4 + (0, 0, 0.5), 0.5) → h_1
  18. Point(Circle[Midpoint[A_5, B_4], (Distance[A_5, B_4] * sqrt(3) / 2), Segment[A_5, B_4]]) → O_1
  19. Octahedron(A_5, B_4, O_1) → k_1, P_1, face27, face28, edge26, edgeAB_2, edge29, edge28, edge33, edge27, edge35, edge30, Q_1, edge31, edge34, edge32, edge36, R_1, face21, face23, face24, face22, face26, face25
  20. Point(Circle[Midpoint[A_6, B_5], (Distance[A_6, B_5] * sqrt(3) / 2), Segment[A_6, B_5]]) → S_1
  21. Icosahedron(A_6, B_5, S_1) → l_1, T_1, face29, face31, face33, face32, face30, face35, face36, face34, face37, face38, U_1, face41, face42, face47, face44, face46, face48, face45, face43, face40, face39, V_1, edge37, edgeAB_3, edge41, edge39, edge46, edge40, edge54, edge38, edge48, edge42, W_1, edge44, edge49, edge43, edge51, edge45, edge47, edge52, edge55, edge53, edge60, Z_1, edge61, edge62, edge65, edge56, edge63, edge59, edge64, edge58, edge57, edge50, C_2, D_2, E_2, F_2
  22. Point(Circle[((A * (1 - sqrt(5))) + (B * (3 + sqrt(5)))) / 4, (Distance[A, B] * sqrt(10 + (2 * sqrt(5))) / 4), Segment[A, B]]) → G_2
  23. Dodecahedron(A, B, G_2) → m_1, H_2, Q_2, R_2, S_2, T_2, U_2, V_2, W_2, Z_2, face49, face51, I_2, face50, face52, face53, face54, face58, face59, face55, face56, face57, face60, J_2, edge66, edgeAB, edge68, edge70, edge72, edge67, edge74, edge82, edge84, edge83, K_2, edge75, edge69, edge76, edge77, edge71, edge78, edge79, edge73, edge80, edge81, L_2, edge88, edge94, edge89, edge91, edge85, edge90, edge86, edge92, edge87, edge93, M_2, N_2, O_2, P_2
  24. Polygon(C_3, D_3, 4, xOyPlane) → poly5, n_1, p_1, q_1, r_1, E_3, F_3
  25. Polygon(G_3, H_3, 3, xOyPlane) → poly6, s_1, t_1, f_2, I_3
  26. Polygon(J_3, K_3, 5, xOyPlane) → poly7, g_2, h_2, i_2, j_2, k_2, L_3, M_3, N_3
  27. Polygon(O_3, P_3, 6, xOyPlane) → poly8, l_2, T_3, m_2, n_2, p_2, q_2, r_2, Q_3, R_3, S_3
  28. Prism(poly5, 2) → o_1, U_3, edge95, edge96, edge97, edge98, edge99, edge101, edge102, edge100, V_3, W_3, Z_3, face61, face63, face64, face62, face65
  29. Prism(poly6, 1) → u_1, C_4, edge105, edge106, edge108, edge107, D_4, E_4, face67, face69, face68, face66, edge103, edge104
  30. Prism(poly7, 1) → v_1, F_4, face71, face75, edge109, edge110, edge111, edge112, edge113, edge114, edge116, edge117, G_4, edge118, edge115, H_4, I_4, J_4, face70, face72, face73, face74
  31. Prism(poly8, 1) → w_1, K_4, face80, face81, face77, face82, edge119, edge120, edge121, edge122, edge123, edge124, L_4, edge125, edge127, edge128, edge129, edge130, edge126, M_4, N_4, O_4, P_4, face76, face78, face79

AI 绘图提示语参考

绘制一个包含基本立体图形的场景,包括立方体、四面体、五棱锥、六棱锥、圆锥、圆柱、棱柱、八面体、二十面体和十二面体。首先画一个立方体,然后画一个四面体,接着画一个五棱锥和一个六棱锥。之后画一个圆锥和一个圆柱,再画一个棱柱。接着画一个八面体,然后画一个二十面体和一个十二面体。最后画一些平面多边形,包括一个四边形、一个三角形和一个五边形,以及一个六边形,每个多边形都位于 xOy 平面上。
以上提示语为根据原始绘图命令整理而来,仅供参考。