4.7 cm Escher91 Escarabajos

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2023-03-22 22:47

In collections geometriadinamica.es

This example demonstrates an Escher-style Escarabajos graph, showcasing geometric shapes' symmetry and transformation. Key mathematical concepts include translation, linear equations, and integration. Construction points include using GeoGebra commands: Line, Point, Intersect, If, Vector, Translate, Polygon, Mirror, Midpoint, OrthogonalLine, Length, Min, Circle, Segment. Suitable for middle to high school students and math enthusiasts.

GeoGebra Commands & Parameters

Line(E, F) → d
Point(d) → I_1
Point(d) → E_1
Point(d) → D_1
Point(d) → W
Line(H, d) → f
Line(C, D) → b
Intersect(b, d) → T
Line(G, b) → e
Intersect(d, e) → R_2
Point(e) → U
Intersect(e, f) → R
Point(e) → Q
Point(e) → I
If(a < 1, a, 1) → d1
If(a < 1, 0, If[a < 2, a - 1, 1]) → d2
If(a < 2.2, 0, If[a < 3.2, a - 2.2, 1]) → d3
If(a < 3.2, 0, If[a < 4.2, a - 3.2, 1]) → d4
If(a < 4.2, 0, If[a < 5.2, a - 4.2, 1]) → d5
If(a < 5.5, 0, a - 5.5) → d6
Intersect(b, f) → S
Vector(R, S) → u
Translate(I, v_{10}) → I'
Translate(J, v_{10}) → J'
Translate(K, v_{10}) → K'
Translate(L, v_{10}) → L'
Translate(M, v_{10}) → M'
Translate(N, v_{10}) → N'
Translate(O, v_{10}) → O'
Translate(P, v_{10}) → P'
Translate(Q, v_{10}) → Q'
Polygon(I', J', K', L', M', N', O', P', Q') → poly1', i', j', k', l', m', n', o', p', q'
Line(T, R) → g
Mirror(I', g) → I''
Mirror(J', g) → J''
Mirror(K', g) → K''
Mirror(L', g) → L''
Mirror(M', g) → M''
Mirror(N', g) → N''
Mirror(O', g) → O''
Mirror(P', g) → P''
Mirror(Q', g) → Q''
Polygon(I'', J'', K'', L'', M'', N'', O'', P'', Q'') → poly1'', i'', j'', k'', l'', m'', n'', o'', p'', q''
Translate(U, v_{10}) → U'
Translate(V, v_{10}) → V'
Translate(R, v_{10}) → R'
Polygon(U', V', R') → poly2', r', u', v'
Mirror(U', g) → U''
Mirror(V', g) → V''
Mirror(R', g) → R''
Polygon(U'', V'', R'') → poly2'', r'', u'', v''
Vector(T, S) → w
Intersect(d, i'') → H_1
Translate(W, z) → W'
Translate(Z, z) → Z'
Translate(A_1, z) → J_1
Translate(B_1, z) → K_1
Translate(C_1, z) → L_1
Translate(D_1, z) → M_1
Polygon(W', Z', J_1, K_1, L_1, M_1) → poly3', w', z', j_1, k_1, l_1, m_1
Translate(E_1, z) → N_1
Translate(F_1, z) → O_1
Translate(G_1, z) → P_1
Translate(I_1, z) → Q_1
Polygon(N_1, O_1, P_1, Q_1) → poly4', n_1, o_1, p_1, q_1
Mirror(W', g) → W''
Mirror(Z', g) → Z''
Mirror(J_1, g) → R_1
Mirror(K_1, g) → S_1
Mirror(L_1, g) → T_1
Mirror(M_1, g) → U_1
Polygon(W'', Z'', R_1, S_1, T_1, U_1) → poly3'', w'', z'', r_1, s_1, t_1, u_2
Mirror(N_1, g) → V_1
Mirror(O_1, g) → W_1
Mirror(P_1, g) → Z_1
Mirror(Q_1, g) → A_2
Polygon(V_1, W_1, Z_1, A_2) → poly4'', v_2, w_2, z_2, a_2
Mirror(W, g) → W'_1
Mirror(Z, g) → Z'_1
Mirror(A_1, g) → B_2
Mirror(B_1, g) → C_2
Mirror(C_1, g) → D_2
Mirror(D_1, g) → E_2
Mirror(E_1, g) → F_2
Mirror(F_1, g) → G_2
Mirror(G_1, g) → H_2
Mirror(I_1, g) → I_2
Mirror(I, g) → I'_1
Mirror(J, g) → J'_1
Mirror(K, g) → K'_1
Mirror(L, g) → L'_1
Mirror(M, g) → M'_1
Mirror(N, g) → N'_1
Mirror(O, g) → O'_1
Mirror(P, g) → P'_1
