Explore Surface Area and Volume of Regular Prisms

Explore Surface Area and Volume of Regular Prisms
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2016-08-03 05:00
This example demonstrates how to explore the surface area and volume of regular prisms by adjusting their height and number of sides. Key math concepts include polygons, trigonometry, solid geometry, surface area calculation, and volume calculation. It uses GeoGebra commands/objects like Circle, Polygon, Segment, Area, Midpoint, Prism, and Net. Suitable for high school students learning solid geometry for a visual understanding of prism properties and calculations.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Radius(c) → polyRad
  3. Circle(B, polySide) → d
  4. Intersect(c, d, 2) → C
  5. Polygon(C, B, counter) → poly1, f, p, m_5, n_5, p_5, q_5, r_5, s_5, t_5, a_5, b_5, c_5, q, d_5, e_5, f_6, g_6, h_6, i_6, j_6, k_6, l_6, m_6, r, n_6, p_6, q_6, r_6, s_6, t_6, a_6, b_6, c_6, d_6, s, e_6, f_7, g_7, h_7, i_7, j_7, k_7, l_7, m_7, n_7, t, p_7, q_7, r_7, s_7, t_7, a_7, b_7, c_7, d_7, e_7, a, f_8, g_8, h_8, i_8, j_8, k_8, l_8, m_8, n_8, p_8, b, q_8, r_8, s_8, t_8, a_8, b_8, c_8, d_8, e_8, f_9, e, g_9, h_9, i_9, j_9, k_9, l_9, m_9, n_9, p_9, q_9, f_1, r_9, D, E, F, G, H, I, J, K, L, g_1, M, N, O, P, Q, R, S, T, U, V, g, h_1, W, Z, A_1, B_1, C_1, D_1, E_1, F_1, G_1, H_1, i_1, I_1, J_1, K_1, L_1, M_1, N_1, O_1, P_1, Q_1, R_1, j_1, S_1, T_1, U_1, V_1, W_1, Z_1, A_2, B_2, C_2, D_2, k_1, E_2, F_2, G_2, H_2, I_2, J_2, K_2, L_2, M_2, N_2, l_1, O_2, P_2, Q_2, R_2, S_2, T_2, U_2, V_2, W_2, Z_2, m_1, A_3, B_3, C_3, D_3, E_3, F_3, G_3, H_3, I_3, J_3, n_1, K_3, L_3, M_3, N_3, O_3, P_3, Q_3, R_3, S_3, T_3, p_1, U_3, V_3, W_3, Z_3, A_4, B_4, C_4, D_4, E_4, F_4, q_1, G_4, H_4, I_4, J_4, K_4, L_4, M_4, N_4, O_4, P_4, r_1, Q_4, R_4, S_4, T_4, U_4, V_4, W_4, Z_4, A_5, B_5, h, s_1, C_5, D_5, E_5, F_5, G_5, H_5, I_5, J_5, K_5, L_5, a_1, M_5, N_5, O_5, P_5, Q_5, R_5, S_5, T_5, U_5, V_5, b_1, W_5, Z_5, A_6, B_6, C_6, D_6, E_6, F_6, G_6, H_6, c_1, I_6, J_6, K_6, L_6, M_6, N_6, O_6, P_6, Q_6, R_6, d_1, S_6, T_6, U_6, V_6, W_6, Z_6, A_7, B_7, C_7, D_7, e_1, E_7, F_7, G_7, H_7, I_7, J_7, K_7, L_7, M_7, f_2, g_2, h_2, i_2, i, j_2, k_2, l_2, m_2, n_2, p_2, q_2, r_2, s_2, t_2, j, a_2, b_2, c_2, d_2, e_2, f_3, g_3, h_3, i_3, j_3, k, k_3, l_3, m_3, n_3, p_3, q_3, r_3, s_3, t_3, a_3, l, b_3, c_3, d_3, e_3, f_4, g_4, h_4, i_4, j_4, k_4, m, l_4, m_4, n_4, p_4, q_4, r_4, s_4, t_4, a_4, b_4, n, c_4, d_4, e_4, f_5, g_5, h_5, i_5, j_5, k_5, l_5
  6. Segment(A, B) → t_1
  7. Area(c) → o
  8. Midpoint(f) → N_7
  9. Segment(A, N_7) → s_9
  10. Polygon(C, B, counter) → poly2, t_9, e_9, d_{14}, e_{14}, f_{15}, g_{15}, h_{15}, i_{15}, j_{15}, k_{15}, l_{15}, m_{15}, f_{10}, n_{15}, p_{15}, q_{15}, r_{15}, s_{15}, t_{15}, a_{15}, b_{15}, c_{15}, d_{15}, h_{10}, e_{15}, f_{16}, g_{16}, h_{16}, i_{16}, j_{16}, k_{16}, l_{16}, m_{16}, n_{16}, j_{10}, p_{16}, q_{16}, r_{16}, s_{16}, t_{16}, a_{16}, b_{16}, c_{16}, d_{16}, e_{16}, l_{10}, f_{17}, g_{17}, h_{17}, i_{17}, j_{17}, k_{17}, l_{17}, m_{17}, n_{17}, p_{17}, n_{10}, q_{17}, O_7, R_7, T_7, V_7, Z_7, L_9, S_9, B_{10}, C_{10}, p_{10}, D_{10}, E_{10}, F_{10}, G_{10}, H_{10}, I_{10}, J_{10}, K_{10}, L_{10}, M_{10}, q_{10}, N_{10}, O_{10}, P_{10}, Q_{10}, R_{10}, S_{10}, T_{10}, U_{10}, V_{10}, E_{16}, r_{10}, F_{16}, G_{16}, B_{17}, C_{17}, D_{17}, W_{17}, Z_{17}, A_{18}, T_{18}, U_{18}, s_{10}, V_{18}, Q_{19}, R_{19}, S_{19}, T_{19}, U_{19}, V_{19}, W_{19}, Z_{19}, A_{20}, a_9, t_{10}, B_{20}, C_{20}, D_{20}, E_{20}, F_{20}, G_{20}, H_{20}, I_{20}, J_{20}, K_{20}, a_{10}, L_{20}, M_{20}, N_{20}, O_{20}, P_{20}, Q_{20}, R_{20}, S_{20}, T_{20}, U_{20}, b_{10}, V_{20}, W_{20}, Z_{20}, A_{21}, B_{21}, C_{21}, D_{21}, E_{21}, F_{21}, G_{21}, c_{10}, H_{21}, I_{21}, J_{21}, K_{21}, L_{21}, M_{21}, N_{21}, O_{21}, P_{21}, Q_{21}, d_{10}, R_{21}, S_{21}, T_{21}, U_{21}, V_{21}, W_{21}, Z_{21}, A_{22}, B_{22}, C_{22}, e_{10}, D_{22}, E_{22}, F_{22}, G_{22}, H_{22}, I_{22}, J_{22}, K_{22}, L_{22}, M_{22}, f_{11}, N_{22}, O_{22}, P_{22}, Q_{22}, R_{22}, S_{22}, T_{22}, U_{22}, V_{22}, W_{22}, g_{11}, Z_{22}, A_{23}, B_{23}, C_{23}, D_{23}, E_{23}, F_{23}, G_{23}, H_{23}, I_{23}, h_{11}, J_{23}, K_{23}, L_{23}, M_{23}, N_{23}, O_{23}, P_{23}, Q_{23}, R_{23}, S_{23}, i_{11}, T_{23}, U_{23}, V_{23}, W_{23}, Z_{23}, A_{24}, B_{24}, C_{24}, D_{24}, b_9, j_{11}, k_{11}, l_{11}, m_{11}, n_{11}, p_{11}, q_{11}, r_{11}, s_{11}, t_{11}, g_{10}, a_{11}, b_{11}, c_{11}, d_{11}, e_{11}, f_{12}, g_{12}, h_{12}, i_{12}, j_{12}, i_{10}, k_{12}, l_{12}, m_{12}, n_{12}, p_{12}, q_{12}, r_{12}, s_{12}, t_{12}, a_{12}, k_{10}, b_{12}, c_{12}, d_{12}, e_{12}, f_{13}, g_{13}, h_{13}, i_{13}, j_{13}, k_{13}, m_{10}, l_{13}, m_{13}, n_{13}, p_{13}, q_{13}, r_{13}, s_{13}, t_{13}, a_{13}, b_{13}, c_9, c_{13}, d_{13}, e_{13}, f_{14}, g_{14}, h_{14}, i_{14}, j_{14}, k_{14}, l_{14}, d_9, m_{14}, n_{14}, p_{14}, q_{14}, r_{14}, s_{14}, t_{14}, a_{14}, b_{14}, c_{14}
  11. Prism(poly2, 0.0001) → u, A_8, W_{10}, N_{26}, O_{26}, P_{26}, Q_{26}, R_{26}, S_{26}, T_{26}, U_{26}, V_{26}, W_{26}, Z_{10}, Z_{26}, A_{27}, B_{27}, C_{27}, D_{27}, E_{27}, F_{27}, G_{27}, H_{27}, I_{27}, A_{11}, J_{27}, K_{27}, L_{27}, M_{27}, N_{27}, O_{27}, P_{27}, Q_{27}, R_{27}, S_{27}, B_{11}, T_{27}, U_{27}, V_{27}, W_{27}, Z_{27}, A_{28}, B_{28}, C_{28}, D_{28}, E_{28}, C_{11}, F_{28}, G_{28}, H_{28}, I_{28}, J_{28}, K_{28}, L_{28}, M_{28}, N_{28}, O_{28}, D_{11}, P_{28}, face2, face3, face4, face14, face17, face20, face23, face26, face29, E_{11}, face32, face33, face34, face35, face36, face37, face38, face39, face40, face41, F_{11}, face42, face43, face44, face45, face46, face47, face48, face49, face50, face51, G_{11}, face52, face95, face96, face97, face104, face105, face106, face113, face114, face115, H_{11}, face122, face123, face124, face131, face132, face133, face134, face135, face136, face137, B_8, I_{11}, face138, face139, face140, face141, face142, face143, face144, face145, face146, face147, J_{11}, face148, face149, face150, face151, face152, face153, face154, face155, face156, face157, K_{11}, face158, face159, face160, face161, face162, face163, face164, face165, face166, face167, L_{11}, face168, face169, face170, face171, face172, face173, face174, face175, face176, face177, M_{11}, face178, face179, face180, face181, face182, face183, face184, face185, face186, face187, N_{11}, face188, face189, face190, face191, face192, face193, face194, face195, face196, face197, O_{11}, face198, face199, face200, face201, face202, face203, face204, face205, face206, face207, P_{11}, face208, face209, face210, face211, face212, face213, face214, face215, face216, face217, Q_{11}, face218, face219, face220, face221, face222, face223, face224, face225, face226, face227, R_{11}, face228, face229, face230, face231, face232, face233, face234, face235, face236, face237, C_8, S_{11}, face238, face1, edge2, edge1, edge3, edge27, edge36, edge45, edge54, edge63, H_{16}, edge72, edge81, edge82, edge83, edge84, edge85, edge86, edge87, edge88, edge89, I_{16}, edge90, edge91, edge92, edge93, edge94, edge95, edge96, edge97, edge98, edge99, J_{16}, edge100, edge101, edge270, edge271, edge272, edge297, edge298, edge299, edge324, edge325, E_{17}, edge326, edge351, edge352, edge353, edge378, edge379, edge380, edge381, edge382, edge383, F_{17}, edge384, edge385, edge386, edge387, edge388, edge389, edge390, edge391, edge392, edge393, G_{17}, edge394, edge395, edge396, edge397, edge398, edge399, edge400, edge401, edge402, edge403, B_{18}, edge404, edge405, edge406, edge407, edge408, edge409, edge410, edge411, edge412, edge413, C_{18}, edge414, edge415, edge416, edge417, edge418, edge419, edge420, edge421, edge422, edge423, D_{18}, edge424, edge425, edge426, edge427, edge428, edge429, edge430, edge431, edge432, edge433, L_8, W_{18}, edge434, edge435, edge436, edge437, edge438, edge439, edge440, edge441, edge442, edge443, Z_{18}, edge444, edge445, edge446, edge447, edge448, edge449, edge450, edge451, edge452, edge453, A_{19}, edge454, edge455, edge456, edge457, edge458, edge459, edge460, edge461, edge462, edge463, E_{24}, edge464, edge465, edge466, edge467, edge468, edge469, edge470, edge471, edge472, edge473, F_{24}, edge474, edge475, edge476, edge477, edge478, edge479, edge480, edge481, edge482, edge483, G_{24}, edge484, edge485, edge4, edge6, edge5, edge28, edge37, edge46, edge55, edge64, H_{24}, edge73, edge102, edge103, edge104, edge105, edge106, edge107, edge108