Truncated Icosahedron by Guillermo Bautista

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2019-12-11 23:38

This example demonstrates the 3D shape of a truncated icosahedron and its properties. Core math concepts include solid geometry, polygons, circles, and line segments. Construction highlights from the summary involve commands like Polygon, Icosahedron, Circle, Midpoint, Intersect, Segment, and Mirror in GeoGebra. Suitable for high school students and teachers learning solid geometry and geometric constructions.

GeoGebra Commands & Parameters

Polygon(A, B, 3, xOyPlane) → poly1, f, g, h, C
Icosahedron(poly1, true) → a, D, faceACF, faceAFG, faceADG, faceABD, faceBDH, faceBEH, faceBCE, faceCEI, faceCFI, faceEHK, E, faceEIK, faceIKL, faceFIL, faceHJK, faceJKL, faceGJL, faceFGL, faceDHJ, faceDGJ, edgeAF, F, edgeCF, edgeAG, edgeFG, edgeAD, edgeDG, edgeBD, edgeBH, edgeDH, edgeBE, edgeEH, G, edgeCE, edgeCI, edgeEI, edgeFI, edgeEK, edgeHK, edgeIK, edgeIL, edgeKL, edgeFL, H, edgeJK, edgeHJ, edgeJL, edgeGL, edgeGJ, edgeDJ, I, J, K, L
Circle(B, t, xOyPlane) → c
Circle(A, t, xOyPlane) → d
Circle(C, t, xOyPlane) → e
Midpoint(E, C) → R
Circle(B, t, xOyPlane) → k
Circle(C, t, xOyPlane) → p
Intersect(f, k, 2) → M
Intersect(g, p, 2) → N
Intersect(h, p, 1) → O
Intersect(g, k, 1) → P
Circle(A, t, xOyPlane) → q
Intersect(f, q, 1) → Q
Intersect(h, q, 2) → S
Midpoint(edgeAF) → T
Midpoint(edgeFI) → U
Midpoint(edgeEI) → V
Midpoint(edgeBE) → W
Segment(U, C) → i
Segment(T, C) → j
Mirror(O, j) → O'
Mirror(O', i) → O''
Segment(V, C) → l
Mirror(O'', l) → O'''
Midpoint(edgeBD) → Z
Midpoint(edgeDG) → A_1
Segment(Z, A) → m
Segment(A, A_1) → n
Mirror(Q, m) → Q'
Mirror(Q', n) → Q''
Midpoint(edgeFG) → B_1
Segment(A, B_1) → r
Mirror(Q'', r) → Q'''
Segment(B, R) → s
Midpoint(edgeEH) → C_1
Midpoint(edgeDH) → D_1
Segment(C_1, B) → f_1
Segment(D_1, B) → g_1
Mirror(P, s) → P'
Mirror(P', f_1) → P''
Mirror(P'', g_1) → P'''
Mirror(P', W) → P''_1
Midpoint(edgeCE) → E_1
Mirror(O''', E_1) → F_1
Midpoint(edgeCI) → G_1
Mirror(O'', G_1) → O'''_1
Midpoint(edgeCF) → H_1
Mirror(O', H_1) → O''_1
Mirror(Q''', T) → I_1
Segment(I, H_1) → h_1
Mirror(O'''_1, h_1) → J_1
Mirror(J_1, U) → K_1
Segment(E, G_1) → i_1
Mirror(F_1, i_1) → L_1
Mirror(L_1, V) → M_1
Midpoint(edgeAD) → N_1
Mirror(Q', N_1) → Q''_1
Mirror(P''', Z) → O_1
Midpoint(edgeBH) → P_1
Mirror(P'', P_1) → P'''_1
Segment(D, P_1) → j_1
Mirror(O_1, j_1) → Q_1
Mirror(P''', j_1) → R_1
Segment(H, W) → k_1
Mirror(P'''_1, k_1) → S_1
Mirror(P'', k_1) → P'''_2
Midpoint(edgeFL) → T_1
Segment(I, T_1) → l_1
Mirror(J_1, l_1) → U_1
Mirror(K_1, l_1) → V_1
Midpoint(edgeIL) → W_1
Segment(W_1, F) → m_1
Mirror(J_1, m_1) → Z_1
Mirror(K_1, m_1) → A_2
Segment(L, B_1) → n_1
Mirror(Z_1, n_1) → B_2
Mirror(A_2, n_1) → C_2
Segment(T_1, G) → p_1
Mirror(C_2, p_1) → D_2
Mirror(B_2, p_1) → E_2
Segment(B_1, A) → q_1
Mirror(I_1, q_1) → F_2
Segment(G, N_1) → r_1
Mirror(F_2, r_1) → G_2
Mirror(Q'', r_1) → Q'''_1
Midpoint(edgeKL) → H_2
Segment(H_2, I) → s_1
Mirror(U_1, s_1) → J_2