Mirror(Q, g) → Q'_1
Mirror(U, g) → U'_1
Mirror(V, g) → V'_1
Mirror(R, g) → R'_1
Polygon(T, R, K, J, I, R_2, W, Z, A_1, B_1, C_1, D_1, V, I_1, G_1, F_1, E_1, U, Q, P, O, N, M, L) → poly5, h, p_2, q_2, r_2, s_2, t_2, a_3, b_3, c_3, d_3, e_3, s, f_3, g_3, h_3, i_3, j_3, t, h_1, j_2, k_2, l_2, m_2, n_2
Mirror(T, g) → T'
Mirror(R, g) → R'_2
Mirror(V, g) → V'_2
Mirror(U, g) → U'_2
Mirror(Q, g) → Q'_2
Mirror(P, g) → P'_2
Mirror(O, g) → O'_2
Mirror(N, g) → N'_2
Mirror(M, g) → M'_2
Mirror(L, g) → L'_2
Mirror(K, g) → K'_2
Mirror(J, g) → J'_2
Mirror(I, g) → I'_2
Mirror(R'', g) → R'''
Mirror(W, g) → W'_2
Mirror(Z, g) → Z'_2
Mirror(A_1, g) → J_2
Mirror(B_1, g) → K_2
Mirror(C_1, g) → L_2
Mirror(D_1, g) → M_2
Mirror(I_1, g) → N_2
Mirror(G_1, g) → O_2
Mirror(F_1, g) → P_2
Mirror(E_1, g) → Q_2
Polygon(T', R'_2, K'_2, J'_2, I'_2, S, W'_2, Z'_2, J_2, K_2, L_2, M_2, V'_2, N_2, O_2, P_2, Q_2, U'_2, Q'_2, P'_2, O'_2, N'_2, M'_2, L'_2) → poly5', k_3, a_4, b_4, c_4, d_4, e_4, f_4, g_4, h_4, i_4, j_4, l_3, k_4, l_4, m_4, n_4, p_4, m_3, n_3, p_3, q_3, r_3, s_3, t_3
Translate(T', i) → T''
Translate(R'_2, i) → S_2
Translate(V'_2, i) → T_2
Translate(U'_2, i) → U_2
Translate(Q'_2, i) → V_2
Translate(P'_2, i) → W_2
Translate(O'_2, i) → Z_2
Translate(N'_2, i) → A_3
Translate(M'_2, i) → B_3
Translate(L'_2, i) → C_3
Translate(K'_2, i) → D_3
Translate(J'_2, i) → E_3
Translate(I'_2, i) → F_3
Translate(S, i) → S'
Translate(W'_2, i) → G_3
Translate(Z'_2, i) → H_3
Translate(J_2, i) → I_3
Translate(K_2, i) → J_3
Translate(L_2, i) → K_3
Translate(M_2, i) → L_3
Translate(N_2, i) → M_3
Translate(O_2, i) → N_3
Translate(P_2, i) → O_3
Translate(Q_2, i) → P_3
Polygon(T'', S_2, D_3, E_3, F_3, S', G_3, H_3, I_3, J_3, K_3, L_3, T_2, M_3, N_3, O_3, P_3, U_2, V_2, W_2, Z_2, A_3, B_3, C_3) → poly5'', t'', c_1, d_1, e_1, f_1, s', g_1, h_2, i_1, j_5, k_5, s_4, l_5, m_5, n_5, o_3, p_5, t_4, u_1, v_1, w_1, z_1, a_1, b_1
Translate(I', i) → I''_1
Translate(J', i) → J''_1
Translate(K', i) → K''_1
Translate(L', i) → L''_1
Translate(M', i) → M''_1
Translate(N', i) → N''_1
Translate(O', i) → O''_1
Translate(P', i) → P''_1
Translate(Q', i) → Q''_1
Polygon(I''_1, J''_1, K''_1, L''_1, M''_1, N''_1, O''_1, P''_1, Q''_1) → poly1''_1, i''_1, j''_1, k''_1, l''_1, m''_1, n''_1, o''_1, p''_1, q''_1
Translate(W', i) → W''_1
Translate(Z', i) → Z''_1
Translate(J_1, i) → Q_3
Translate(K_1, i) → R_3
Translate(L_1, i) → S_3
Translate(M_1, i) → T_3
Polygon(W''_1, Z''_1, Q_3, R_3, S_3, T_3) → poly3''_1, w''_1, z''_1, q_4, r_4, s_5, t_5
Translate(N_1, i) → U_3
Translate(O_1, i) → V_3
Translate(P_1, i) → W_3
Translate(Q_1, i) → Z_3
Polygon(U_3, V_3, W_3, Z_3) → poly4''_1, u_3, v_3, w_3, z_3
Translate(U', i) → U''_1
Translate(V', i) → V''_1
Translate(R', i) → R''_1
Polygon(U''_1, V''_1, R''_1) → poly2''_1, r''_1, u''_1, v''_1
Translate(T, i) → T'_1
Translate(R, i) → R'_3
Translate(V, i) → V'_3
Translate(U, i) → U'_3
Translate(Q, i) → Q'_3
Translate(P, i) → P'_3
Translate(O, i) → O'_3
Translate(N, i) → N'_3
Translate(M, i) → M'_3
Translate(L, i) → L'_3
Translate(K, i) → K'_3
Translate(J, i) → J'_3
