Escher-like “Seahorse Dance”: a Transform Geometry Construction

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2023-03-22 22:50

In collections geometriadinamica.es

This example demonstrates an Escher-inspired geometric pattern where a basic motif is turned into a “dancing/entwined” visual effect by applying rotation, translation, and mirror transformations and then assembling the results into a coherent design. The key mathematical ideas are geometric transformations (Rotate, Translate, Mirror), construction of points and directions via vectors (Vector, Point), and using intersection and midpoints to enforce symmetry and controlled positioning (Intersect, Midpoint). Finally, polygonal pieces are used to form the visible contours (Polygon). From the construction summary, the build relies on commands: If (conditional choices), Line (constructing lines), Intersect (computing intersection points), Midpoint (taking midpoints), Rotate (rotations), Polygon (building polygonal shapes), Point (points), Vector (vectors), Translate (translations), Segment (segments), and Mirror (reflections). The involved objects include several construction points (e.g., A, B, C, D…) and auxiliary variables (e.g., d1–d6, dif) to control centers, directions, and assembly. Suitable for secondary-school geometry enrichment and classroom visualization of “transformation-driven pattern generation,” and also good for clubs or challenges focused on algorithmic geometric constructions.

GeoGebra Commands & Parameters

If(a < 1, a, 1) → d1
If(a < 1, 0, If[a < 2, a - 1, 1]) → d2
If(a < 2.35, 0, If[a < 3.35, a - 2.35, 1]) → d3
If(a < 3.35, 0, If[a < 4.35, a - 3.35, 1]) → d4
If(a < 4.35, 0, If[a < 5.35, a - 4.35, 1]) → d5
If(a < 5.5, 0, a - 5.5) → d6
Line(C, D) → b
Line(E, F) → d
Line(G, b) → e
Line(H, d) → f
Intersect(d, e) → I
Intersect(b, f) → J
Intersect(e, f) → K
Midpoint(E, J) → L
Midpoint(I, K) → M
Rotate(L, (d1 * 180°), L) → L'
Rotate(N, (d1 * 180°), L) → N'
Rotate(O, (d1 * 180°), L) → O'
Rotate(P, (d1 * 180°), L) → P'
Rotate(Q, (d1 * 180°), L) → Q'
Rotate(R, (d1 * 180°), L) → R'
Rotate(S, (d1 * 180°), L) → S'
Rotate(T, (d1 * 180°), L) → T'
Rotate(J, (d1 * 180°), L) → J'
Polygon(L', N', O', P', Q', R', S', T', J') → poly1', l', n', o', p', q', r', s', t', j'
Point(e) → V
Rotate(M, ((-d1) * 180°), M) → M'
Rotate(U, ((-d1) * 180°), M) → U'
Rotate(V, ((-d1) * 180°), M) → V'
Polygon(M', U', V') → poly1'_1, v', m', u'
Point(d) → W
Point(e) → E_1
Point(e) → F_1
Point(d) → J_1
Point(d) → K_1
Point(e) → N_1
Rotate(W, (d1 * 180°), M) → W'
Rotate(Z, (d1 * 180°), M) → Z'
Rotate(A_1, (d1 * 180°), M) → O_1
Rotate(B_1, (d1 * 180°), M) → P_1
Rotate(C_1, (d1 * 180°), M) → Q_1
Rotate(D_1, (d1 * 180°), M) → R_1
Rotate(E_1, (d1 * 180°), M) → S_1
Rotate(F_1, (d1 * 180°), M) → T_1
Rotate(G_1, (d1 * 180°), M) → U_1
Rotate(H_1, (d1 * 180°), M) → V_1
Rotate(I_1, (d1 * 180°), M) → W_1
Rotate(J_1, (d1 * 180°), M) → Z_1
Rotate(K_1, (d1 * 180°), M) → A_2
Rotate(L_1, (d1 * 180°), M) → B_2
Rotate(M_1, (d1 * 180°), M) → C_2
Rotate(N_1, (d1 * 180°), M) → D_2
Rotate(I, (d1 * 180°), M) → I'