, edge109, edge110, I_{24}, edge111, edge112, edge113, edge114, edge115, edge116, edge117, edge118, edge119, edge120, J_{24}, edge121, edge122, edge273, edge274, edge275, edge300, edge301, edge302, edge327, edge328, K_{24}, edge329, edge354, edge355, edge356, edge486, edge487, edge488, edge489, edge490, edge491, R_8, L_{24}, edge492, edge493, edge494, edge495, edge496, edge497, edge498, edge499, edge500, edge501, M_{24}, edge502, edge503, edge504, edge505, edge506, edge507, edge508, edge509, edge510, edge511, N_{24}, edge512, edge513, edge514, edge515, edge516, edge517, edge518, edge519, edge520, edge521, O_{24}, edge522, edge523, edge524, edge525, edge526, edge527, edge528, edge529, edge530, edge531, P_{24}, edge532, edge533, edge534, edge535, edge536, edge537, edge538, edge539, edge540, edge541, Q_{24}, edge542, edge543, edge544, edge545, edge546, edge547, edge548, edge549, edge550, edge551, R_{24}, edge552, edge553, edge554, edge555, edge556, edge557, edge558, edge559, edge560, edge561, S_{24}, edge562, edge563, edge564, edge565, edge566, edge567, edge568, edge569, edge570, edge571, T_{24}, edge572, edge573, edge574, edge575, edge576, edge577, edge578, edge579, edge580, edge581, U_{24}, edge582, edge583, edge584, edge585, edge586, edge587, edge588, edge589, edge590, edge591, Z_8, V_{24}, edge592, edge593, W_{24}, Z_{24}, A_{25}, B_{25}, C_{25}, D_{25}, E_{25}, F_{25}, G_{25}, F_9, H_{25}, I_{25}, J_{25}, K_{25}, L_{25}, M_{25}, N_{25}, O_{25}, P_{25}, Q_{25}, M_9, R_{25}, S_{25}, T_{25}, U_{25}, V_{25}, W_{25}, Z_{25}, A_{26}, B_{26}, C_{26}, T_9, D_{26}, E_{26}, F_{26}, G_{26}, H_{26}, I_{26}, J_{26}, K_{26}, L_{26}, M_{26}
  12. Prism(face1, Prism_Height) → v, P_7, T_{11}, B_{31}, C_{31}, D_{31}, E_{31}, F_{31}, G_{31}, H_{31}, I_{31}, J_{31}, K_{31}, U_{11}, L_{31}, M_{31}, N_{31}, O_{31}, P_{31}, Q_{31}, R_{31}, S_{31}, T_{31}, U_{31}, V_{11}, V_{31}, W_{31}, Z_{31}, A_{32}, B_{32}, C_{32}, D_{32}, E_{32}, F_{32}, G_{32}, W_{11}, H_{32}, I_{32}, J_{32}, K_{32}, L_{32}, M_{32}, N_{32}, O_{32}, P_{32}, Q_{32}, Z_{11}, R_{32}, S_{32}, T_{32}, U_{32}, V_{32}, W_{32}, Z_{32}, A_{33}, B_{33}, C_{33}, A_{12}, D_{33}, face6, face8, face7, face15, face18, face21, face24, face27, face30, B_{12}, face53, face54, face55, face56, face57, face58, face59, face60, face61, face62, C_{12}, face63, face64, face65, face66, face67, face68, face69, face70, face71, face72, D_{12}, face73, face98, face99, face100, face107, face108, face109, face116, face117, face118, E_{12}, face125, face126, face127, face239, face240, face241, face242, face243, face244, face245, Q_7, F_{12}, face246, face247, face248, face249, face250, face251, face252, face253, face254, face255, G_{12}, face256, face257, face258, face259, face260, face261, face262, face263, face264, face265, H_{12}, face266, face267, face268, face269, face270, face271, face272, face273, face274, face275, I_{12}, face276, face277, face278, face279, face280, face281, face282, face283, face284, face285, J_{12}, face286, face287, face288, face289, face290, face291, face292, face293, face294, face295, K_{12}, face296, face297, face298, face299, face300, face301, face302, face303, face304, face305, L_{12}, face306, face307, face308, face309, face310, face311, face312, face313, face314, face315, M_{12}, face316, face317, face318, face319, face320, face321, face322, face323, face324, face325, N_{12}, face326, face327, face328, face329, face330, face331, face332, face333, face334, face335, O_{12}, face336, face337, face338, face339, face340, face341, face342, face343, face344, face345, S_7, P_{12}, face346, face5, edge7, edge8, edge9, edge29, edge38, edge47, edge56, edge65, K_{16}, edge74, edge123, edge124, edge125, edge126, edge127, edge128, edge129, edge130, edge131, L_{16}, edge132, edge133, edge134, edge135, edge136, edge137, edge138, edge139, edge140, edge141, M_{16}, edge142, edge143, edge276, edge277, edge278, edge303, edge304, edge305, edge330, edge331, H_{17}, edge332, edge357, edge358, edge359, edge594, edge595, edge596, edge597, edge598, edge599, I_{17}, edge600, edge601, edge602, edge603, edge604, edge605, edge606, edge607, edge608, edge609, J_{17}, edge610, edge611, edge612, edge613, edge614, edge615, edge616, edge617, edge618, edge619, E_{18