Translate(I, i) → I'_3
Translate(R_2, i) → A_4
Translate(W, i) → W'_3
Translate(Z, i) → Z'_3
Translate(A_1, i) → B_4
Translate(B_1, i) → C_4
Translate(C_1, i) → D_4
Translate(D_1, i) → E_4
Translate(I_1, i) → F_4
Translate(G_1, i) → G_4
Translate(F_1, i) → H_4
Translate(E_1, i) → I_4
Polygon(T'_1, R'_3, K'_3, J'_3, I'_3, A_4, W'_3, Z'_3, B_4, C_4, D_4, E_4, V'_3, F_4, G_4, H_4, I_4, U'_3, Q'_3, P'_3, O'_3, N'_3, M'_3, L'_3) → poly5'_1, t'_1, l'_3, k'_3, j'_3, i'_3, a_5, w'_3, z'_3, b_2, c_2, d_2, r'_3, e_2, f_2, g_2, h_5, i_2, v'_3, u'_3, q'_3, p'_3, o'_3, n'_3, m'_3
Translate(I'', i) → I'''
Translate(J'', i) → J'''
Translate(K'', i) → K'''
Translate(L'', i) → L'''
Translate(M'', i) → M'''
Translate(N'', i) → N'''
Translate(O'', i) → O'''
Translate(P'', i) → P'''
Translate(Q'', i) → Q'''
Polygon(I''', J''', K''', L''', M''', N''', O''', P''', Q''') → poly1''', i''', j''', k''', l''', m''', n''', o''', p''', q'''
Translate(U'', i) → U'''
Translate(V'', i) → V'''
Translate(R'', i) → R'''_1
Polygon(U''', V''', R'''_1) → poly2''', r'''_1, u''', v'''
Translate(W'', i) → W'''
Translate(Z'', i) → Z'''
Translate(R_1, i) → J_4
Translate(S_1, i) → K_4
Translate(T_1, i) → L_4
Translate(U_1, i) → M_4
Polygon(W''', Z''', J_4, K_4, L_4, M_4) → poly3''', w''', z''', j_6, k_6, l_6, m_6
Translate(V_1, i) → N_4
Translate(W_1, i) → O_4
Translate(Z_1, i) → P_4
Translate(A_2, i) → Q_4
Polygon(N_4, O_4, P_4, Q_4) → poly4''', n_6, o_4, p_6, q_5
Vector(R, T) → j
Translate(T', k) → T''_1
Translate(R'_2, k) → R_4
Translate(V'_2, k) → S_4
Translate(U'_2, k) → T_4
Translate(Q'_2, k) → U_4
Translate(P'_2, k) → V_4
Translate(O'_2, k) → W_4
Translate(N'_2, k) → Z_4
Translate(M'_2, k) → A_5
Translate(L'_2, k) → B_5
Translate(K'_2, k) → C_5
Translate(J'_2, k) → D_5
Translate(I'_2, k) → E_5
Translate(S, k) → S'_1
Translate(W'_2, k) → F_5
Translate(Z'_2, k) → G_5
Translate(J_2, k) → H_5
Translate(K_2, k) → I_5
Translate(L_2, k) → J_5
Translate(M_2, k) → K_5
Translate(N_2, k) → L_5
Translate(O_2, k) → M_5
Translate(P_2, k) → N_5
Translate(Q_2, k) → O_5
Polygon(T''_1, R_4, C_5, D_5, E_5, S'_1, F_5, G_5, H_5, I_5, J_5, K_5, S_4, L_5, M_5, N_5, O_5, T_4, U_4, V_4, W_4, Z_4, A_5, B_5) → poly5''_1, t''_1, b_5, c_5, d_5, e_5, s'_1, f_5, g_5, h_6, i_5, j_7, r_5, k_7, l_7, m_7, n_7, o_5, s_6, t_6, u_4, v_4, w_4, z_4, a_6
Translate(I', k) → I''_2
Translate(J', k) → J''_2
Translate(K', k) → K''_2
Translate(L', k) → L''_2
Translate(M', k) → M''_2
Translate(N', k) → N''_2
Translate(O', k) → O''_2
Translate(P', k) → P''_2
Translate(Q', k) → Q''_2
Polygon(I''_2, J''_2, K''_2, L''_2, M''_2, N''_2, O''_2, P''_2, Q''_2) → poly1''_2, i''_2, j''_2, k''_2, l''_2, m''_2, n''_2, o''_2, p''_2, q''_2
Translate(N_1, k) → P_5
Translate(O_1, k) → Q_5
Translate(P_1, k) → R_5
Translate(Q_1, k) → S_5
Polygon(P_5, Q_5, R_5, S_5) → poly4''_2, p_7, q_6, r_6, s_7
Translate(W', k) → W''_2
Translate(Z', k) → Z''_2
Translate(J_1, k) → T_5
Translate(K_1, k) → U_5
Translate(L_1, k) → V_5
Translate(M_1, k) → W_5
Polygon(W''_2, Z''_2, T_5, U_5, V_5, W_5) → poly3''_2, w''_2, z''_2, t_7, u_5, v_5, w_5
