截半二十面体 by chris cambré
几何画板及绘图内容加载中,请稍等……
①本范例演示了截半二十面体的几何构造与性质;②涉及的核心数学概念包括多面体、欧拉示性数、对称性;③作图要点——从下方『构造摘要』提炼用到了Midpoint(中点)、Angle(角度)、Plane(平面)、OrthogonalLine(垂线)、Rotate(旋转)、Polygon(多边形)等GeoGebra命令/对象;④适合高中及以上学生学习立体几何、几何作图及多面体理论。
GeoGebra 命令及参数
Midpoint(D5, D3) → AMidpoint(D7, D69) → CAngle(A, B, C) → δPlane(A, B, C) → aOrthogonalLine(B, a) → bRotate(D1, δ, b) → E1Rotate(D2, δ, b) → E2Rotate(D3, δ, b) → E3Rotate(D4, δ, b) → E4Rotate(D5, δ, b) → E5Rotate(D6, δ, b) → E6Rotate(D7, δ, b) → E7Rotate(D8, δ, b) → E8Rotate(D9, δ, b) → E9Rotate(D10, δ, b) → E10Rotate(D11, δ, b) → E11Rotate(D12, δ, b) → E12Rotate(D13, δ, b) → E13Rotate(D14, δ, b) → E14Rotate(D15, δ, b) → E15Rotate(D16, δ, b) → E16Rotate(D17, δ, b) → E17Rotate(D18, δ, b) → E18Rotate(D19, δ, b) → E19Rotate(D20, δ, b) → E20Rotate(D21, δ, b) → E21Rotate(D22, δ, b) → E22Rotate(D23, δ, b) → E23Rotate(D24, δ, b) → E24Rotate(D25, δ, b) → E25Rotate(D26, δ, b) → E26Rotate(D27, δ, b) → E27Rotate(D28, δ, b) → E28Rotate(D29, δ, b) → E29Rotate(D30, δ, b) → E30Rotate(D31, δ, b) → E31Rotate(D32, δ, b) → E32Rotate(D33, δ, b) → E33Rotate(D34, δ, b) → E34Rotate(D35, δ, b) → E35Rotate(D36, δ, b) → E36Rotate(D37, δ, b) → E37Rotate(D38, δ, b) → E38Rotate(D39, δ, b) → E39Rotate(D40, δ, b) → E40Rotate(D41, δ, b) → E41Rotate(D42, δ, b) → E42Rotate(D43, δ, b) → E43Rotate(D44, δ, b) → E44Rotate(D45, δ, b) → E45Rotate(D46, δ, b) → E46Rotate(D47, δ, b) → E47Rotate(D48, δ, b) → E48Rotate(D49, δ, b) → E49Rotate(D50, δ, b) → E50Rotate(D51, δ, b) → E51Rotate(D52, δ, b) → E52Rotate(D53, δ, b) → E53Rotate(D54, δ, b) → E54Rotate(D55, δ, b) → E55Rotate(D56, δ, b) → E56Rotate(D57, δ, b) → E57Rotate(D58, δ, b) → E58Rotate(D59, δ, b) → E59Rotate(D60, δ, b) → E60Rotate(D61, δ, b) → E61Rotate(D62, δ, b) → E62Rotate(D63, δ, b) → E63Rotate(D64, δ, b) → E64Rotate(D65, δ, b) → E65Rotate(D66, δ, b) → E66Rotate(D67, δ, b) → E67Rotate(D68, δ, b) → E68Rotate(D69, δ, b) → E69Rotate(D70, δ, b) → E70Rotate(D71, δ, b) → E71Rotate(D72, δ, b) → E72Rotate(D73, δ, b) → E73Rotate(D74, δ, b) → E74Rotate(D75, δ, b) → E75Rotate(D76, δ, b) → E76Rotate(D77, δ, b) → E77Rotate(D78, δ, b) → E78Rotate(D79, δ, b) → E79Rotate(D80, δ, b) → E80Rotate(D81, δ, b) → E81Rotate(D82, δ, b) → E82Rotate(D83, δ, b) → E83Rotate(D84, δ, b) → E84Rotate(D85, δ, b) → E85Rotate(D86, δ, b) → E86Rotate(D87, δ, b) → E87Rotate(D88, δ, b) → E88Rotate(D89, δ, b) → E89Rotate(D90, δ, b) → E90Rotate(D91, δ, b) → E91Rotate(D92, δ, b) → E92Rotate(D93, δ, b) → E93Rotate(D94, δ, b) → E94Rotate(D95, δ, b) → E95Rotate(D96, δ, b) → E96Rotate(D97, δ, b) → E97Rotate(D98, δ, b) → E98Rotate(D99, δ, b) → E99Rotate(D100, δ, b) → E100Rotate(D101, δ, b) → E101Rotate(D102, δ, b) → E102Rotate(D103, δ, b) → E103Rotate(D104, δ, b) → E104Rotate(D105, δ, b) → E105Rotate(D106, δ, b) → E106Rotate(D107, δ, b) → E107Rotate(D108, δ, b) → E108Rotate(D109, δ, b) → E109Rotate(D110, δ, b) → E110Rotate(D111, δ, b) → E111Rotate(D112, δ, b) → E112Rotate(D113, δ, b) → E113Rotate(D114, δ, b) → E114Rotate(D115, δ, b) → E115Rotate(D116, δ, b) → E116Rotate(D117, δ, b) → E117Rotate(D118, δ, b) → E118Rotate(D119, δ, b) → E119Rotate(D120, δ, b) → E120Polygon(E28, E4, E2, E26, E74, E114, E66, E68, E116, E76) → wielokąt1, e28, e76, e4, e2, e26, e74, e114, e66, e68, e116Midpoint(E26, E74) → DMidpoint(E76, E116) → EMidpoint(E84, E108) → FMidpoint(E74, E114) → GMidpoint(E28, E76) → HMidpoint(E52, E100) → IRotate(E100, α, Line[E76, E116]) → E100'Rotate(E84, α, Line[E76, E116]) → E84'Rotate(E108, α, Line[E76, E116]) → E108'Rotate(E92, α, Line[E76, E116]) → E92'Polygon(E100', E76, E116, E92', E108', E84') → wielokąt2, e100', e76_1, e116_1, e92', e108', e84'Rotate(E92, β, Line[E116, E68]) → E92'_1Rotate(E44, β, Line[E116, E68]) → E44'Polygon(E92'_1, E116, E68, E44') → wielokąt3, e92'_1, e116_2, e68_1, e44'Rotate(E44, α, Line[E68, E66]) → E44'_1Rotate(E20, α, Line[E68, E66]) → E20'Rotate(E18, α, Line[E68, E66]) → E18'Rotate(E42, α, Line[E68, E66]) → E42'Polygon(E44'_1, E68, E66, E42', E18', E20') → wielokąt4, e44'_1, e68_2, e66_1, e42', e18', e20'Rotate(E42, β, Line[E66, E114]) → E42'_1Rotate(E90, β, Line[E66, E114]) → E90'Polygon(E42'_1, E66, E114, E90') → wielokąt5, e42'_1, e66_2, e114_1, e90'Rotate(E90, α, Line[E114, E74]) → E90'_1Rotate(E106, α, Line[E114, E74]) → E106'Rotate(E82, α, Line[E114, E74]) → E82'Rotate(E98, α, Line[E114, E74]) → E98'Polygon(E90'_1, E114, E74, E98', E82', E106') → wielokąt6, e90'_1, e114_2, e74_1, e98', e82', e106'Rotate(E98, β, Line[E74, E26]) → E98'_1Rotate(E50, β, Line[E74, E26]) → E50'Polygon(E98'_1, E74, E26, E50') → wielokąt7, e98'_1, e74_2, e26_1, e50'Rotate(E50, α, Line[E26, E2]) → E50'_1Rotate(E54, α, Line[E26, E2]) → E54'Rotate(E30, α, Line[E26, E2]) → E30'Rotate(E6, α, Line[E26, E2]) → E6'Polygon(E50'_1, E26, E2, E6', E30', E54') → wielokąt8, e50'_1, e26_2, e2_1, e6', e30', e54'Rotate(E6, β, Line[E2, E4]) → E6'_1Rotate(E8, β, Line[E2, E4]) → E8'Polygon(E6'_1, E2, E4, E8') → wielokąt9, e6'_1, e2_2, e4_1, e8'Rotate(E8, α, Line[E4, E28]) → E8'_1Rotate(E32, α, Line[E4, E28]) → E32'Rotate(E56, α, Line[E4, E28]) → E56'Rotate(E52, α, Line[E4, E28]) → E52'Polygon(E8'_1, E4, E28, E52', E56', E32') → wielokąt10, e8'_1, e4_2, e28_1, e52', e56', e32'Rotate(E52, β, Line[E28, E76]) → E52'_1Rotate(E100, β, Line[E28, E76]) → E100'_1Polygon(E52'_1, E28, E76, E100'_1) → wielokąt11, e52'_1, e28_2, e76_2, e100'_1Rotate(Rotate[E56, β, Line[E52, E100]], β, Line[E28, E76]) → JRotate(Rotate[E104, β, Line[E52, E100]], β, Line[E28, E76]) → KRotate(Rotate[E88, β, Line[E52, E100]], β, Line[E28, E76]) → LRotate(Rotate[E40, β, Line[E52, E100]], β, Line[E28, E76]) → MRotate(Rotate[E16, β, Line[E52, E100]], β, Line[E28, E76]) → NRotate(Rotate[E12, β, Line[E52, E100]], β, Line[E28, E76]) → ORotate(Rotate[E36, β, Line[E52, E100]], β, Line[E28, E76]) → PRotate(Rotate[E84, β, Line[E52, E100]], β, Line[E28, E76]) → QPolygon(E52'_1, E100'_1, Q, P, O, N, M, L, K, J) → wielokąt12, e52'_2, j, e100'_2, q, p, o, n, m, l, kRotate(Rotate[E108, β, Line[E92, E44]], β, Line[E116, E68]) → RRotate(Rotate[E60, β, Line[E92, E44]], β, Line[E116, E68]) → SRotate(Rotate[E59, β, Line[E92, E44]], β, Line[E116, E68]) → TRotate(Rotate[E107, β, Line[E92, E44]], β, Line[E116, E68]) → URotate(Rotate[E91, β, Line[E92, E44]], β, Line[E116, E68]) → VRotate(Rotate[E43, β, Line[E92, E44]], β, Line[E116, E68]) → WRotate(Rotate[E19, β, Line[E92, E44]], β, Line[E116, E68]) → ZRotate(Rotate[E20, β, Line[E92, E44]], β, Line[E116, E68]) → A_1Polygon(E92'_1, R, S, T, U, V, W, Z, A_1, E44') → wielokąt13, e92'_2, e44'_2, r, s_1, t, u, v, w, z_1, a_1Rotate(Rotate[E18, β, Line[E42, E90]], β, Line[E66, E114]) → B_1Rotate(Rotate[E17, β, Line[E42, E90]], β, Line[E66, E114]) → C_1Rotate(Rotate[E41, β, Line[E42, E90]], β, Line[E66, E114]) → D_1Rotate(Rotate[E89, β, Line[E42, E90]], β, Line[E66, E114]) → E_1Rotate(Rotate[E105, β, Line[E42, E90]], β, Line[E66, E114]) → F_1Rotate(Rotate[E57, β, Line[E42, E90]], β, Line[E66, E114]) → G_1Rotate(Rotate[E58, β, Line[E42, E90]], β, Line[E66, E114]) → H_1Rotate(Rotate[E106, β, Line[E42, E90]], β, Line[E66, E114]) → I_1Polygon(E42'_1, E90', I_1, H_1, G_1, F_1, E_1, D_1, C_1, B_1) → wielokąt14, e42'_2, b_1, e90'_2, i_1, h_1, g_1, f_1, e_1, d_1, c_1Rotate(Rotate[E54, β, Line[E98, E50]], β, Line[E74, E26]) → J_1Rotate(Rotate[E102, β, Line[E98, E50]], β, Line[E74, E26]) → K_1Rotate(Rotate[E86, β, Line[E98, E50]], β, Line[E74, E26]) → L_1Rotate(Rotate[E38, β, Line[E98, E50]], β, Line[E74, E26]) → M_1Rotate(Rotate[E14, β, Line[E98, E50]], β, Line[E74, E26]) → N_1Rotate(Rotate[E10, β, Line[E98, E50]], β, Line[E74, E26]) → O_1Rotate(Rotate[E34, β, Line[E98, E50]], β, Line[E74, E