}, edge620, edge621, edge622, edge623, edge624, edge625, edge626, edge627, edge628, edge629, F_{18}, edge630, edge631, edge632, edge633, edge634, edge635, edge636, edge637, edge638, edge639, G_{18}, edge640, edge641, edge642, edge643, edge644, edge645, edge646, edge647, edge648, edge649, M_8, B_{19}, edge650, edge651, edge652, edge653, edge654, edge655, edge656, edge657, edge658, edge659, C_{19}, edge660, edge661, edge662, edge663, edge664, edge665, edge666, edge667, edge668, edge669, D_{19}, edge670, edge671, edge672, edge673, edge674, edge675, edge676, edge677, edge678, edge679, Q_{28}, edge680, edge681, edge682, edge683, edge684, edge685, edge686, edge687, edge688, edge689, R_{28}, edge690, edge691, edge692, edge693, edge694, edge695, edge696, edge697, edge698, edge699, S_{28}, edge700, edge701, edge10, edge12, edge11, edge30, edge39, edge48, edge57, edge66, T_{28}, edge75, edge144, edge145, edge146, edge147, edge148, edge149, edge150, edge151, edge152, U_{28}, edge153, edge154, edge155, edge156, edge157, edge158, edge159, edge160, edge161, edge162, V_{28}, edge163, edge164, edge279, edge280, edge281, edge306, edge307, edge308, edge333, edge334, W_{28}, edge335, edge360, edge361, edge362, edge702, edge703, edge704, edge705, edge706, edge707, S_8, Z_{28}, edge708, edge709, edge710, edge711, edge712, edge713, edge714, edge715, edge716, edge717, A_{29}, edge718, edge719, edge720, edge721, edge722, edge723, edge724, edge725, edge726, edge727, B_{29}, edge728, edge729, edge730, edge731, edge732, edge733, edge734, edge735, edge736, edge737, C_{29}, edge738, edge739, edge740, edge741, edge742, edge743, edge744, edge745, edge746, edge747, D_{29}, edge748, edge749, edge750, edge751, edge752, edge753, edge754, edge755, edge756, edge757, E_{29}, edge758, edge759, edge760, edge761, edge762, edge763, edge764, edge765, edge766, edge767, F_{29}, edge768, edge769, edge770, edge771, edge772, edge773, edge774, edge775, edge776, edge777, G_{29}, edge778, edge779, edge780, edge781, edge782, edge783, edge784, edge785, edge786, edge787, H_{29}, edge788, edge789, edge790, edge791, edge792, edge793, edge794, edge795, edge796, edge797, I_{29}, edge798, edge799, edge800, edge801, edge802, edge803, edge804, edge805, edge806, edge807, A_9, J_{29}, edge808, edge809, K_{29}, L_{29}, M_{29}, N_{29}, O_{29}, P_{29}, Q_{29}, R_{29}, S_{29}, G_9, T_{29}, U_{29}, V_{29}, W_{29}, Z_{29}, A_{30}, B_{30}, C_{30}, D_{30}, E_{30}, N_9, F_{30}, G_{30}, H_{30}, I_{30}, J_{30}, K_{30}, L_{30}, M_{30}, N_{30}, O_{30}, U_9, P_{30}, Q_{30}, R_{30}, S_{30}, T_{30}, U_{30}, V_{30}, W_{30}, Z_{30}, A_{31}
  13. Net(v, w) → o_1, U_7, Q_{12}, N_{35}, edge315, edge316, edge317, edge318, edge319, edge320, edge321, edge322, edge323, edge342, O_{35}, edge343, edge344, edge345, edge346, edge347, edge348, edge349, edge350, edge369, edge370, P_{35}, edge371, edge372, edge373, edge374, edge375, edge376, edge377, edge1026, edge1027, edge1028, Q_{35}, edge1029, edge1030, edge1031, edge1032, edge1033, edge1034, edge1035, edge1036, edge1037, edge1038, R_{35}, edge1039, edge1040, edge1041, edge1042, edge1043, edge1044, edge1045, edge1046, edge1047, edge1048, S_{35}, edge1049, edge1050, edge1051, edge1052, edge1053, edge1054, edge1055, edge1056, edge1057, edge1058, T_{35}, edge1059, edge1060, edge1061, edge1062, edge1063, edge1064, edge1065, edge1066, edge1067, edge1068, U_{35}, edge1069, edge1070, edge1071, edge1072, edge1073, edge1074, edge1075, edge1076, edge1077, edge1078, V_{35}, edge1079, edge1080, edge1081, edge1082, edge1083, edge1084, edge1085, edge1086, edge1087, edge1088, W_{35}, edge1089, edge1090, edge1091, edge1092, edge1093, edge1094, edge1095, edge1096, edge1097, edge1098, R_{12}, Z_{35}, edge1099, edge1100, edge1101, edge1102, edge1103, edge1104, edge1105, edge1106, edge1107, edge1108, A_{36}, edge1109, edge1110, edge1111, edge1112, edge1113, edge1114, edge1115, edge1116, edge1117, edge1118, B_{36}, edge1119, edge1120, edge1121, edge1122, edge1123, edge1124, edge1125, edge1126, edge1127, edge1128, C_{36}, edge1129, edge1130, edge1131, edge1132, edge1133, edge1134, edge1135, edge1136, edge1137, edge1138, D_{36}, edge1139, edge1140, edge1141, edge1142, edge1143, edge1144, edge1145, edge1146, edge1147, edge1148, E_{36}, edge1149