Mirror(V_1, s_1) → K_2
Segment(W_1, K) → t_1
Mirror(K_2, t_1) → I_2
Mirror(J_2, t_1) → L_2
Segment(K, V) → a_1
Mirror(J_2, a_1) → M_2
Mirror(K_2, a_1) → N_2
Segment(K, C_1) → b_1
Mirror(N_2, b_1) → O_2
Mirror(M_2, b_1) → P_2
Midpoint(edgeHJ) → Q_2
Segment(Q_2, D) → c_1
Mirror(Q_1, c_1) → R_2
Mirror(R_1, c_1) → S_2
Segment(J, D_1) → d_1
Mirror(S_2, d_1) → T_2
Mirror(R_2, d_1) → U_2
Segment(A_1, J) → e_1
Mirror(S_2, e_1) → V_2
Mirror(R_2, e_1) → W_2
Midpoint(edgeGJ) → Z_2
Segment(L, Z_2) → f_2
Mirror(B_2, f_2) → A_3
Mirror(C_2, f_2) → B_3
Segment(H_2, J) → g_2
Mirror(B_3, g_2) → C_3
Mirror(A_3, g_2) → D_3
Polygon(V_2, S_2, T_2, C_3, B_3) → poly2, v_2, s_2, t_2, c_3, b_3
Polygon(V_1, Z_1, B_2, A_3, L_2) → poly3, v_1, z_1, b_2, a_3, l_2
Polygon(M_1, O'''_1, J_1, U_1, J_2) → poly4, h_2, o'''_1, i_2, u_1, j_2
Polygon(D_2, F_2, G_2, W_2, C_2) → poly6, d_2, n_2, p_2, w_2, c_2
Polygon(Q'''_1, R_2, Q_1, O_1, Q''_1) → poly7, q'''_1, r_2, q_2, o_1, q''_1
Polygon(O_2, N_2, K_2, I_2, D_3) → poly8, o_2, f_3, g_3, h_3, d_3
Polygon(L_1, F_1, P''_1, P'''_2, M_2) → poly9, i_3, j_3, p''_1, p'''_2, k_3
Polygon(Q'', Q', Q, S, Q''') → poly10, q'', q', q_3, s_3, q'''
Segment(A, B) → l_3
Segment(B, C) → m_3
Segment(C, A) → n_3
Polygon(P_2, S_1, P'''_1, R_1, U_2) → poly11, p_3, r_3, p'''_1, t_3, u_2
Polygon(O''', N, O, O', O'') → poly12, o''', n_4, o, o', o''
Polygon(P, P', P'', P''', M) → poly13, p_4, p', p'', p''', m_4
Polygon(A_3, B_2, C_2, W_2, V_2, B_3) → poly14, e_3, f_4, g_4, h_4, i_4, j_4
Polygon(V_2, W_2, G_2, Q'''_1, R_2, S_2) → poly15, k_4, l_4, q_4, r_4, s_4, t_4
Polygon(S_2, T_2, U_2, R_1, Q_1, R_2) → poly16, a_4, b_4, c_4, d_4, e_4, f_5
Polygon(C_3, T_2, U_2, P_2, O_2, D_3) → poly17, g_5, h_5, i_5, j_5, k_5, l_5
Polygon(Q_1, O_1, P''', P'', P'''_1, R_1) → poly18, m_5, n_5, p_5, q_5, r_5, s_5
Polygon(L_2, A_3, B_3, C_3, D_3, I_2) → poly19, t_5, a_5, b_5, c_5, d_5, e_5
Polygon(P_2, S_1, P'''_2, M_2, N_2, O_2) → poly20, f_6, g_6, h_6, i_6, j_6, k_6
Polygon(P'''_1, S_1, P'''_2, P''_1, P', P'') → poly21, l_6, m_6, n_6, p_6, q_6, r_6
Polygon(N_2, M_2, L_1, M_1, J_2, K_2) → poly22, s_6, t_6, a_6, b_6, c_6, d_6
Polygon(K_2, J_2, U_1, V_1, L_2, I_2) → poly23, e_6, f_7, g_7, h_7, i_7, j_7
Polygon(U_1, J_1, K_1, A_2, Z_1, V_1) → poly24, k_7, l_7, m_7, n_7, p_7, q_7
Polygon(G_2, F_2, Q'', Q', Q''_1, Q'''_1) → poly27, j_8, k_8, l_8, m_8, n_8, p_8
Polygon(P''_1, P', P, N, O''', F_1) → poly28, q_8, r_8, p_9, n_9, s_8, t_8
Polygon(J_1, O'''_1, O'', O', O''_1, K_1) → poly29, a_8, b_8, c_8, d_8, e_8, f_9
Polygon(O''_1, O', O, S, Q''', I_1) → poly30, g_9, h_9, o_3, s_9, i_9, j_9
Polygon(O, N, P, M, Q, S) → poly31, o_4, n_{10}, p_{10}, m_9, q_9, s_{10}
Polygon(Q''_1, Q', Q, M, P''', O_1) → poly32, k_9, l_9, q_{10}, m_{10}, r_9, t_9
Midpoint(edgeFG) → E_3
Mirror(D_2, E_3) → F_3
Polygon(A_2, F_3, I_1, O''_1, K_1) → poly5, a_2, k_2, m_2, o''_1, e_2
Polygon(F_3, I_1, Q''', Q'', F_2, D_2) → poly25, r_7, s_7, t_7, a_7, b_7, c_7
Polygon(Z_1, A_2, F_3, D_2, C_2, B_2) → poly26, d_7, e_7, f_8, g_8, h_8, i_8