26]) → P_1Rotate(Rotate[E82, β, Line[E98, E50]], β, Line[E74, E26]) → Q_1Polygon(E98'_1, E50', J_1, K_1, L_1, M_1, N_1, O_1, P_1, Q_1) → wielokąt15, e98'_2, q_1, e50'_2, j_1, k_1, l_1, m_1, n_1, o_1, p_1Rotate(Rotate[E30, β, Line[E6, E8]], β, Line[E2, E4]) → R_1Rotate(Rotate[E78, β, Line[E6, E8]], β, Line[E2, E4]) → S_1Rotate(Rotate[E118, β, Line[E6, E8]], β, Line[E2, E4]) → T_1Rotate(Rotate[E70, β, Line[E6, E8]], β, Line[E2, E4]) → U_1Rotate(Rotate[E72, β, Line[E6, E8]], β, Line[E2, E4]) → V_1Rotate(Rotate[E120, β, Line[E6, E8]], β, Line[E2, E4]) → W_1Rotate(Rotate[E80, β, Line[E6, E8]], β, Line[E2, E4]) → Z_1Rotate(Rotate[E32, β, Line[E6, E8]], β, Line[E2, E4]) → A_2Polygon(R_1, E6'_1, E8', A_2, Z_1, W_1, V_1, U_1, T_1, S_1) → wielokąt16, r_1, s_2, e6'_2, e8'_2, a_2, z_2, w_1, v_1, u_1, t_1Rotate(Rotate[Rotate[E78, β, Line[E102, E54]], β, Line[E98, E50]], β, Line[E74, E26]) → B_2Rotate(Rotate[Rotate[E30, β, Line[E102, E54]], β, Line[E98, E50]], β, Line[E74, E26]) → C_2Polygon(J_1, C_2, B_2, K_1) → wielokąt17, j_2, c_2, b_2, k_2Rotate(Rotate[Rotate[E34, β, Line[E58, E106]], β, Line[E42, E90]], β, Line[E66, E114]) → D_2Rotate(Rotate[Rotate[E82, β, Line[E58, E106]], β, Line[E42, E90]], β, Line[E66, E114]) → E_2Polygon(I_1, E_2, D_2, H_1) → wielokąt18, i_2, e_2, d_2, h_2Rotate(Rotate[Rotate[E104, β, Line[E80, E32]], β, Line[E6, E8]], β, Line[E2, E4]) → F_2Rotate(Rotate[Rotate[E56, β, Line[E80, E32]], β, Line[E6, E8]], β, Line[E2, E4]) → G_2Polygon(A_2, G_2, F_2, Z_1) → wielokąt19, a_3, g_2, f_2, z_3Rotate(Rotate[Rotate[E60, β, Line[E36, E84]], β, Line[E52, E100]], β, Line[E28, E76]) → H_2Rotate(Rotate[Rotate[E108, β, Line[E36, E84]], β, Line[E52, E100]], β, Line[E28, E76]) → I_2Polygon(Q, I_2, H_2, P) → wielokąt20, q_2, i_3, h_3, p_2Rotate(Rotate[Rotate[E17, β, Line[E19, E20]], β, Line[E92, E44]], β, Line[E116, E68]) → J_2Rotate(Rotate[Rotate[E18, β, Line[E19, E20]], β, Line[E92, E44]], β, Line[E116, E68]) → K_2Polygon(A_1, K_2, J_2, Z) → wielokąt21, a_4, k_3, j_3, z_4Rotate(Rotate[Rotate[E67, α, Line[E43, E19]], β, Line[E92, E44]], β, Line[E116, E68]) → L_2Rotate(Rotate[Rotate[E65, α, Line[E43, E19]], β, Line[E92, E44]], β, Line[E116, E68]) → M_2Rotate(Rotate[Rotate[E41, α, Line[E43, E19]], β, Line[E92, E44]], β, Line[E116, E68]) → N_2Rotate(Rotate[Rotate[E17, α, Line[E43, E19]], β, Line[E92, E44]], β, Line[E116, E68]) → O_2Polygon(Z, O_2, N_2, M_2, L_2, W) → wielokąt22, z_5, o_2, n_2, m_2, l_2, w_2Rotate(Rotate[Rotate[E11, α, Line[E12, E36]], β, Line[E52, E100]], β, Line[E28, E76]) → P_2Rotate(Rotate[Rotate[E35, α, Line[E12, E36]], β, Line[E52, E100]], β, Line[E28, E76]) → Q_2Rotate(Rotate[Rotate[E59, α, Line[E12, E36]], β, Line[E52, E100]], β, Line[E28, E76]) → R_2Rotate(Rotate[Rotate[E60, α, Line[E12, E36]], β, Line[E52, E100]], β, Line[E28, E76]) → S_2Polygon(S_2, R_2, Q_2, P_2, O, P) → wielokąt23, s_3, r_2, q_3, p_3, o_3, p_4Rotate(Rotate[Rotate[E96, α, Line[E120, E80]], β, Line[E6, E8]], β, Line[E2, E4]) → T_2Rotate(Rotate[Rotate[E98, α, Line[E120, E80]], β, Line[E6, E8]], β, Line[E2, E4]) → V_2Rotate(Rotate[Rotate[E112, α, Line[E120, E80]], β, Line[E6, E8]], β, Line[E2, E4]) → U_2Rotate(Rotate[Rotate[E88, α, Line[E120, E80]], β, Line[E6, E8]], β, Line[E2, E4]) → W_2Rotate(Rotate[Rotate[E104, α, Line[E120, E80]], β, Line[E6, E8]], β, Line[E2, E4]) → Z_2Polygon(Z_1, Z_2, W_2, U_2, T_2, W_1) → wielokąt24, z_6, z_7, w_3, u_2, t_2, w_4Rotate(Rotate[Rotate[E110, α, Line[E86, E102]], β, Line[E98, E50]], β, Line[E74, E26]) → A_3Rotate(Rotate[Rotate[E94, α, Line[E86, E102]], β, Line[E98, E50]], β, Line[E74, E26]) → B_3Rotate(Rotate[Rotate[E118, α, Line[E86, E102]], β, Line[E98, E50]], β, Line[E74, E26]) → C_3Rotate(Rotate[Rotate[E78, α, Line[E86, E102]], β, Line[E98, E50]], β, Line[E74, E26]) → D_3Polygon(K_1, D_3, C_3, B_3, A_3, L_1) → wielokąt25