, edge1150, edge1151, edge1152, edge1153, edge1154, edge1155, edge1156, edge1157, edge1158, F_{36}, edge1159, edge1160, edge1161, edge1162, edge1163, edge1164, edge1165, edge1166, edge1167, edge1168, G_{36}, edge1169, edge1170, edge1171, edge1172, edge1173, edge1174, edge1175, edge1176, edge1177, edge1178, H_{36}, edge1179, edge1180, edge1181, edge1182, edge1183, edge1184, edge1185, edge1186, edge1187, edge1188, I_{36}, edge1189, edge1190, edge1191, edge1192, edge1193, edge1194, edge1195, edge1196, edge1197, edge1198, S_{12}, J_{36}, edge1199, edge1200, edge1201, edge1202, edge1203, edge1204, edge1205, edge1206, edge1207, edge1208, K_{36}, edge1209, edge1210, edge1211, edge1212, edge1213, edge1214, edge1215, edge1216, edge1217, edge1218, L_{36}, edge1219, edge1220, edge1221, edge1222, edge1223, edge1224, edge1225, edge1226, edge1227, edge1228, M_{36}, edge1229, edge1230, edge1231, edge1232, edge1233, edge1234, edge1235, edge1236, edge1237, edge1238, N_{36}, edge1239, edge1240, edge1241, edge1242, edge1243, edge1244, edge1245, edge1246, edge1247, edge1248, O_{36}, edge1249, edge1250, edge1251, edge1252, edge1253, edge1254, edge1255, edge1256, edge1257, edge1258, P_{36}, edge1259, edge1260, edge1261, edge1262, edge1263, edge1264, edge1265, edge1266, edge1267, edge1268, Q_{36}, edge1269, edge1270, edge1271, edge1272, edge1273, edge1274, edge1275, edge1276, edge1277, edge1278, R_{36}, edge1279, edge1280, edge1281, edge1282, edge1283, edge1284, edge1285, edge1286, edge1287, edge1288, S_{36}, edge1289, edge1290, edge1291, edge1292, edge1293, edge1294, edge1295, edge1296, edge1297, edge1298, T_{12}, T_{36}, edge1299, edge1300, edge1301, edge1302, edge1303, edge1304, edge1305, edge1306, edge1307, edge1308, U_{36}, edge1309, edge1310, edge1311, edge1312, edge1313, edge1314, edge1315, edge1316, edge1317, edge1318, V_{36}, edge1319, edge1320, edge1321, edge1322, edge1323, edge1324, edge1325, edge1326, edge1327, edge1328, W_{36}, edge1329, edge1330, edge1331, edge1332, edge1333, edge1334, edge1335, edge1336, edge1337, edge1338, Z_{36}, edge1339, edge1340, edge1341, edge1342, edge1343, edge1344, edge1345, edge1346, edge1347, edge1348, A_{37}, edge1349, edge24, edge23, edge31, edge40, edge49, edge58, edge67, edge76, edge165, B_{37}, edge166, edge167, edge168, edge169, edge170, edge171, edge172, edge173, edge174, edge175, C_{37}, edge176, edge177, edge178, edge179, edge180, edge181, edge182, edge183, edge184, edge185, D_{37}, edge282, edge283, edge284, edge309, edge310, edge311, edge336, edge337, edge338, edge363, E_{37}, edge364, edge365, edge810, edge811, edge812, edge813, edge814, edge815, edge816, edge817, U_{12}, F_{37}, edge818, edge819, edge820, edge821, edge822, edge823, edge824, edge825, edge826, edge827, G_{37}, edge828, edge829, edge830, edge831, edge832, edge833, edge834, edge835, edge836, edge837, H_{37}, edge838, edge839, edge840, edge841, edge842, edge843, edge844, edge845, edge846, edge847, I_{37}, edge848, edge849, edge850, edge851, edge852, edge853, edge854, edge855, edge856, edge857, J_{37}, edge858, edge859, edge860, edge861, edge862, edge863, edge864, edge865, edge866, edge867, K_{37}, edge868, edge869, edge870, edge871, edge872, edge873, edge874, edge875, edge876, edge877, L_{37}, edge878, edge879, edge880, edge881, edge882, edge883, edge884, edge885, edge886, edge887, M_{37}, edge888, edge889, edge890, edge891, edge892, edge893, edge894, edge895, edge896, edge897, N_{37}, edge898, edge899, edge900, edge901, edge902, edge903, edge904, edge905, edge906, edge907, O_{37}, edge908, edge909, edge910, edge911, edge912, edge913, edge914, edge915, edge916, edge917, V_{12}, P_{37}, E_8, F_8, G_8, H_8, I_8, J_8, P_8, Q_8, V_8, W_{12}, W_8, D_9, E_9, J_9, K_9, Q_9, R_9, Z_9, A_{10}, K_{14}, Z_{12}, L_{14}, M_{14}, N_{14}, O_{14}, P_{14}, Q_{14}, R_{14}, S_{14}, T_{14}, U_{14}, A_{13}, V_{14}, W_{14}, Z_{14}, A_{15}, B_{15}, C_{15}, D_{15}, E_{15}, F_{15}, G_{15}, B_{13}, H_{15}, I_{15}, J_{15}, K_{15}, L_{15}, M_{15}, N_{15}, O_{15}, P_{15}, Q_{15}, W_7, C_{13}, R_{15}, S_{15}, T_{15}, U_{15}, V_{15}, W_{15}, Z_{15}, A_{16}, B_{16}, C_{16}, D_{13}, D_{16}, T_{16}, U_{16}, V_{16}, W_{16}, Z_{16}, A_{17}, Q_{17}, R_{17}, S_{17}, E_{13}, T_{17}, U_{17}, V_{17}, N_{18}, O_{18}, P_{18}, Q_