Translate(U', k) → U''_2
Translate(V', k) → V''_2
Translate(R', k) → R''_2
Polygon(U''_2, V''_2, R''_2) → poly2''_2, r''_2, u''_2, v''_2
Translate(I'', k) → I'''_1
Translate(J'', k) → J'''_1
Translate(K'', k) → K'''_1
Translate(L'', k) → L'''_1
Translate(M'', k) → M'''_1
Translate(N'', k) → N'''_1
Translate(O'', k) → O'''_1
Translate(P'', k) → P'''_1
Translate(Q'', k) → Q'''_1
Polygon(I'''_1, J'''_1, K'''_1, L'''_1, M'''_1, N'''_1, O'''_1, P'''_1, Q'''_1) → poly1'''_1, i'''_1, j'''_1, k'''_1, l'''_1, m'''_1, n'''_1, o'''_1, p'''_1, q'''_1
Translate(U'', k) → U'''_1
Translate(V'', k) → V'''_1
Translate(R'', k) → R'''_2
Polygon(U'''_1, V'''_1, R'''_2) → poly2'''_1, r'''_2, u'''_1, v'''_1
Translate(V_1, k) → Z_5
Translate(W_1, k) → A_6
Translate(Z_1, k) → B_6
Translate(A_2, k) → C_6
Polygon(Z_5, A_6, B_6, C_6) → poly4'''_1, z_5, a_7, b_6, c_6
Translate(W'', k) → W'''_1
Translate(Z'', k) → Z'''_1
Translate(R_1, k) → D_6
Translate(S_1, k) → E_6
Translate(T_1, k) → F_6
Translate(U_1, k) → G_6
Polygon(W'''_1, Z'''_1, D_6, E_6, F_6, G_6) → poly3'''_1, w'''_1, z'''_1, d_6, e_6, f_6, g_6
Translate(T, k) → T'_2
Translate(R, k) → R'_4
Translate(V, k) → V'_4
Translate(U, k) → U'_4
Translate(Q, k) → Q'_4
Translate(P, k) → P'_4
Translate(O, k) → O'_4
Translate(N, k) → N'_4
Translate(M, k) → M'_4
Translate(L, k) → L'_4
Translate(K, k) → K'_4
Translate(J, k) → J'_4
Translate(I, k) → I'_4
Translate(R_2, k) → H_6
Translate(W, k) → W'_4
Translate(Z, k) → Z'_4
Translate(A_1, k) → I_6
Translate(B_1, k) → J_6
Translate(C_1, k) → K_6
Translate(D_1, k) → L_6
Translate(I_1, k) → M_6
Translate(G_1, k) → N_6
Translate(F_1, k) → O_6
Translate(E_1, k) → P_6
Polygon(T'_2, R'_4, K'_4, J'_4, I'_4, H_6, W'_4, Z'_4, I_6, J_6, K_6, L_6, V'_4, M_6, N_6, O_6, P_6, U'_4, Q'_4, P'_4, O'_4, N'_4, M'_4, L'_4) → poly5'_2, t'_2, l'_4, k'_4, j'_4, i'_4, h_7, w'_4, z'_4, i_6, j_8, k_8, r'_4, l_8, m_8, n_8, o_6, p_8, v'_4, u'_4, q'_4, p'_4, o'_4, n'_4, m'_4
Translate(T'_1, k) → Q_6
Translate(R'_3, k) → R_6
Translate(V'_3, k) → S_6
Translate(U'_3, k) → T_6
Translate(Q'_3, k) → U_6
Translate(P'_3, k) → V_6
Translate(O'_3, k) → W_6
Translate(N'_3, k) → Z_6
Translate(M'_3, k) → A_7
Translate(L'_3, k) → B_7
Translate(K'_3, k) → C_7
Translate(J'_3, k) → D_7
Translate(I'_3, k) → E_7
Translate(A_4, k) → F_7
Translate(W'_3, k) → G_7
Translate(Z'_3, k) → H_7
Translate(B_4, k) → I_7
Translate(C_4, k) → J_7
Translate(D_4, k) → K_7
Translate(E_4, k) → L_7
Translate(F_4, k) → M_7
Translate(G_4, k) → N_7
Translate(H_4, k) → O_7
Translate(I_4, k) → P_7
Polygon(Q_6, R_6, C_7, D_7, E_7, F_7, G_7, H_7, I_7, J_7, K_7, L_7, S_6, M_7, N_7, O_7, P_7, T_6, U_6, V_6, W_6, Z_6, A_7, B_7) → poly1, q_7, b_7, c_7, d_7, e_7, f_7, g_7, h_8, i_7, j_9, k_9, r_7, l_9, m_9, n_9, o_7, p_9, s_8, t_8, u_6, v_6, w_6, z_6, a_8
Translate(I''', k) → Q_7
Translate(J''', k) → R_7
Translate(K''', k) → S_7
Translate(L''', k) → T_7
Translate(M''', k) → U_7
Translate(N''', k) → V_7
Translate(O''', k) → W_7
Translate(P''', k) → Z_7
Translate(Q''', k) → A_8
