Pyramid Net with Regular Polygon Base
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This example demonstrates the net of a pyramid with a regular polygon base. Key mathematical concepts include solid geometry and geometric construction. Using GeoGebra commands such as CurveCartesian, Point, Polygon, Pyramid, and Net, the net of the pyramid can be constructed. Suitable for high school students and teachers.
GeoGebra Commands & Parameters
CurveCartesian((4 * sin(t)), (4 * cos(t)), 0, t, 0, 6.28319) → aPoint(a) → BPolygon(B, A, Faces, xOyPlane) → poly1, c, r, C_{11}, D_{11}, E_{11}, F_{11}, W_{16}, H_{17}, Q_{17}, R_{17}, S_{17}, T_{17}, s, U_{17}, V_{17}, W_{17}, Z_{17}, A_{18}, B_{18}, C_{18}, D_{18}, E_{18}, t, a_1, b_1, c_1, d_1, e_1, f_1, g_1, d, h_1, i_1, j_1, k_1, l_1, m_1, n_1, p_1, q_1, r_1, e, s_1, t_1, a_2, b_2, c_2, d_2, e_2, f_2, g_2, h_2, k, i_2, j_2, k_2, l_2, m_2, n_2, p_2, q_2, r_2, s_2, l, t_2, a_3, b_3, c_3, d_3, e_3, f_3, g_3, h_3, i_3, m, j_3, C, E_1, F_1, W_1, Z_1, A_2, B_2, C_2, D_2, n, E_2, F_2, G_2, H_2, I_2, J_2, K_2, L_2, E_7, F_7, p, G_7, H_7, I_7, J_7, K_7, L_7, M_7, N_{10}, O_{10}, P_{10}, q, Q_{10}, R_{10}, S_{10}, T_{10}, U_{10}, V_{10}, W_{10}, Z_{10}, A_{11}, B_{11}Pyramid(poly1, 4) → f, D, face18, edge344, edge345, edge346, edge347, edge348, edge349, edge350, edge555, edge568, edge581, face19, edge582, edge583, edge584, edge585, edge586, edge587, edge588, edge589, edge590, edge591, face20, edge592, edge593, face21, face22, face23, face24, face25, face26, face27, faceABD, face28, face85, face86, face87, face88, face89, face90, face91, face92, face93, faceACD, face130, face131, face132, face133, face134, face135, face136, face137, face138, face139, faceBCD, face140, face141, face142, face143, face144, face145, face146, face215, face220, face225, face5, face226, face227, face228, face229, face230, face231, face232, face233, face234, face235, face6, face236, face237, edgeBD, edgeAD, edgeCD, edge9, edge10, edge35, edge36, edge37, face15, edge38, edge39, edge40, edge41, edge42, edge43, edge44, edge45, edge46, edge47, face16, edge48, edge217, edge218, edge219, edge220, edge221, edge222, edge223, edge224, edge225, face17, edge334, edge335, edge336, edge337, edge338, edge339, edge340, edge341, edge342, edge343Net(f, g) → b, Q, A_5, G_{15}, H_{15}, I_{15}, J_{15}, K_{15}, L_{15}, E_{17}, N_{17}, W_{20}, Z_{20}, B_5, A_{21}, B_{21}, C_{21}, D_{21}, E_{21}, F_{21}, G_{21}, H_{21}, I_{21}, J_{21}, C_5, K_{21}, faceQRS, faceQRT, faceRSU, faceQSV, face11, face12, face57, face58, face59, D_5, face60, face61, face62, face63, face64, face65, face66, face67, face68, face69, E_5, face70, face112, face113, face114, face115, face116, face117, face118, face119, face120, F_5, face181, face182, face183, face184, face185, face186, face187, face188, face189, face190, G_5, face191, face192, face193, face194, face195, face196, face197, face218, face223, face264, H_5, face265, face266, face267, face268, face269, face270, face271, face272, face273, face274, I_5, face275, face276, edgeQR, edgeRS, edgeQS, edge23, edge24, edge133, edge134, edge135, J_5, edge136, edge137, edge138, edge139, edge140, edge141, edge142, edge143, edge144, edge145, R, B_9, edge146, edge280, edge281, edge282, edge283, edge284, edge285, edge286, edge287, edge288, C_9, edge453, edge454, edge455, edge456, edge457, edge458, edge459, edge460, edge461, edge462, D_9, edge463, edge464, edge465, edge466, edge467, edge468, edge469, edge562, edge575, edge672, E_9, edge673, edge674, edge675, edge676, edge677, edge678, edge679, edge680, edge681, edge682, F_9, edge683, edge684, edgeQT, edgeRT, edgeRU, edgeSU, edgeSV, edgeQV, edge25, edge26, G_9, edge27, edge28, edge147, edge148, edge149, edge150, edge151, edge152, edge153, edge154, H_9, edge155, edge156, edge157, edge158, edge159, edge160, edge161, edge162, edge163, edge164, I_9, edge165, edge166, edge167, edge168, edge169, edge170, edge171, edge172, edge173, edge174, J_9, edge289, edge290, edge291, edge292, edge293, edge294, edge295, edge296, edge297, edge298, C_{14}, edge299, edge300, edge301, edge302, edge303, edge304, edge305, edge306, edge470, edge471, S, D_{14}, edge472, edge473, edge474, edge475, edge476, edge477, edge478, edge479, edge480, edge481, E_{14}, edge482, edge483, edge484, edge485, edge486, edge487, edge488, edge489, edge490, edge491, F_{14}, edge492, edge493, edge494, edge495, edge496, edge497, edge498, edge499, edge500, edge501, G_{14}, edge502, edge503, edge563, edge564, edge576, edge577, edge685, edge686, edge687, edge688, H_{14}, edge689, edge690, edge691, edge692, edge693, edge694, edge695, edge696, edge697, edge698, I_{14}, edge699, edge700, edge701, edge702, edge703, edge704, edge705, edge706, edge707, edge708, J_{14}, edge709, edge710, K_{14}, L_{14}, M_{14}, O_1, N_{14}, O_{14}, P_{14}, Q_{14}, R_{14}, S_{14}, D_{17}, M_{17}, J_{20}, K_{20}, P_1, L_{20}, M_{20}, N_{20}, O_{20}, P_{20}, Q_{20}, R_{20}, S_{20}, T_{20}, U_{20}, U_4, V_{20}, T, U, V, Q_1, R_1, K_5, L_5, M_5, N_5, V_4, O_5, P_5, Q_5, R_5, S_5, T_5, U_5, V_5, W_5, Z_5, W_4, K_9, L_9, M_9, N_9, O_9, P_9, Q_9, R_9, S_9, T_{14}, Z_4, U_{14}, V_{14}, W_{14}, Z_{14}, A_{15}, B_{15}, C_{15}, D_{15}, E_{15}, F_{15}Net(f, g) → h, E, T_1, face100, face101, face102, face103, face104, face105, face106, face107, face108, face109, N_2, face110, face111, face147, face148, face149, face150, face151, face152, face153, face154, P_2, face155, face156, edgeEF, edgeFG, edgeEG, edge1, edge5, edge8, edge15, edge20, R_2, edge31, edge34, edge51, edge54, edge57, edge60, edge61, edge62, edge69, edge70, T_2, edge75, edge76, edge77, edge78, edge87, edge88, edge89, edge90, edge93, edge94, U_2, edge95, edge110, edge111, edge112, edge113, edge114, edge115, edge116, edge117, edge118, V_2, edge119, edge120, edgeEK, edgeFK, edgeFL, edgeGL, edgeGM, edgeEM, edge2, edge3, B_3, edge6, edge7, edge13, edge14, edge16, edge19, edge21, edge22, edge32, edge33, C_3, edge49, edge50, edge52, edge53, edge55, edge56, edge58, edge59, edge63, edge64, F_3, edge65, edge66, edge67, edge68, edge71, edge72, edge73, edge74, edge79, edge80, F, G_3, edge81, edge82, edge83, edge84, edge85, edge86, edge96, edge97, edge98, edge99, H_3, edge100, edge101, edge102, edge103, edge104, edge105, edge106, edge107, edge108, edge109, I_3, edge121, edge122, edge123, edge124, edge125, edge126, edge127, edge128, edge129, edge130, N_3, edge131, edge132, edge189, edge190, edge191, edge192, edge193, edge194, edge195, edge196, O_3, edge197, edge198, P_3, Q_3, R_3, S_3, T_3, G, D_4, E_4, F_4, G_4, H_4, I_4, J_4, K_4, L_4, M_4, W, N_4, K, L, M, Z, G_1, I_1, K_1, M_1, S_1, A_1, M_2, O_2, Q_2, S_2, W_2, Z_2, A_3, D_3, E_3, J_3, H_1, K_3, L_3, M_3, U_3, V_3, W_3, Z_3, A_4, B_4, C_4, J_1, O_4, P_4, Q_4, R_4, S_4, T_4, A_6, B_6, C_6, D_6, L_1, E_6, faceEFG, faceEFK, faceFGL, faceEGM, face1, face3, face36, face37, face38, N_1, face39, face40, face41, face42, face94, face95, face96, face97, face98, face99
AI Drawing Prompt Reference
Draw the net of a pyramid with a regular polygon base. Start with a circle and place a point on it to define one vertex of the base polygon, then construct the regular polygon on the horizontal plane. Build a pyramid above this base with its apex directly above the center. Finally, unfold all lateral faces onto the plane along the base edges, resulting in a flat net consisting of the base polygon and several triangular faces sharing edges with it, showing the complete surface development.
The prompt above was compiled from the original drawing commands and is for reference only.