{18}, R_{18}, S_{18}, K_{19}, F_{13}, L_{19}, M_{19}, N_{19}, O_{19}, P_{19}, E_{42}, F_{42}, G_{42}, H_{42}, I_{42}, G_{13}, J_{42}, K_{42}, L_{42}, M_{42}, N_{42}, O_{42}, P_{42}, Q_{42}, R_{42}, S_{42}, H_{13}, T_{42}, U_{42}, V_{42}, W_{42}, Z_{42}, A_{43}, B_{43}, C_{43}, D_{43}, E_{43}, I_{13}, F_{43}, G_{43}, H_{43}, I_{43}, J_{43}, K_{43}, L_{43}, M_{43}, N_{43}, O_{43}, J_{13}, P_{43}, Q_{43}, R_{43}, S_{43}, T_{43}, U_{43}, V_{43}, W_{43}, Z_{43}, A_{44}, K_{13}, B_{44}, C_{44}, D_{44}, E_{44}, F_{44}, G_{44}, H_{44}, I_{44}, J_{44}, K_{44}, L_{13}, L_{44}, M_{44}, N_{44}, O_{44}, P_{44}, Q_{44}, R_{44}, S_{44}, T_{44}, U_{44}, D_8, M_{13}, V_{44}, W_{44}, Z_{44}, A_{45}, B_{45}, C_{45}, D_{45}, E_{45}, F_{45}, G_{45}, N_{16}, H_{45}, I_{45}, J_{45}, K_{45}, L_{45}, M_{45}, N_{45}, O_{45}, P_{45}, Q_{45}, O_{16}, R_{45}, S_{45}, T_{45}, U_{45}, V_{45}, W_{45}, Z_{45}, A_{46}, B_{46}, C_{46}, P_{16}, D_{46}, E_{46}, F_{46}, G_{46}, H_{46}, I_{46}, J_{46}, K_{46}, L_{46}, M_{46}, K_{17}, N_{46}, O_{46}, P_{46}, Q_{46}, R_{46}, S_{46}, T_{46}, U_{46}, V_{46}, W_{46}, L_{17}, Z_{46}, A_{47}, B_{47}, C_{47}, D_{47}, E_{47}, F_{47}, G_{47}, H_{47}, I_{47}, M_{17}, J_{47}, K_{47}, L_{47}, M_{47}, N_{47}, O_{47}, P_{47}, Q_{47}, R_{47}, S_{47}, H_{18}, T_{47}, U_{47}, V_{47}, W_{47}, Z_{47}, A_{48}, B_{48}, C_{48}, D_{48}, E_{48}, I_{18}, F_{48}, G_{48}, H_{48}, I_{48}, J_{48}, K_{48}, L_{48}, M_{48}, N_{48}, O_{48}, J_{18}, P_{48}, Q_{48}, R_{48}, S_{48}, T_{48}, U_{48}, V_{48}, W_{48}, Z_{48}, A_{49}, N_8, E_{19}, B_{49}, C_{49}, D_{49}, E_{49}, F_{49}, G_{49}, H_{49}, I_{49}, J_{49}, K_{49}, F_{19}, L_{49}, M_{49}, N_{49}, O_{49}, P_{49}, Q_{49}, R_{49}, S_{49}, T_{49}, U_{49}, G_{19}, V_{49}, W_{49}, Z_{49}, A_{50}, B_{50}, C_{50}, D_{50}, E_{50}, F_{50}, G_{50}, E_{33}, H_{50}, I_{50}, J_{50}, K_{50}, L_{50}, M_{50}, N_{50}, O_{50}, P_{50}, Q_{50}, F_{33}, R_{50}, S_{50}, T_{50}, U_{50}, V_{50}, W_{50}, Z_{50}, A_{51}, B_{51}, C_{51}, G_{33}, D_{51}, K_8, O_8, U_8, C_9, I_9, P_9, W_9, N_{13}, O_{13}, H_{33}, P_{13}, Q_{13}, R_{13}, S_{13}, T_{13}, U_{13}, V_{13}, W_{13}, Z_{13}, A_{14}, I_{33}, B_{14}, C_{14}, D_{14}, E_{14}, F_{14}, G_{14}, H_{14}, I_{14}, J_{14}, Q_{16}, J_{33}, R_{16}, S_{16}, N_{17}, O_{17}, P_{17}, K_{18}, L_{18}, M_{18}, H_{19}, I_{19}, K_{33}, J_{19}, Q_{37}, R_{37}, S_{37}, T_{37}, U_{37}, V_{37}, W_{37}, Z_{37}, A_{38}, T_8, L_{33}, B_{38}, C_{38}, D_{38}, E_{38}, F_{38}, G_{38}, H_{38}, I_{38}, J_{38}, K_{38}, M_{33}, L_{38}, M_{38}, N_{38}, O_{38}, P_{38}, Q_{38}, R_{38}, S_{38}, T_{38}, U_{38}, N_{33}, V_{38}, W_{38}, Z_{38}, A_{39}, B_{39}, C_{39}, D_{39}, E_{39}, F_{39}, G_{39}, O_{33}, H_{39}, I_{39}, J_{39}, K_{39}, L_{39}, M_{39}, N_{39}, O_{39}, P_{39}, Q_{39}, P_{33}, R_{39}, S_{39}, T_{39}, U_{39}, V_{39}, W_{39}, Z_{39}, A_{40}, B_{40}, C_{40}, Q_{33}, D_{40}, E_{40}, F_{40}, G_{40}, H_{40}, I_{40}, J_{40}, K_{40}, L_{40}, M_{40}, R_{33}, N_{40}, O_{40}, P_{40}, Q_{40}, R_{40}, S_{40}, T_{40}, U_{40}, V_{40}, W_{40}, S_{33}, Z_{40}, A_{41}, B_{41}, C_{41}, D_{41}, E_{41}, F_{41}, G_{41}, H_{41}, I_{41}, T_{33}, J_{41}, K_{41}, L_{41}, M_{41}, N_{41}, O_{41}, P_{41}, Q_{41}, R_{41}, S_{41}, U_{33}, T_{41}, U_{41}, V_{41}, W_{41}, Z_{41}, A_{42}, B_{42}, C_{42}, D_{42}, face9, B_9, V_{33}, face11, face13, face12, face16, face19, face22, face25, face28, face31, face74, W_{33}, face75, face76, face77, face78, face79, face80, face81, face82, face83, face84, Z_{33}, face85, face86, face87, face88, face89, face90, face91, face92, face93, face94, A_{34}, face101, face102, face103, face110, face111, face112, face119, face120, face121, face128, B_{34}, face129, face130, face347, face348, face349, face350, face351, face352, face353, face354, C_{34}, face355, face356, face357, face358, face359, face360, face361, face362, face363, face364, D_{34}, face365, face366, face367, face368, face369, face370, face371, face372, face373, face374, E_{34}, face375, face376, face377, face378, face379, face380, face381, face382, face383, face384, F_{34}, face385, face386, face387, face388, face389, face390, face391, face392, face393, face394, G_{34}, face395, face396, face397, face398, face399, face400, face401, face402, face403, face404, H_9, H_{34}, face405, face