, k_4, d_3, c_3, b_3, a_5, l_3Rotate(Rotate[Rotate[E33, α, Line[E57, E58]], β, Line[E42, E90]], β, Line[E66, E114]) → E_3Rotate(Rotate[Rotate[E9, α, Line[E57, E58]], β, Line[E42, E90]], β, Line[E66, E114]) → F_3Rotate(Rotate[Rotate[E10, α, Line[E57, E58]], β, Line[E42, E90]], β, Line[E66, E114]) → G_3Rotate(Rotate[Rotate[E34, α, Line[E57, E58]], β, Line[E42, E90]], β, Line[E66, E114]) → H_3Polygon(H_1, H_3, G_3, F_3, E_3, G_1) → wielokąt26, h_4, h_5, g_3, f_3, e_3, g_4Rotate(Rotate[Rotate[E81, β, Line[E105, E57]], β, Line[E42, E90]], β, Line[E66, E114]) → I_3Rotate(Rotate[Rotate[E33, β, Line[E105, E57]], β, Line[E42, E90]], β, Line[E66, E114]) → J_3Polygon(F_1, G_1, J_3, I_3) → wielokąt27, f_4, g_5, j_4, i_4Rotate(Rotate[Rotate[E115, β, Line[E91, E43]], β, Line[E92, E44]], β, Line[E116, E68]) → K_3Rotate(Rotate[Rotate[E67, β, Line[E91, E43]], β, Line[E92, E44]], β, Line[E116, E68]) → L_3Polygon(W, L_3, K_3, V) → wielokąt28, w_5, l_4, k_5, v_2Rotate(Rotate[Rotate[E15, β, Line[E16, E12]], β, Line[E52, E100]], β, Line[E28, E76]) → M_3Rotate(Rotate[Rotate[E11, β, Line[E16, E12]], β, Line[E52, E100]], β, Line[E28, E76]) → N_3Polygon(O, N_3, M_3, N) → wielokąt29, o_4, n_3, m_3, n_4Rotate(Rotate[Rotate[E48, β, Line[E72, E120]], β, Line[E6, E8]], β, Line[E2, E4]) → O_3Rotate(Rotate[Rotate[E96, β, Line[E72, E120]], β, Line[E6, E8]], β, Line[E2, E4]) → P_3Polygon(W_1, P_3, O_3, V_1) → wielokąt30, w_6, p_5, o_5, v_3Rotate(Rotate[Rotate[E62, β, Line[E38, E86]], β, Line[E98, E50]], β, Line[E74, E26]) → Q_3Rotate(Rotate[Rotate[E110, β, Line[E38, E86]], β, Line[E98, E50]], β, Line[E74, E26]) → R_3Polygon(L_1, R_3, Q_3, M_1) → wielokąt31, l_5, r_3, q_4, m_4Rotate(Rotate[Rotate[E83, α, Line[E107, E91]], β, Line[E92, E44]], β, Line[E116, E68]) → S_3Rotate(Rotate[Rotate[E99, α, Line[E107, E91]], β, Line[E92, E44]], β, Line[E116, E68]) → T_3Rotate(Rotate[Rotate[E75, α, Line[E107, E91]], β, Line[E92, E44]], β, Line[E116, E68]) → U_3Rotate(Rotate[Rotate[E115, α, Line[E107, E91]], β, Line[E92, E44]], β, Line[E116, E68]) → V_3Polygon(V, V_3, U_3, T_3, S_3, U) → wielokąt32, v_4, v_5, u_3, t_3, s_4, u_4Rotate(Rotate[Rotate[E64, α, Line[E40, E16]], β, Line[E52, E100]], β, Line[E28, E76]) → W_3Rotate(Rotate[Rotate[E63, α, Line[E40, E16]], β, Line[E52, E100]], β, Line[E28, E76]) → Z_3Rotate(Rotate[Rotate[E39, α, Line[E40, E16]], β, Line[E52, E100]], β, Line[E28, E76]) → A_4Rotate(Rotate[Rotate[E15, α, Line[E40, E16]], β, Line[E52, E100]], β, Line[E28, E76]) → B_4Polygon(N, B_4, A_4, Z_3, W_3, M) → wielokąt33, n_5, b_4, a_6, z_8, w_7, m_5Rotate(Rotate[Rotate[E46, α, Line[E70, E72]], β, Line[E6, E8]], β, Line[E2, E4]) → C_4Rotate(Rotate[Rotate[E22, α, Line[E70, E72]], β, Line[E6, E8]], β, Line[E2, E4]) → D_4Rotate(Rotate[Rotate[E24, α, Line[E70, E72]], β, Line[E6, E8]], β, Line[E2, E4]) → E_4Rotate(Rotate[Rotate[E48, α, Line[E70, E72]], β, Line[E6, E8]], β, Line[E2, E4]) → F_4Polygon(V_1, F_4, E_4, D_4, C_4, U_1) → wielokąt34, v_6, f_5, e_4, d_4, c_4, u_5Rotate(Rotate[Rotate[E13, α, Line[E14, E38]], β, Line[E98, E50]], β, Line[E74, E26]) → G_4Rotate(Rotate[Rotate[E37, α, Line[E14, E38]], β, Line[E98, E50]], β, Line[E74, E26]) → H_4Rotate(Rotate[Rotate[E61, α, Line[E14, E38]], β, Line[E98, E50]], β, Line[E74, E26]) → I_4Rotate(Rotate[Rotate[E62, α, Line[E14, E38]], β, Line[E98, E50]], β, Line[E74, E26]) → J_4Polygon(G_4, N_1, M_1, J_4, I_4, H_4) → wielokąt35, g_6, n_6, m_6, j_5, i_5, h_6Rotate(Rotate[Rotate[E113, α, Line[E89, E105]], β, Line[E42, E90]], β, Line[E66, E114]) → K_4Rotate(Rotate[Rotate[E73, α, Line[E89, E105]], β, Line[E42, E90]], β, Line[E66, E114]) → L_4Rotate(Rotate[Rotate[E97, α, Line[E89, E105]], β, Line[E42, E90]], β, Line[E66, E114]) → M_4Rotate(Rotate[Rotate[E81, α, Line[E89, E105]], β, Line[E42, E90]], β, Line[E66, E114]) → N_4Polygon(F_1, N_4, M_4, L_4, K_4, E_1) → wielokąt36, f_6, n_7, m_7, l_6, k_6, e_5Rotate(Rotate[Rotate[E65, β, Line[E41, E89]], β, Line[E42, E90]], β, Line[E66, E114]) → O_4Rotate(Rotate[Rotate[E113, β, Line[E41, E89]], β, Line[E42, E90]], β, Line[E66, E114]) → P_4Polygon(O_4, D_1, E_1, P_4) → wielokąt37, o_6, d_5, e_6, p_6Rotate(Rotate[Rotate[E35, β, Line[E59, E107]], β, Line[E92, E44]], β, Line[E116, E68]) → Q_4Rotate(Rotate[Rotate[E83, β, Line[E59, E107]], β, Line[E92, E44]], β, Line[E116, E68]) → R_4Polygon(U, R_4, Q_4, T) → wielokąt38, u_6, r_4, q_5, t_4Rotate(Rotate[Rotate[E112, β, Line[E88, E40]], β, Line[E52, E100]], β, Line[E28, E76]) → S_4Rotate(Rotate[Rotate[E64, β, Line[E88, E40]], β, Line[E52, E100]], β, Line[E28, E76]) → T_4Polygon(M, T_4, S_4, L) → wielokąt39, m_8, t_5, s_5, l_7Rotate(Rotate[Rotate[E94, β, Line[E118, E70]], β, Line[E6, E8]], β, Line[E2, E4]) → U_4Rotate(Rotate[Rotate[E46, β, Line[E118, E70]], β, Line[E6, E8]], β, Line[E2, E4]) → V_4Polygon(U_1, V_4, U_4, T_1) → wielokąt40, u_7, v_7, u_8, t_6Rotate(Rotate[Rotate[E9, β, Line[E10, E14]], β, Line[E98, E50]], β, Line[E74, E26]) → W_4Rotate(Rotate[Rotate[E13, β, Line[E10, E14]], β, Line[E98, E50]], β, Line[E74, E26]) → Z_4Polygon(Z_4, N_1, O_1, W_4) → wielokąt41, z_9, n_8, o_7, w_8Rotate(Rotate[Rotate[Rotate[E48, α, Line[E96, E112]], α, Line[E120, E80]], β, Line[E6, E8]], β, Line[E2, E4]) → A_5Rotate(Rotate[Rotate[Rotate[E24, α, Line[E96, E112]], α, Line[E120, E80]], β, Line[E6, E8]], β, Line[E2, E4]) → B_5Rotate(Rotate[Rotate[Rotate[E23, α, Line[E96, E112]], α, Line[E120, E80]], β, Line[E6, E8]], β, Line[E2, E4]) → C_5Rotate(Rotate[Rotate[Rotate[E47, α, Line[E96, E112]], α, Line[E120, E80]], β, Line[E6, E8]], β, Line[E2, E4]) → D_5Rotate(Rotate[Rotate[Rotate[E95, α, Line[E96, E112]], α, Line[E120, E80]], β, Line[E6, E8]], β, Line[E2, E4]) → E_5Rotate(Rotate[Rotate[Rotate[E111, α, Line[E96, E112]], α, Line[E120, E80]], β, Line[E6, E8]], β, Line[E2, E4]) → F_5Rotate(Rotate[Rotate[Rotate[E63, α, Line[E96, E112]], α, Line[E120, E80]], β, Line[E6, E8]], β, Line[E2, E4]) → G_5Rotate(Rotate[Rotate[Rotate[E64, α, Line[E96, E112]], α, Line[E120, E80]], β, Line[E6, E8]], β, Line[E2, E4]) → H_5Polygon(A_5, T_2, U_2, H_5, G_5, F_5, E_5, D_5, C_5, B_5) → wielokąt42, a_7, b_5, t_7, u_9, h_7, g_7, f_7, e_7, d_6, c_5Rotate(Rotate[Rotate[Rotate[E15, α, Line[E11, E35]], α, Line[E12, E36]], β, Line[E52, E100]], β, Line[E28, E76]) → I_5Rotate(Rotate[Rotate[Rotate[E39, α, Line[E11, E35]], α, Line[E12, E36]], β, Line[E52, E100]], β, Line[E28, E76]) → J_5Rotate(Rotate[Rotate[Rotate[E87, α, Line[E11, E35]], α, Line[E12, E36]], β, Line[E52, E100]], β, Line[E28, E76]) → K_5Rotate(Rotate[Rotate[Rotate[E103, α, Line[E11, E35]], α, Line[E12, E36]], β, Line[E52, E100]], β, Line[E28, E76]) → L_5Rotate(Rotate[Rotate[Rotate[E55, α, Line[E11, E35]], α, Line[E12, E36]], β, Line[E52, E100]], β, Line[E28, E76]) → M_5Rotate(Rotate[Rotate[Rotate[E51, α, Line[E11, E35]], α, Line[E12, E36]], β, Line[E52, E100]], β, Line[E28, E76]) → N_5Rotate(Rotate[Rotate[Rotate[E99, α, Line[E11, E35]], α, Line[E12, E36]], β, Line[E52, E100]], β, Line[E28, E76]) → O_5Rotate(Rotate[Rotate[Rotate[E83, α, Line[E11, E35]], α, Line[E12, E36]], β, Line[E52, E100]], β, Line[E28, E76]) → P_5Polygon(I_5, P_2, Q_2, P_5, O_5, N_5, M_5, L_5, K_5, J_5) → wielokąt43, i_6, j_6, p_7, q_6, p_8, o_8, n_9, m_9, l_8, k_7Rotate(Rotate[Rotate[Rotate[E115, α, Line[E67, E65]], α, Line[E43, E19]], β, Line[E92, E44]], β, Line[E116, E68]) → Q_5Rotate(Rotate[Rotate[Rotate[E75, α, Line[E67, E65]], α, Line[E43, E19]], β, Line[E92, E44]], β, Line[E116, E68]) → R_5Rotate(Rotate[Rotate[Rotate[E27, α, Line[E67, E65]], α, Line[E43, E19]], β, Line[E92, E44]], β, Line[E116, E68]) → S_5Rotate(Rotate[Rotate[Rotate[E3, α, Line[E67, E65]], α, Line[E43, E19]], β, Line[E92, E44]], β, Line[E116