Polygon(Q_7, R_7, S_7, T_7, U_7, V_7, W_7, Z_7, A_8) → poly2, q_8, r_8, s_9, t_9, u_7, v_7, w_7, z_7, a_9
Translate(I''_1, k) → B_8
Translate(J''_1, k) → C_8
Translate(K''_1, k) → D_8
Translate(L''_1, k) → E_8
Translate(M''_1, k) → F_8
Translate(N''_1, k) → G_8
Translate(O''_1, k) → H_8
Translate(P''_1, k) → I_8
Translate(Q''_1, k) → J_8
Polygon(B_8, C_8, D_8, E_8, F_8, G_8, H_8, I_8, J_8) → poly3, b_8, c_8, d_8, e_8, f_8, g_8, h_9, i_8, j_{10}
Translate(U''', k) → K_8
Translate(V''', k) → L_8
Translate(R'''_1, k) → M_8
Polygon(K_8, L_8, M_8) → poly4, m_{10}, k_{10}, l_{10}
Translate(N_4, k) → N_8
Translate(O_4, k) → O_8
Translate(P_4, k) → P_8
Translate(Q_4, k) → Q_8
Polygon(N_8, O_8, P_8, Q_8) → poly6, n_{10}, o_8, p_{10}, q_9
Translate(U''_1, k) → R_8
Translate(V''_1, k) → S_8
Translate(R''_1, k) → T_8
Polygon(R_8, S_8, T_8) → poly7, t_{10}, r_9, s_{10}
Translate(U_3, k) → U_8
Translate(V_3, k) → V_8
Translate(W_3, k) → W_8
Translate(Z_3, k) → Z_8
Polygon(U_8, V_8, W_8, Z_8) → poly8, u_8, v_8, w_8, z_8
Translate(W''_1, k) → A_9
Translate(Z''_1, k) → B_9
Translate(Q_3, k) → C_9
Translate(R_3, k) → D_9
Translate(S_3, k) → E_9
Translate(T_3, k) → F_9
Polygon(A_9, B_9, C_9, D_9, E_9, F_9) → poly9, a_{10}, b_9, c_9, d_9, e_9, f_9
Translate(T'', k) → T'''
Translate(S_2, k) → G_9
Translate(T_2, k) → H_9
Translate(U_2, k) → I_9
Translate(V_2, k) → J_9
Translate(W_2, k) → K_9
Translate(Z_2, k) → L_9
Translate(A_3, k) → M_9
Translate(B_3, k) → N_9
Translate(C_3, k) → O_9
Translate(D_3, k) → P_9
Translate(E_3, k) → Q_9
Translate(F_3, k) → R_9
Translate(S', k) → S''
Translate(G_3, k) → S_9
Translate(H_3, k) → T_9
Translate(I_3, k) → U_9
Translate(J_3, k) → V_9
Translate(K_3, k) → W_9
Translate(L_3, k) → Z_9
Translate(M_3, k) → A_{10}
Translate(N_3, k) → B_{10}
Translate(O_3, k) → C_{10}
Translate(P_3, k) → D_{10}
Polygon(T''', G_9, P_9, Q_9, R_9, S'', S_9, T_9, U_9, V_9, W_9, Z_9, H_9, A_{10}, B_{10}, C_{10}, D_{10}, I_9, J_9, K_9, L_9, M_9, N_9, O_9) → poly5''', t''', o_9, p_{11}, q_{10}, r_{10}, s'', s_{11}, t_{11}, u_9, v_9, w_9, g_9, z_9, a_{11}, b_{10}, c_{10}, d_{10}, h_{10}, i_9, j_{11}, k_{11}, l_{11}, m_{11}, n_{11}
Translate(W''', k) → E_{10}
Translate(Z''', k) → F_{10}
Translate(J_4, k) → G_{10}
Translate(K_4, k) → H_{10}
Translate(L_4, k) → I_{10}
Translate(M_4, k) → J_{10}
Polygon(E_{10}, F_{10}, G_{10}, H_{10}, I_{10}, J_{10}) → poly10, e_{10}, f_{10}, g_{10}, h_{11}, i_{10}, j_{12}
Midpoint(T, S) → K_{10}
Line(K_{10}, g) → l
Line(S, g) → m
Mirror(l, m) → l'_1
Mirror(m, l'_1) → m'_1
Mirror(l'_1, m'_1) → n
Mirror(m'_1, n) → p
Mirror(l, g) → l'_2
Mirror(g, l'_2) → g'
OrthogonalLine(S, g) → q
Intersect(g, q) → L_{10}
Line(L_{10}, Q_6) → r
OrthogonalLine(Q_6, m'_1) → b_{11}
Intersect(l'_1, b_{11}) → M_{10}
Intersect(l'_1, r) → N_{10}
Intersect(d, l) → O_{10}
Vector(K_{10}, O_{10}) → u1
Mirror(T', l) → T''_2
Mirror(R'_2, l) → P_{10}
Mirror(V'_2, l) → Q_{10}
Mirror(U'_2, l) → R_{10}
Mirror(Q'_2, l) → S_{10}
Mirror(P'_2, l) → T_{10}
Mirror(O'_2, l) → U_{10}
Mirror(N'_2, l) → V_{10}
Mirror(M'_2, l) → W_{10}
Mirror(L'_2, l) → Z_{10}