406, face407, face408, face409, face410, face411, face412, face413, face414, I_{34}, face415, face416, face417, face418, face419, face420, face421, face422, face423, face424, J_{34}, face425, face426, face427, face428, face429, face430, face431, face432, face433, face434, K_{34}, face435, face436, face437, face438, face439, face440, face441, face442, face443, face444, L_{34}, face445, face446, face447, face448, face449, face450, face451, face452, face453, face454, M_{34}, face10, edge13, edge17, edge14, edge32, edge41, edge50, edge59, edge68, edge77, N_{34}, edge186, edge187, edge188, edge189, edge190, edge191, edge192, edge193, edge194, edge195, O_{34}, edge196, edge197, edge198, edge199, edge200, edge201, edge202, edge203, edge204, edge205, P_{34}, edge206, edge285, edge286, edge287, edge312, edge313, edge314, edge339, edge340, edge341, Q_{34}, edge366, edge367, edge368, edge918, edge919, edge920, edge921, edge922, edge923, edge924, O_9, R_{34}, edge925, edge926, edge927, edge928, edge929, edge930, edge931, edge932, edge933, edge934, S_{34}, edge935, edge936, edge937, edge938, edge939, edge940, edge941, edge942, edge943, edge944, T_{34}, edge945, edge946, edge947, edge948, edge949, edge950, edge951, edge952, edge953, edge954, U_{34}, edge955, edge956, edge957, edge958, edge959, edge960, edge961, edge962, edge963, edge964, V_{34}, edge965, edge966, edge967, edge968, edge969, edge970, edge971, edge972, edge973, edge974, W_{34}, edge975, edge976, edge977, edge978, edge979, edge980, edge981, edge982, edge983, edge984, Z_{34}, edge985, edge986, edge987, edge988, edge989, edge990, edge991, edge992, edge993, edge994, A_{35}, edge995, edge996, edge997, edge998, edge999, edge1000, edge1001, edge1002, edge1003, edge1004, B_{35}, edge1005, edge1006, edge1007, edge1008, edge1009, edge1010, edge1011, edge1012, edge1013, edge1014, C_{35}, edge1015, edge1016, edge1017, edge1018, edge1019, edge1020, edge1021, edge1022, edge1023, edge1024, V_9, D_{35}, edge1025, edge15, edge22, edge18, edge19, edge25, edge20, edge21, edge26, edge16, E_{35}, edge33, edge34, edge35, edge42, edge43, edge44, edge51, edge52, edge53, edge60, F_{35}, edge61, edge62, edge69, edge70, edge71, edge78, edge79, edge80, edge207, edge208, G_{35}, edge209, edge210, edge211, edge212, edge213, edge214, edge215, edge216, edge217, edge218, H_{35}, edge219, edge220, edge221, edge222, edge223, edge224, edge225, edge226, edge227, edge228, I_{35}, edge229, edge230, edge231, edge232, edge233, edge234, edge235, edge236, edge237, edge238, J_{35}, edge239, edge240, edge241, edge242, edge243, edge244, edge245, edge246, edge247, edge248, K_{35}, edge249, edge250, edge251, edge252, edge253, edge254, edge255, edge256, edge257, edge258, L_{35}, edge259, edge260, edge261, edge262, edge263, edge264, edge265, edge266, edge267, edge268, M_{35}, edge269, edge288, edge289, edge290, edge291, edge292, edge293, edge294, edge295, edge296
  14. Circle(A_{52}, B_{52}) → c_{17}
  15. Radius(c_{17}) → polyRad_1
  16. Circle(B_{52}, polySide_1) → d_{17}
  17. Intersect(c_{17}, d_{17}, 2) → C_{52}
  18. Polygon(C_{52}, B_{52}, counter_1) → poly1_1, f_{18}, p_{18}, m_{23}, n_{23}, p_{23}, q_{23}, r_{22}, s_{22}, t_{21}, a_{22}, b_{22}, c_{22}, q_{18}, d_{22}, e_{22}, f_{24}, g_{24}, h_{24}, i_{24}, j_{24}, k_{24}, l_{24}, m_{24}, r_{17}, n_{24}, p_{24}, q_{24}, r_{23}, s_{23}, t_{22}, a_{23}, b_{23}, c_{23}, d_{23}, s_{17}, e_{23}, f_{25}, g_{25}, h_{25}, i_{25}, j_{25}, k_{25}, l_{25}, m_{25}, n_{25}, t_{17}, p_{25}, q_{25}, r_{24}, s_{24}, t_{23}, a_{24}, b_{24}, c_{24}, d_{24}, e_{24}, a_{17}, f_{26}, g_{26}, h_{26}, i_{26}, j_{26}, k_{26}, l_{26}, m_{26}, n_{26}, p_{26}, b_{17}, q_{26}, r_{25}, s_{25}, t_{24}, a_{25}, b_{25}, c_{25}, d_{25}, e_{25}, f_{27}, e_{17}, g_{27}, h_{27}, i_{27}, j_{27}, k_{27}, l_{27}, m_{27}, n_{27}, p_{27}, q_{27}, f_{19}, r_{26}, D_{52}, E_{51}, F_{51}, G_{51}, H_{51}, I_{51}, J_{51}, K_{51}, L_{51}, g_{19}, M_{51}, N_{52}, O_{51}, P_{51}, Q_{51}, R_{51}, S_{51}, T_{51}, U_{51}, V_{51}, g_{18}, h_{19}, W_{51}, Z_{51}, A_{53}, B_{53}, C_{53}, D_{53}, E_{52}, F_{52}, G_{52}, H_{52}, i_{19}, I_{52}, J_{52}, K_{52}, L_{52}, M_{52}, N_{53}, O_{52}, P_{52}, Q_{52}, R_{52}, j_{19}, S_{52}, T_{52}, U_{52}, V_{52}, W_{52}, Z_{52}, A_{54