, E68]) → T_5Rotate(Rotate[Rotate[Rotate[E1, α, Line[E67, E65]], α, Line[E43, E19]], β, Line[E92, E44]], β, Line[E116, E68]) → U_5Rotate(Rotate[Rotate[Rotate[E25, α, Line[E67, E65]], α, Line[E43, E19]], β, Line[E92, E44]], β, Line[E116, E68]) → V_5Rotate(Rotate[Rotate[Rotate[E73, α, Line[E67, E65]], α, Line[E43, E19]], β, Line[E92, E44]], β, Line[E116, E68]) → W_5Rotate(Rotate[Rotate[Rotate[E113, α, Line[E67, E65]], α, Line[E43, E19]], β, Line[E92, E44]], β, Line[E116, E68]) → Z_5Polygon(Q_5, L_2, M_2, Z_5, W_5, V_5, U_5, T_5, S_5, R_5) → wielokąt44, q_7, r_5, l_9, m_{10}, z_{10}, w_9, v_8, u_{10}, t_8, s_6Rotate(Rotate[Rotate[Rotate[E81, α, Line[E33, E9]], α, Line[E57, E58]], β, Line[E42, E90]], β, Line[E66, E114]) → A_6Rotate(Rotate[Rotate[Rotate[E97, α, Line[E33, E9]], α, Line[E57, E58]], β, Line[E42, E90]], β, Line[E66, E114]) → B_6Rotate(Rotate[Rotate[Rotate[E49, α, Line[E33, E9]], α, Line[E57, E58]], β, Line[E42, E90]], β, Line[E66, E114]) → C_6Rotate(Rotate[Rotate[Rotate[E53, α, Line[E33, E9]], α, Line[E57, E58]], β, Line[E42, E90]], β, Line[E66, E114]) → D_6Rotate(Rotate[Rotate[Rotate[E101, α, Line[E33, E9]], α, Line[E57, E58]], β, Line[E42, E90]], β, Line[E66, E114]) → E_6Rotate(Rotate[Rotate[Rotate[E85, α, Line[E33, E9]], α, Line[E57, E58]], β, Line[E42, E90]], β, Line[E66, E114]) → F_6Rotate(Rotate[Rotate[Rotate[E37, α, Line[E33, E9]], α, Line[E57, E58]], β, Line[E42, E90]], β, Line[E66, E114]) → G_6Rotate(Rotate[Rotate[Rotate[E13, α, Line[E33, E9]], α, Line[E57, E58]], β, Line[E42, E90]], β, Line[E66, E114]) → H_6Polygon(A_6, E_3, F_3, H_6, G_6, F_6, E_6, D_6, C_6, B_6) → wielokąt45, a_8, b_6, e_8, f_8, h_8, g_8, f_9, e_9, d_7, c_6Rotate(Rotate[Rotate[Rotate[E62, α, Line[E110, E94]], α, Line[E86, E102]], β, Line[E98, E50]], β, Line[E74, E26]) → I_6Rotate(Rotate[Rotate[Rotate[E61, α, Line[E110, E94]], α, Line[E86, E102]], β, Line[E98, E50]], β, Line[E74, E26]) → J_6Rotate(Rotate[Rotate[Rotate[E109, α, Line[E110, E94]], α, Line[E86, E102]], β, Line[E98, E50]], β, Line[E74, E26]) → K_6Rotate(Rotate[Rotate[Rotate[E93, α, Line[E110, E94]], α, Line[E86, E102]], β, Line[E98, E50]], β, Line[E74, E26]) → L_6Rotate(Rotate[Rotate[Rotate[E45, α, Line[E110, E94]], α, Line[E86, E102]], β, Line[E98, E50]], β, Line[E74, E26]) → M_6Rotate(Rotate[Rotate[Rotate[E21, α, Line[E110, E94]], α, Line[E86, E102]], β, Line[E98, E50]], β, Line[E74, E26]) → N_6Rotate(Rotate[Rotate[Rotate[E22, α, Line[E110, E94]], α, Line[E86, E102]], β, Line[E98, E50]], β, Line[E74, E26]) → O_6Rotate(Rotate[Rotate[Rotate[E46, α, Line[E110, E94]], α, Line[E86, E102]], β, Line[E98, E50]], β, Line[E74, E26]) → P_6Polygon(I_6, A_3, B_3, P_6, O_6, N_6, M_6, L_6, K_6, J_6) → wielokąt46, i_7, j_7, a_9, b_7, p_9, o_9, n_{10}, m_{11}, l_{10}, k_8Rotate(Rotate[Rotate[Rotate[Rotate[E23, β, Line[E21, E22]], α, Line[E110, E94]], α, Line[E86, E102]], β, Line[E98, E50]], β, Line[E74, E26]) → Q_6Rotate(Rotate[Rotate[Rotate[Rotate[E24, β, Line[E21, E22]], α, Line[E110, E94]], α, Line[E86, E102]], β, Line[E98, E50]], β, Line[E74, E26]) → R_6Polygon(Q_6, N_6, O_6, R_6) → wielokąt47, q_8, n_{11}, o_{10}, r_6Rotate(Rotate[Rotate[Rotate[Rotate[E87, β, Line[E111, E63]], α, Line[E96, E112]], α, Line[E120, E80]], β, Line[E6, E8]], β, Line[E2, E4]) → S_6Rotate(Rotate[Rotate[Rotate[Rotate[E39, β, Line[E111, E63]], α, Line[E96, E112]], α, Line[E120, E80]], β, Line[E6, E8]], β, Line[E2, E4]) → T_6Polygon(S_6, F_5, G_5, T_6) → wielokąt48, s_7, f_{10}, g_9, t_9Rotate(Rotate[Rotate[Rotate[Rotate[E27, β, Line[E51, E99]], α, Line[E11, E35]], α, Line[E12, E36]], β, Line[E52, E100]], β, Line[E28, E76]) → U_6Rotate(Rotate[Rotate[Rotate[Rotate[E75, β, Line[E51, E99]], α, Line[E11, E35]], α, Line[E12, E36]], β, Line[E52, E100]], β, Line[E28, E76]) → V_6Polygon(U_6, N_5, O_5, V_6) → wielokąt49, u_{11}, n_{12}, o_{11}