Mirror(K'_2, l) → A_{11}
Mirror(J'_2, l) → B_{11}
Mirror(I'_2, l) → C_{11}
Mirror(S, l) → S'_2
Mirror(W'_2, l) → D_{11}
Mirror(Z'_2, l) → E_{11}
Mirror(J_2, l) → F_{11}
Mirror(K_2, l) → G_{11}
Mirror(L_2, l) → H_{11}
Mirror(M_2, l) → I_{11}
Mirror(N_2, l) → J_{11}
Mirror(O_2, l) → K_{11}
Mirror(P_2, l) → L_{11}
Mirror(Q_2, l) → M_{11}
Polygon(T''_2, P_{10}, A_{11}, B_{11}, C_{11}, S'_2, D_{11}, E_{11}, F_{11}, G_{11}, H_{11}, I_{11}, Q_{10}, J_{11}, K_{11}, L_{11}, M_{11}, R_{10}, S_{10}, T_{10}, U_{10}, V_{10}, W_{10}, Z_{10}) → poly5''_2, t''_2, z_{10}, a_{12}, b_{12}, c_{11}, s'_2, d_{11}, e_{11}, f_{11}, g_{11}, h_{12}, p_{12}, i_{11}, j_{13}, k_{12}, l_{12}, m_{12}, q_{11}, r_{11}, s_{12}, t_{12}, u_{11}, v_{11}, w_{10}
Mirror(T, l) → T'_3
Mirror(R, l) → R'_5
Mirror(V, l) → V'_5
Mirror(U, l) → U'_5
Mirror(Q, l) → Q'_5
Mirror(P, l) → P'_5
Mirror(O, l) → O'_5
Mirror(N, l) → N'_5
Mirror(M, l) → M'_5
Mirror(L, l) → L'_5
Mirror(K, l) → K'_5
Mirror(J, l) → J'_5
Mirror(I, l) → I'_5
Mirror(R_2, l) → N_{11}
Mirror(W, l) → W'_5
Mirror(Z, l) → Z'_5
Mirror(A_1, l) → O_{11}
Mirror(B_1, l) → P_{11}
Mirror(C_1, l) → Q_{11}
Mirror(D_1, l) → R_{11}
Mirror(I_1, l) → S_{11}
Mirror(G_1, l) → T_{11}
Mirror(F_1, l) → U_{11}
Mirror(E_1, l) → V_{11}
Polygon(T'_3, R'_5, K'_5, J'_5, I'_5, N_{11}, W'_5, Z'_5, O_{11}, P_{11}, Q_{11}, R_{11}, V'_5, S_{11}, T_{11}, U_{11}, V_{11}, U'_5, Q'_5, P'_5, O'_5, N'_5, M'_5, L'_5) → poly5'_3, t'_3, l'_5, k'_5, j'_5, i'_5, n_{12}, w'_5, z'_5, o_{11}, p_{13}, q_{12}, r'_5, r_{12}, s_{13}, t_{13}, u_{12}, v_{12}, v'_5, u'_5, q'_5, p'_5, o'_5, n'_5, m'_5
Mirror(I'', l) → I'''_2
Mirror(J'', l) → J'''_2
Mirror(K'', l) → K'''_2
Mirror(L'', l) → L'''_2
Mirror(M'', l) → M'''_2
Mirror(N'', l) → N'''_2
Mirror(O'', l) → O'''_2
Mirror(P'', l) → P'''_2
Mirror(Q'', l) → Q'''_2
Polygon(I'''_2, J'''_2, K'''_2, L'''_2, M'''_2, N'''_2, O'''_2, P'''_2, Q'''_2) → poly1'''_2, i'''_2, j'''_2, k'''_2, l'''_2, m'''_2, n'''_2, o'''_2, p'''_2, q'''_2
Mirror(I', l) → I''_3
Mirror(J', l) → J''_3
Mirror(K', l) → K''_3
Mirror(L', l) → L''_3
Mirror(M', l) → M''_3
Mirror(N', l) → N''_3
Mirror(O', l) → O''_3
Mirror(P', l) → P''_3
Mirror(Q', l) → Q''_3
Polygon(I''_3, J''_3, K''_3, L''_3, M''_3, N''_3, O''_3, P''_3, Q''_3) → poly1''_3, i''_3, j''_3, k''_3, l''_3, m''_3, n''_3, o''_3, p''_3, q''_3
Mirror(W'', l) → W'''_2
Mirror(Z'', l) → Z'''_2
Mirror(R_1, l) → W_{11}
Mirror(S_1, l) → Z_{11}
Mirror(T_1, l) → A_{12}
Mirror(U_1, l) → B_{12}
Polygon(W'''_2, Z'''_2, W_{11}, Z_{11}, A_{12}, B_{12}) → poly3'''_2, w'''_2, z'''_2, w_{11}, z_{11}, a_{13}, b_{13}
Mirror(W', l) → W''_3
Mirror(Z', l) → Z''_3
Mirror(J_1, l) → C_{12}
Mirror(K_1, l) → D_{12}
Mirror(L_1, l) → E_{12}
Mirror(M_1, l) → F_{12}
Polygon(W''_3, Z''_3, C_{12}, D_{12}, E_{12}, F_{12}) → poly3''_3, w''_3, z''_3, c_{12}, d_{12}, e_{12}, f_{12}
Length(u1) → p1
Min(p1, ((a - 6.5) * p1)) → p2
OrthogonalLine(G_{12}, b_{11}) → g_{12}
Circle(G_{12}, p2) → c_{13}
Intersect(c_{13}, g_{12}, 1) → H_{12}
Vector(G_{12}, H_{12}) → u_{10}
Translate(T''_2, u_{10}) → I_{12}
Translate(P_{10}, u_{10}) → J_{12}
Translate(Q_{10}, u_{10}) → K_{12}
Translate(R_{10}, u_{10}) → L_{12}
Translate(S_{10}, u_{10}) → M_{12}
Translate(T_{10}, u_{10}) → N_{12}
Translate(U_{10}, u_{10}) → O_{12}
Translate(V_{10}, u_{10}) → P_{12}
Translate(W_{10}, u_{10}) → Q_{12}
Translate(Z_{10}, u_{10}) → R_{12}
Translate(A_{11}, u_{10}) → S_{12}
Translate(B_{11}, u_{10}) → T_{12}
Translate(C_{11}, u_{10}) → U_{12}
Translate(S'_2, u_{10}) → V_{12}
Translate(D_{11}, u_{10}) → W_{12}
Translate(E_{11}, u_{10}) → Z_{12}
Translate(F_{11}, u_{10}) → A_{13}
Translate(G_{11}, u_{10}) → B_{13}
Translate(H_{11}, u_{10}) → C_{13}
Translate(I_{11}, u_{10}) → D_{13}
Translate(J_{11}, u_{10}) → E_{13}
Translate(K_{11}, u_{10}) → F_{13}
Translate(L_{11}, u_{10}) → G_{13}
Translate(M_{11}, u_{10}) → H_{13}
Polygon(I_{12}, J_{12}, S_{12}, T_{12}, U_{12}, V_{12}, W_{12}, Z_{12}, A_{13}, B_{13}, C_{13}, D_{13}, K_{12}, E_{13}, F_{13}, G_{13}, H_{13}, L_{12}, M_{12}, N_{12}, O_{12}, P_{12}, Q_{12}, R_{12}) → poly11, i_{12}, r_{13}, s_{14}, t_{14}, u_{13}, v_{13}, w_{12}, z_{12}, a_{14}, b_{14}, c_{14}, j_{14}, d_{13}, e_{13}, f_{13}, g_{13}, h_{13}, k_{13}, l_{13}, m_{13}, n_{13}, o_{12}, p_{14}, q_{13}
Translate(T'_3, u_{10}) → I_{13}
Translate(R'_5, u_{10}) → J_{13}
Translate(V'_5, u_{10}) → K_{13}
Translate(U'_5, u_{10}) → L_{13}
Translate(Q'_5, u_{10}) → M_{13}
Translate(P'_5, u_{10}) → N_{13}
Translate(O'_5, u_{10}) → O_{13}
Translate(N'_5, u_{10}) → P_{13}
Translate(M'_5, u_{10}) → Q_{13}
Translate(L'_5, u_{10}) → R_{13}
Translate(K'_5, u_{10}) → S_{13}
Translate(J'_5, u_{10}) → T_{13}
Translate(I'_5, u_{10}) → U_{13}
Translate(N_{11}, u_{10}) → V_{13}
Translate(W'_5, u_{10}) → W_{13}
Translate(Z'_5, u_{10}) → Z_{13}
Translate(O_{11}, u_{10}) → A_{14}
Translate(P_{11}, u_{10}) → B_{14}
Translate(Q_{11}, u_{10}) → C_{14}
Translate(R_{11}, u_{10}) → D_{14}
Translate(S_{11}, u_{10}) → E_{14}
Translate(T_{11}, u_{10}) → F_{14}
Translate(U_{11}, u_{10}) → G_{14}
Translate(V_{11}, u_{10}) → H_{14}
Polygon(I_{13}, J_{13}, S_{13}, T_{13}, U_{13}, V_{13}, W_{13}, Z_{13}, A_{14}, B_{14}, C_{14}, D_{14}, K_{13}, E_{14}, F_{14}, G_{14}, H_{14}, L_{13}, M_{13}, N_{13}, O_{13}, P_{13}, Q_{13}, R_{13}) → poly12, i_{13}, r_{14}, s_{15}, t_{15}, u_{14}, v_{14}, w_{13}, z_{13}, a_{15}, b_{15}, c_{15}, j_{15}, d_{14}, e_{14}, f_{14}, g_{14}, h_{14}, k_{14}, l_{14}, m_{14}, n_{14}, o_{13}, p_{15}, q_{14}
Translate(I'''_2, u_{10}) → I_{14}
Translate(J'''_2, u_{10}) → J_{14}
Translate(K'''_2, u_{10}) → K_{14}
Translate(L'''_2, u_{10}) → L_{14}
Translate(M'''_2, u_{10}) → M_{14}
Translate(N'''_2, u_{10}) → N_{14}
Translate(O'''_2, u_{10}) → O_{14}
Translate(P'''_2, u_{10}) → P_{14}
Translate(Q'''_2, u_{10}) → Q_{14}
Polygon(I_{14}, J_{14}, K_{14}, L_{14}, M_{14}, N_{14}, O_{14}, P_{14}, Q_{14}) → poly13, i_{14}, j_{16}, k_{15}, l_{15}, m_{15}, n_{15}, o_{14}, p_{16}, q_{15}
Translate(I''_3, u_{10}) → R_{14}
Translate(J''_3, u_{10}) → S_{14}
Translate(K''_3, u_{10}) → T_{14}
Translate(L''_3, u_{10}) → U_{14}
Translate(M''_3, u_{10}) → V_{14}
Translate(N''_3, u_{10}) → W_{14}