}, B_{54}, C_{54}, D_{54}, k_{19}, E_{53}, F_{53}, G_{53}, H_{53}, I_{53}, J_{53}, K_{53}, L_{53}, M_{53}, N_{54}, l_{19}, O_{53}, P_{53}, Q_{53}, R_{53}, S_{53}, T_{53}, U_{53}, V_{53}, W_{53}, Z_{53}, m_{19}, A_{55}, B_{55}, C_{55}, D_{55}, E_{54}, F_{54}, G_{54}, H_{54}, I_{54}, J_{54}, n_{19}, K_{54}, L_{54}, M_{54}, N_{55}, O_{54}, P_{54}, Q_{54}, R_{54}, S_{54}, T_{54}, p_{19}, U_{54}, V_{54}, W_{54}, Z_{54}, A_{56}, B_{56}, C_{56}, D_{56}, E_{55}, F_{55}, q_{19}, G_{55}, H_{55}, I_{55}, J_{55}, K_{55}, L_{55}, M_{55}, N_{56}, O_{55}, P_{55}, r_{18}, Q_{55}, R_{55}, S_{55}, T_{55}, U_{55}, V_{55}, W_{55}, Z_{55}, A_{57}, B_{57}, h_{18}, s_{18}, C_{57}, D_{57}, E_{56}, F_{56}, G_{56}, H_{56}, I_{56}, J_{56}, K_{56}, L_{56}, a_{18}, M_{56}, N_{57}, O_{56}, P_{56}, Q_{56}, R_{56}, S_{56}, T_{56}, U_{56}, V_{56}, b_{18}, W_{56}, Z_{56}, A_{58}, B_{58}, C_{58}, D_{58}, E_{57}, F_{57}, G_{57}, H_{57}, c_{18}, I_{57}, J_{57}, K_{57}, L_{57}, M_{57}, N_{58}, O_{57}, P_{57}, Q_{57}, R_{57}, d_{18}, S_{57}, T_{57}, U_{57}, V_{57}, W_{57}, Z_{57}, A_{59}, B_{59}, C_{59}, D_{59}, e_{18}, E_{58}, F_{58}, G_{58}, H_{58}, I_{58}, J_{58}, K_{58}, L_{58}, M_{58}, f_{20}, g_{20}, h_{20}, i_{20}, i_{18}, j_{20}, k_{20}, l_{20}, m_{20}, n_{20}, p_{20}, q_{20}, r_{19}, s_{19}, t_{18}, j_{18}, a_{19}, b_{19}, c_{19}, d_{19}, e_{19}, f_{21}, g_{21}, h_{21}, i_{21}, j_{21}, k_{18}, k_{21}, l_{21}, m_{21}, n_{21}, p_{21}, q_{21}, r_{20}, s_{20}, t_{19}, a_{20}, l_{18}, b_{20}, c_{20}, d_{20}, e_{20}, f_{22}, g_{22}, h_{22}, i_{22}, j_{22}, k_{22}, m_{18}, l_{22}, m_{22}, n_{22}, p_{22}, q_{22}, r_{21}, s_{21}, t_{20}, a_{21}, b_{21}, n_{18}, c_{21}, d_{21}, e_{21}, f_{23}, g_{23}, h_{23}, i_{23}, j_{23}, k_{23}, l_{23}
  19. Segment(A_{52}, B_{52}) → t_{33}
  20. Area(c_{17}) → o_2
  21. Midpoint(f_{18}) → N_{51}
  22. Polygon(C_{52}, B_{52}, counter_1) → poly2_1, t_{25}, e_{26}, d_{31}, e_{31}, f_{33}, g_{33}, h_{33}, i_{33}, j_{33}, k_{33}, l_{33}, m_{33}, f_{28}, n_{33}, p_{33}, q_{33}, r_{32}, s_{31}, t_{31}, a_{32}, b_{32}, c_{32}, d_{32}, h_{28}, e_{32}, f_{34}, g_{34}, h_{34}, i_{34}, j_{34}, k_{34}, l_{34}, m_{34}, n_{34}, j_{28}, p_{34}, q_{34}, r_{33}, s_{32}, t_{32}, a_{33}, b_{33}, c_{33}, d_{33}, e_{33}, l_{28}, f_{35}, g_{35}, h_{35}, i_{35}, j_{35}, k_{35}, l_{35}, m_{35}, n_{35}, p_{35}, n_{28}, q_{35}, O_{58}, R_{58}, T_{58}, V_{58}, Z_{58}, L_{59}, S_{58}, B_{60}, C_{60}, p_{28}, D_{60}, E_{59}, F_{59}, G_{59}, H_{59}, I_{59}, J_{59}, K_{59}, L_{60}, M_{59}, q_{28}, N_{59}, O_{59}, P_{58}, Q_{58}, R_{59}, S_{59}, T_{59}, U_{58}, V_{59}, E_{60}, r_{27}, F_{60}, G_{60}, B_{61}, C_{61}, D_{61}, W_{58}, Z_{59}, A_{60}, T_{60}, U_{59}, s_{26}, V_{60}, Q_{59}, R_{60}, S_{60}, T_{61}, U_{60}, V_{61}, W_{59}, Z_{60}, A_{61}, a_{26}, t_{26}, B_{62}, C_{62}, D_{62}, E_{61}, F_{61}, G_{61}, H_{60}, I_{60}, J_{60}, K_{60}, a_{27}, L_{61}, M_{60}, N_{60}, O_{60}, P_{59}, Q_{60}, R_{61}, S_{61}, T_{62}, U_{61}, b_{27}, V_{62}, W_{60}, Z_{61}, A_{62}, B_{63}, C_{63}, D_{63}, E_{62}, F_{62}, G_{62}, c_{27}, H_{61}, I_{61}, J_{61}, K_{61}, L_{62}, M_{61}, N_{61}, O_{61}, P_{60}, Q_{61}, d_{27}, R_{62}, S_{62}, T_{63}, U_{62}, V_{63}, W_{61}, Z_{62}, A_{63}, B_{64}, C_{64}, e_{27}, D_{64}, E_{63}, F_{63}, G_{63}, H_{62}, I_{62}, J_{62}, K_{62}, L_{63}, M_{62}, f_{29}, N_{62}, O_{62}, P_{61}, Q_{62}, R_{63}, S_{63}, T_{64}, U_{63}, V_{64}, W_{62}, g_{29}, Z_{63}, A_{64}, B_{65}, C_{65}, D_{65}, E_{64}, F_{64}, G_{64}, H_{63}, I_{63}, h_{29}, J_{63}, K_{63}, L_{64}, M_{63}, N_{63}, O_{63}, P_{62}, Q_{63}, R_{64}, S_{64}, i_{29}, T_{65}, U_{64}, V_{65}, W_{63}, Z_{64}, A_{65}, B_{66}, C_{66}, D_{66}, b_{26}, j_{29}, k_{29}, l_{29}, m_{29}, n_{29}, p_{29}, q_{29}, r_{28}, s_{27}, t_{27}, g_{28}, a_{28}, b_{28}, c_{28}, d_{28}, e_{28}, f_{30}, g_{30}, h_{30}, i_{30}, j_{30}, i_{28}, k_{30}, l_{30}, m_{30}, n_{30}, p_{30}, q_{30}, r_{29}, s_{28}, t_{28}, a_{29}, k_{28}, b_{29}, c_{29}, d_{29}, e_{29}, f_{31}, g_{31}, h_{31}, i_{31}, j_{31}, k_{31}, m_{28}, l_{31}, m_{31}, n_{31}, p_{31}, q_{31}, r_{30}, s_{29}, t_{29}, a_{30}, b_{30}, c_{26}, c_{30}, d_{30}, e_{30}, f_{32}, g_{32}, h_{32}, i_{32}, j_{32}, k_{32}, l_{32}, d_{26}, m_{32}, n_{32}, p_{32}, q_{32}, r_{31}, s_{30}, t_{30}, a_{31}, b_{31}, c_{31}