, v_9Rotate(Rotate[Rotate[Rotate[Rotate[E49, β, Line[E25, E73]], α, Line[E67, E65]], α, Line[E43, E19]], β, Line[E92, E44]], β, Line[E116, E68]) → W_6Rotate(Rotate[Rotate[Rotate[Rotate[E97, β, Line[E25, E73]], α, Line[E67, E65]], α, Line[E43, E19]], β, Line[E92, E44]], β, Line[E116, E68]) → Z_6Polygon(W_5, Z_6, W_6, V_5) → wielokąt50, w_{10}, z_{11}, w_{11}, v_{10}Rotate(Rotate[Rotate[Rotate[Rotate[E109, β, Line[E85, E37]], α, Line[E33, E9]], α, Line[E57, E58]], β, Line[E42, E90]], β, Line[E66, E114]) → A_7Rotate(Rotate[Rotate[Rotate[Rotate[E61, β, Line[E85, E37]], α, Line[E33, E9]], α, Line[E57, E58]], β, Line[E42, E90]], β, Line[E66, E114]) → B_7Polygon(A_7, F_6, G_6, B_7) → wielokąt51, a_{10}, f_{11}, g_{10}, b_8Rotate(Rotate[Rotate[Rotate[Rotate[E77, α, Line[E101, E85]], α, Line[E33, E9]], α, Line[E57, E58]], β, Line[E42, E90]], β, Line[E66, E114]) → C_7Rotate(Rotate[Rotate[Rotate[Rotate[E117, α, Line[E101, E85]], α, Line[E33, E9]], α, Line[E57, E58]], β, Line[E42, E90]], β, Line[E66, E114]) → D_7Rotate(Rotate[Rotate[Rotate[Rotate[E93, α, Line[E101, E85]], α, Line[E33, E9]], α, Line[E57, E58]], β, Line[E42, E90]], β, Line[E66, E114]) → E_7Rotate(Rotate[Rotate[Rotate[Rotate[E109, α, Line[E101, E85]], α, Line[E33, E9]], α, Line[E57, E58]], β, Line[E42, E90]], β, Line[E66, E114]) → F_7Polygon(F_6, F_7, E_7, D_7, C_7, E_6) → wielokąt52, f_{12}, f_{13}, e_{10}, d_8, c_7, e_{11}Rotate(Rotate[Rotate[Rotate[Rotate[E5, α, Line[E1, E25]], α, Line[E67, E65]], α, Line[E43, E19]], β, Line[E92, E44]], β, Line[E116, E68]) → G_7Rotate(Rotate[Rotate[Rotate[Rotate[E29, α, Line[E1, E25]], α, Line[E67, E65]], α, Line[E43, E19]], β, Line[E92, E44]], β, Line[E116, E68]) → H_7Rotate(Rotate[Rotate[Rotate[Rotate[E53, α, Line[E1, E25]], α, Line[E67, E65]], α, Line[E43, E19]], β, Line[E92, E44]], β, Line[E116, E68]) → I_7Rotate(Rotate[Rotate[Rotate[Rotate[E49, α, Line[E1, E25]], α, Line[E67, E65]], α, Line[E43, E19]], β, Line[E92, E44]], β, Line[E116, E68]) → J_7Polygon(V_5, J_7, I_7, H_7, G_7, U_5) → wielokąt53, v_{11}, j_8, i_8, h_9, g_{11}, u_{12}Rotate(Rotate[Rotate[Rotate[Rotate[E31, α, Line[E55, E51]], α, Line[E11, E35]], α, Line[E12, E36]], β, Line[E52, E100]], β, Line[E28, E76]) → K_7Rotate(Rotate[Rotate[Rotate[Rotate[E7, α, Line[E55, E51]], α, Line[E11, E35]], α, Line[E12, E36]], β, Line[E52, E100]], β, Line[E28, E76]) → L_7Rotate(Rotate[Rotate[Rotate[Rotate[E3, α, Line[E55, E51]], α, Line[E11, E35]], α, Line[E12, E36]], β, Line[E52, E100]], β, Line[E28, E76]) → M_7Rotate(Rotate[Rotate[Rotate[Rotate[E27, α, Line[E55, E51]], α, Line[E11, E35]], α, Line[E12, E36]], β, Line[E52, E100]], β, Line[E28, E76]) → N_7Polygon(N_5, N_7, M_7, L_7, K_7, M_5) → wielokąt54, n_{13}, n_{14}, m_{12}, l_{11}, k_9, m_{13}Rotate(Rotate[Rotate[Rotate[Rotate[E119, α, Line[E95, E111]], α, Line[E96, E112]], α, Line[E120, E80]], β, Line[E6, E8]], β, Line[E2, E4]) → O_7Rotate(Rotate[Rotate[Rotate[Rotate[E79, α, Line[E95, E111]], α, Line[E96, E112]], α, Line[E120, E80]], β, Line[E6, E8]], β, Line[E2, E4]) → P_7Rotate(Rotate[Rotate[Rotate[Rotate[E103, α, Line[E95, E111]], α, Line[E96, E112]], α, Line[E120, E80]], β, Line[E6, E8]], β, Line[E2, E4]) → Q_7Rotate(Rotate[Rotate[Rotate[Rotate[E87, α, Line[E95, E111]], α, Line[E96, E112]], α, Line[E120, E80]], β, Line[E6, E8]], β, Line[E2, E4]) → R_7Polygon(F_5, R_7, Q_7, P_7, O_7, E_5) → wielokąt55, f_{14}, r_7, q_9, p_{10}, o_{12}, e_{12}Rotate(Rotate[Rotate[Rotate[Rotate[E69, α, Line[E45, E21]], α, Line[E110, E94]], α, Line[E86, E102]], β, Line[E98, E50]], β, Line[E74, E26]) → S_7Rotate(Rotate[Rotate[Rotate[Rotate[E71, α, Line[E45, E21]], α, Line[E110, E94]], α, Line[E86, E102]], β, Line[E98, E50]], β, Line[E74, E26]) → T_7Rotate(Rotate[Rotate[Rotate[Rotate[E47, α, Line[E45, E21]], α, Line[E110, E94]], α, Line[E86, E102]], β, Line[E98, E50]], β, Line[E74, E26]) → U_7Rotate(Rotate[Rotate[Rotate[Rotate[E23, α, Line[E45, E21]], α, Line[E110, E94]], α, Line[E86, E102]], β, Line[E98, E50]], β, Line[E74, E26]) → V_7Polygon(N_6, V_7, U_7, T_7, S_7, M_6) → wielokąt56, n_{15}, v_{12}, u_{13}, t_{10}, s_8, m_{14}Rotate(Rotate[Rotate[Rotate[Rotate[E117, β, Line[E93, E45]], α, Line[E110, E94]], α, Line[E86, E102]], β, Line[E98, E50]], β, Line[E74, E26]) → W_7Rotate(Rotate[Rotate[Rotate[Rotate[E69, β, Line[E93, E45]], α, Line[E110, E94]], α, Line[E86, E102]], β, Line[E98, E50]], β, Line[E74, E26]) → Z_7Polygon(M_6, Z_7, W_7, L_6) → wielokąt57, m_{15}, z_{12}, w_{12}, l_{12}Rotate(Rotate[Rotate[Rotate[Rotate[E71, β, Line[E47, E95]], α, Line[E96, E112]], α, Line[E120, E80]], β, Line[E6, E8]], β, Line[E2, E4]) → A_8Rotate(Rotate[Rotate[Rotate[Rotate[E119, β, Line[E47, E95]], α, Line[E96, E112]], α, Line[E120, E80]], β, Line[E6, E8]], β, Line[E2, E4]) → B_8Polygon(E_5, B_8, A_8, D_5) → wielokąt58, e_{13}, b_9, a_{11}, d_9Rotate(Rotate[Rotate[Rotate[Rotate[E31, β, Line[E103, E55]], α, Line[E11, E35]], α, Line[E12, E36]], β, Line[E52, E100]], β, Line[E28, E76]) → D_8Rotate(Rotate[Rotate[Rotate[Rotate[E79, β, Line[E103, E55]], α, Line[E11, E35]], α, Line[E12, E36]], β, Line[E52, E100]], β, Line[E28, E76]) → C_8Polygon(M_5, D_8, C_8, L_5) → wielokąt59, m_{16}, d_{10}, c_8, l_{13}Rotate(Rotate[Rotate[Rotate[Rotate[E7, β, Line[E3, E1]], α, Line[E67, E65]], α, Line[E43, E19]], β, Line[E92, E44]], β, Line[E116, E68]) → E_8Rotate(Rotate[Rotate[Rotate[Rotate[E5, β, Line[E3, E1]], α, Line[E67, E65]], α, Line[E43, E19]], β, Line[E92, E44]], β, Line[E116, E68]) → F_8Polygon(U_5, F_8, E_8, T_5) → wielokąt60, u_{14}, f_{15}, e_{14}, t_{11}Rotate(Rotate[Rotate[Rotate[Rotate[E29, β, Line[E53, E101]], α, Line[E33, E9]], α, Line[E57, E58]], β, Line[E42, E90]], β, Line[E66, E114]) → G_8Rotate(Rotate[Rotate[Rotate[Rotate[E77, β, Line[E53, E101]], α, Line[E33, E9]], α, Line[E57, E58]], β, Line[E42, E90]], β, Line[E66, E114]) → H_8Polygon(E_6, H_8, G_8, D_6) → wielokąt61, e_{15}, h_{10}, g_{12}, d_{11}Rotate(Rotate[Rotate[Rotate[Rotate[Rotate[E29, α, Line[E77, E117]], α, Line[E101, E85]], α, Line[E33, E9]], α, Line[E57, E58]], β, Line[E42, E90]], β, Line[E66, E114]) → I_8Rotate(Rotate[Rotate[Rotate[Rotate[Rotate[E5, α, Line[E77, E117]], α, Line[E101, E85]], α, Line[E33, E9]], α, Line[E57, E58]], β, Line[E42, E90]], β, Line[E66, E114]) → J_8Rotate(Rotate[Rotate[Rotate[Rotate[Rotate[E7, α, Line[E77, E117]], α, Line[E101, E85]], α, Line[E33, E9]], α, Line[E57, E58]], β, Line[E42, E90]], β, Line[E66, E114]) → K_8Rotate(Rotate[Rotate[Rotate[Rotate[Rotate[E31, α, Line[E77, E117]], α, Line[E101, E85]], α, Line[E33, E9]], α, Line[E57, E58]], β, Line[E42, E90]], β, Line[E66, E114]) → L_8Rotate(Rotate[Rotate[Rotate[Rotate[Rotate[E79, α, Line[E77, E117]], α, Line[E101, E85]], α, Line[E33, E9]], α, Line[E57, E58]], β, Line[E42, E90]], β, Line[E66, E114]) → M_8Rotate(Rotate[Rotate[Rotate[Rotate[Rotate[E119, α, Line[E77, E117]], α, Line[E101, E85]], α, Line[E33, E9]], α, Line[E57, E58]], β, Line[E42, E90]], β, Line[E66, E114]) → N_8Rotate(Rotate[Rotate[Rotate[Rotate[Rotate[E71, α, Line[E77, E117]], α, Line[E101, E85]], α, Line[E33, E9]], α, Line[E57, E58]], β, Line[E42, E90]], β, Line[E66, E114]) → O_8Rotate(Rotate[Rotate[Rotate[Rotate[Rotate[E69, α, Line[E77, E117]], α, Line[E101, E85]], α, Line[E33, E9]], α, Line[E57, E58]], β, Line[E42, E90]], β, Line[E66, E114]) → P_8Polygon(I_8, C_7, D_7, P_8, O_8, N_8, M_8, L_8, K_8, J_8) → wielokąt62, i_9, j_9, c_9, d_{12}, p_{11}, o_{13}, n_{16}, m_{17}, l_{14}, k_{10}
AI 绘图提示语参考
绘制一个截角二十面十二面体,这是一个具有高度对称性的多面体。首先确定三个关键点,其中两个是棱的中点,第三个是另一条棱上的点,由这三个点构成一个平面,并测量该平面上的一个角。然后过第三个点作此平面的垂线,以该垂线为旋转轴,将多面体的所有顶点按上述角度绕轴旋转,得到一组新顶点。用这些新顶点与原顶点共同构建出截角后的多面体表面,展示其由正多边形面组成的复杂结构,体现欧拉示性数与对称性。
以上提示语为根据原始绘图命令整理而来,仅供参考。