八面体构造与展开

几何画板及绘图内容加载中，请稍等……

2019-12-06 09:50

①本范例演示了八面体的三维构造及其展开图；②涉及的核心数学概念包括三维向量、三角函数、多边形几何、立体几何；③作图要点提炼自构造摘要，使用了Sequence（数列）、Octahedron（八面体）、Net（展开图）等GeoGebra命令与对象；④适合高中及以上学生及数学爱好者学习空间几何与几何建模。

GeoGebra 命令及参数

Sequence((r; (((360 * j)) / n)°), j, 0, n) → l1
Octahedron(Element[l1, 1], Element[l1, 2], Element[l1, 3]) → tetrae, A, cara7, cara8, arista1, arista2, arista3, arista4, arista5, arista6, arista7, arista8, H, arista9, arista10, arista11, arista12, I, cara1, cara2, cara3, cara4, cara5, cara6
Net(tetrae, b) → d, B, M, caraBCD, caraBDE, caraBEF, caraBCK, caraCKL, caraCDM, caraDEJ, caraEFG, aristaBD, C, aristaBC, aristaCD, aristaDE, aristaBE, aristaEF, aristaBF, aristaBK, aristaCK, aristaKL, aristaCL, D, aristaCM, aristaDM, aristaDJ, aristaEJ, aristaEG, aristaFG, E, F, G, J, K, L
Net(tetrae, e) → f, N, W, caraNOP, caraNPQ, caraNQR, caraNOU, caraOUV, caraOPW, caraPQT, caraQRS, aristaNP, O, aristaNO, aristaOP, aristaPQ, aristaNQ, aristaQR, aristaNR, aristaNU, aristaOU, aristaUV, aristaOV, P, aristaOW, aristaPW, aristaPT, aristaQT, aristaQS, aristaRS, Q, R, S, T, U, V
Net(tetrae, g) → h, Z, I_1, cara9, cara11, cara12, cara10, cara14, cara13, cara15, cara16, arista14, A_1, arista13, arista18, arista22, arista15, arista25, arista16, arista17, arista19, arista29, arista20, B_1, arista21, arista24, arista23, arista27, arista26, arista28, C_1, D_1, E_1, F_1, G_1, H_1
Net(tetrae, i) → j, J_1, S_1, cara17, cara19, cara20, cara18, cara22, cara21, cara23, cara24, arista31, K_1, arista30, arista35, arista39, arista32, arista42, arista33, arista34, arista36, arista46, arista37, L_1, arista38, arista41, arista40, arista44, arista43, arista45, M_1, N_1, O_1, P_1, Q_1, R_1
Net(tetrae, k) → l, T_1, E_2, cara25, cara27, cara28, cara26, cara30, cara29, cara31, cara32, arista48, U_1, arista47, arista52, arista56, arista49, arista59, arista50, arista51, arista53, arista63, arista54, V_1, arista55, arista58, arista57, arista61, arista60, arista62, W_1, Z_1, A_2, B_2, C_2, D_2
Net(tetrae, m) → o, F_2, O_2, cara33, cara35, cara36, cara34, cara38, cara37, cara39, cara40, arista65, G_2, arista64, arista69, arista73, arista66, arista76, arista67, arista68, arista70, arista80, arista71, H_2, arista72, arista75, arista74, arista78, arista77, arista79, I_2, J_2, K_2, L_2, M_2, N_2
Net(tetrae, p) → q, P_2, A_3, cara41, cara43, cara44, cara42, cara46, cara45, cara47, cara48, arista82, Q_2, arista81, arista86, arista90, arista83, arista93, arista84, arista85, arista87, arista97, arista88, R_2, arista89, arista92, arista91, arista95, arista94, arista96, S_2, T_2, U_2, V_2, W_2, Z_2
Net(tetrae, s) → t, B_3, K_3, cara49, cara51, cara52, cara50, cara54, cara53, cara55, cara56, arista99, C_3, arista98, arista103, arista107, arista100, arista110, arista101, arista102, arista104, arista114, arista105, D_3, arista106, arista109, arista108, arista112, arista111, arista113, E_3, F_3, G_3, H_3, I_3, J_3
Net(tetrae, u) → v, L_3, U_3, cara57, cara59, cara60, cara58, cara62, cara61, cara63, cara64, arista116, M_3, arista115, arista120, arista124, arista117, arista127, arista118, arista119, arista121, arista131, arista122, N_3, arista123, arista126, arista125, arista129, arista128, arista130, O_3, P_3, Q_3, R_3, S_3, T_3
Net(tetrae, w) → a_1, V_3, G_4, cara65, cara67, cara68, cara66, cara70, cara69, cara71, cara72, arista133, W_3, arista132, arista137, arista141, arista134, arista144, arista135, arista136, arista138, arista148, arista139, Z_3, arista140, arista143, arista142, arista146, arista145, arista147, A_4, B_4, C_4, D_4, E_4, F_4
Net(tetrae, b_1) → c_1, H_4, Q_4, cara73, cara75, cara76, cara74, cara78, cara77, cara79, cara80, arista150, I_4, arista149, arista154, arista158, arista151, arista161, arista152, arista153, arista155, arista165, arista156, J_4, arista157, arista160, arista159, arista163, arista162, arista164, K_4, L_4, M_4, N_4, O_4, P_4
Net(tetrae, d_1) → e_1, R_4, C_5, cara81, cara83, cara84, cara82, cara86, cara85, cara87, cara88, arista167, S_4, arista166, arista171, arista175, arista168, arista178, arista169, arista170, arista172, arista182, arista173, T_4, arista174, arista177, arista176, arista180, arista179, arista181, U_4, V_4, W_4, Z_4, A_5, B_5
Net(tetrae, f_1) → g_1, D_5, M_5, cara89, cara91, cara92, cara90, cara94, cara93, cara95, cara96, arista184, E_5, arista183, arista188, arista192, arista185, arista195, arista186, arista187, arista189, arista199, arista190, F_5, arista191, arista194, arista193, arista197, arista196, arista198, G_5, H_5, I_5, J_5, K_5, L_5
Net(tetrae, h_1) → i_1, N_5, W_5, cara97, cara99, cara100, cara98, cara102, cara101, cara103, cara104, arista201, O_5, arista200, arista205, arista209, arista202, arista212, arista203, arista204, arista206, arista216, arista207, P_5, arista208, arista211, arista210, arista214, arista213, arista215, Q_5, R_5, S_5, T_5, U_5, V_5
Net(tetrae, j_1) → k_1, Z_5, I_6, cara105, cara107, cara108, cara106, cara110, cara109, cara111, cara112, arista218, A_6, arista217, arista222, arista226, arista219, arista229, arista220, arista221, arista223, arista233, arista224, B_6, arista225, arista228, arista227, arista231, arista230, arista232, C_6, D_6, E_6, F_6, G_6, H_6
Net(tetrae, l_1) → m_1, J_6, S_6, cara113, cara115, cara116, cara114, cara118, cara117, cara119, cara120, arista235, K_6, arista234, arista239, arista243, arista236, arista246, arista237, arista238, arista240, arista250, arista241, L_6, arista242, arista245, arista244, arista248, arista247, arista249, M_6, N_6, O_6, P_6, Q_6, R_6
Net(tetrae, n_1) → o_1, T_6, E_7, cara121, cara123, cara124, cara122, cara126, cara125, cara127, cara128, arista252, U_6, arista251, arista256, arista260, arista253, arista263, arista254, arista255, arista257, arista267, arista258, V_6, arista259, arista262, arista261, arista265, arista264, arista266, W_6, Z_6, A_7, B_7, C_7, D_7