Translate(O''_3, u_{10}) → Z_{14}
Translate(P''_3, u_{10}) → A_{15}
Translate(Q''_3, u_{10}) → B_{15}
Polygon(R_{14}, S_{14}, T_{14}, U_{14}, V_{14}, W_{14}, Z_{14}, A_{15}, B_{15}) → poly14, r_{15}, s_{16}, t_{16}, u_{15}, v_{15}, w_{14}, z_{14}, a_{16}, b_{16}
Translate(W''_3, u_{10}) → C_{15}
Translate(Z''_3, u_{10}) → D_{15}
Translate(C_{12}, u_{10}) → E_{15}
Translate(D_{12}, u_{10}) → F_{15}
Translate(E_{12}, u_{10}) → G_{15}
Translate(F_{12}, u_{10}) → H_{15}
Polygon(C_{15}, D_{15}, E_{15}, F_{15}, G_{15}, H_{15}) → poly15, c_{16}, d_{15}, e_{15}, f_{15}, g_{15}, h_{15}
Translate(W'''_2, u_{10}) → I_{15}
Translate(Z'''_2, u_{10}) → J_{15}
Translate(W_{11}, u_{10}) → K_{15}
Translate(Z_{11}, u_{10}) → L_{15}
Translate(A_{12}, u_{10}) → M_{15}
Translate(B_{12}, u_{10}) → N_{15}
Polygon(I_{15}, J_{15}, K_{15}, L_{15}, M_{15}, N_{15}) → poly16, i_{15}, j_{17}, k_{16}, l_{16}, m_{16}, n_{16}
Mirror(V_1, l) → O_{15}
Mirror(W_1, l) → P_{15}
Mirror(Z_1, l) → Q_{15}
Mirror(A_2, l) → R_{15}
Polygon(O_{15}, P_{15}, Q_{15}, R_{15}) → poly4'''_2, o_{15}, p_{17}, q_{16}, r_{16}
Mirror(N_1, l) → S_{15}
Mirror(O_1, l) → T_{15}
Mirror(P_1, l) → U_{15}
Mirror(Q_1, l) → V_{15}
Polygon(S_{15}, T_{15}, U_{15}, V_{15}) → poly4''_3, s_{17}, t_{17}, u_{16}, v_{16}
Translate(S_{15}, u_{10}) → W_{15}
Translate(T_{15}, u_{10}) → Z_{15}
Translate(U_{15}, u_{10}) → A_{16}
Translate(V_{15}, u_{10}) → B_{16}
Polygon(W_{15}, Z_{15}, A_{16}, B_{16}) → poly17, w_{15}, z_{15}, a_{17}, b_{17}
Translate(O_{15}, u_{10}) → C_{16}
Translate(P_{15}, u_{10}) → D_{16}
Translate(Q_{15}, u_{10}) → E_{16}
Translate(R_{15}, u_{10}) → F_{16}
Polygon(C_{16}, D_{16}, E_{16}, F_{16}) → poly18, c_{17}, d_{16}, e_{16}, f_{16}
Vector(S, T'') → w_{16}
Vector(S, V_{12}) → z_{16}
Intersect(f, b_{11}) → G_{16}
Vector(S, G_{16}) → g_{16}
Vector(S, T) → h_{16}
Vector(H_{16}, I_{16}) → i_{16}
Vector(H_{16}, J_{16}) → u_{17}
Mirror(U'', l) → U'''_2
Mirror(V'', l) → V'''_2
Mirror(R'', l) → R'''_3
Polygon(U'''_2, V'''_2, R'''_3) → poly2'''_2, r'''_3, u'''_2, v'''_2
Mirror(U', l) → U''_3
Mirror(V', l) → V''_3
Mirror(R', l) → R''_3
Polygon(U''_3, V''_3, R''_3) → poly2''_3, r''_3, u''_3, v''_3
Translate(U''_3, u_{10}) → K_{16}
Translate(V''_3, u_{10}) → L_{16}
Translate(R''_3, u_{10}) → M_{16}
Polygon(K_{16}, L_{16}, M_{16}) → poly19, m_{17}, k_{17}, l_{17}
Translate(R'''_3, u_{10}) → N_{16}
Translate(U'''_2, u_{10}) → O_{16}
Segment(N_{16}, O_{16}) → d_{17}
Translate(U'''_2, u_{10}) → P_{16}
Translate(V'''_2, u_{10}) → Q_{16}
Translate(R'''_3, u_{10}) → R_{16}
Polygon(P_{16}, Q_{16}, R_{16}) → poly20, r_{17}, p_{18}, q_{17}

AI Drawing Prompt Reference

Draw an Escher-style geometric graph showcasing symmetry and transformation. Start by creating several line segments and intersection points, then use vector translation and reflection to form multiple polygons, and finally combine them into a complex pattern to demonstrate the beauty of geometric transformations.

The prompt above was compiled from the original drawing commands and is for reference only.