Polygon(W', Z', W_1, Z_1, A_2, B_2, C_2, D_2, I', O_1, P_1, Q_1, R_1, S_1, T_1, U_1, V_1) → poly1'_2, w', v_1, w_1, z_1, a_2, b_2, c_2, d_2, i', z', o_1, p_1, q_1, r_1, s_1, t_1, u_1
Point(f) → E_2
Point(f) → F_2
Point(e) → I_2
Point(e) → J_2
Rotate(E_2, ((-d1) * 180°), K) → M_2
Rotate(F_2, ((-d1) * 180°), K) → N_2
Rotate(G_2, ((-d1) * 180°), K) → O_2
Rotate(H_2, ((-d1) * 180°), K) → P_2
Rotate(I_2, ((-d1) * 180°), K) → Q_2
Rotate(J_2, ((-d1) * 180°), K) → R_2
Rotate(K_2, ((-d1) * 180°), K) → S_2
Rotate(L_2, ((-d1) * 180°), K) → T_2
Polygon(M_2, N_2, O_2, P_2, Q_2, R_2, S_2, T_2) → poly1'_3, m_2, n_2, o_2, p_2, q_2, r_2, s_2, t_2
Vector(E, J) → u
Point(d) → U_2
Point(f) → V_2
Translate(K_1, v_{19}) → W_2
Translate(L_1, v_{19}) → Z_2
Translate(M_1, v_{19}) → A_3
Translate(N_1, v_{19}) → B_3
Translate(F_1, v_{19}) → C_3
Translate(G_1, v_{19}) → D_3
Translate(H_1, v_{19}) → E_3
Translate(I_1, v_{19}) → F_3
Translate(J_1, v_{19}) → G_3
Polygon(W_2, Z_2, A_3, B_3, C_3, D_3, E_3, F_3, G_3) → poly2', w_2, z_2, a_3, b_3, c_3, d_3, e_3, f_3, g_3
Translate(W, v_{19}) → W'_1
Translate(Z, v_{19}) → Z'_1
Translate(U_2, v_{19}) → H_3
Polygon(W'_1, Z'_1, H_3) → poly1'_4, h_3, w'_1, z'_1
Translate(J, g) → J'_1
Translate(T, g) → T'_1
Translate(V_2, g) → I_3
Polygon(J'_1, T'_1, I_3) → poly3', i_3, j'_1, t'_1
Polygon(E, L, E_2, L_2, K_2, J_2, I_2, H_2, G_2, F_2, K, V, N, U, M, E_1, D_1, C_1, B_1, A_1, Z, U_2, O, P, Q, R, S, T, V_2) → poly1, e_1, v_2, e_2, l_2, k_2, j_2, i_2, h_2, g_2, f_2, k, l, v_3, u_2, m, e_4, d_1, c_1, b_1, a_1, z, u_3, n, o, p, q, r, s, t
Rotate(E, (d3 * 180°), L) → E'
Rotate(L, (d3 * 180°), L) → L'_1
Rotate(N, (d3 * 180°), L) → N'_1
Rotate(O, (d3 * 180°), L) → O'_1
Rotate(P, (d3 * 180°), L) → P'_1
Rotate(Q, (d3 * 180°), L) → Q'_1
Rotate(R, (d3 * 180°), L) → R'_1
Rotate(S, (d3 * 180°), L) → S'_1
Rotate(T, (d3 * 180°), L) → T'_2
Rotate(V_2, (d3 * 180°), L) → J_3
Rotate(E_2, (d3 * 180°), L) → K_3
Rotate(L_2, (d3 * 180°), L) → L_3
Rotate(K_2, (d3 * 180°), L) → M_3
Rotate(J_2, (d3 * 180°), L) → N_3
Rotate(I_2, (d3 * 180°), L) → O_3
Rotate(H_2, (d3 * 180°), L) → P_3
Rotate(G_2, (d3 * 180°), L) → Q_3
Rotate(F_2, (d3 * 180°), L) → R_3
Rotate(K, (d3 * 180°), L) → K'
Rotate(V, (d3 * 180°), L) → V'_1
Rotate(U, (d3 * 180°), L) → U'_1
Rotate(M, (d3 * 180°), L) → M'_1
Rotate(E_1, (d3 * 180°), L) → S_3
Rotate(D_1, (d3 * 180°), L) → T_3
Rotate(C_1, (d3 * 180°), L) → U_3
Rotate(B_1, (d3 * 180°), L) → V_3
Rotate(A_1, (d3 * 180°), L) → W_3
Rotate(Z, (d3 * 180°), L) → Z'_2
Rotate(U_2, (d3 * 180°), L) → Z_3
Polygon(E', L'_1, K_3, L_3, M_3, N_3, O_3, P_3, Q_3, R_3, K', V'_1, N'_1, U'_1, M'_1, S_3, T_3, U_3, V_3, W_3, Z'_2, Z_3, O'_1, P'_1, Q'_1, R'_1, S'_1, T'_2, J_3) → poly1'_5, e', j_3, k_3, l_3, m_3, n_3, o_3, p_3, q_3, r_3, k', l'_1, v'_1, u'_1, m'_1, s_3, t_3, u_4, v_4, w_3, z'_2, z_3, n'_1, o'_1, p'_1, q'_1, r'_1, s'_1, t'_2
Rotate(L', (d3 * 180°), L) → L''
Rotate(N', (d3 * 180°), L) → N''
Rotate(O', (d3 * 180°), L) → O''
Rotate(P', (d3 * 180°), L) → P''
Rotate(Q', (d3 * 180°), L) → Q''
Rotate(R', (d3 * 180°), L) → R''
Rotate(S', (d3 * 180°), L) → S''
Rotate(T', (d3 * 180°), L) → T''
Rotate(J', (d3 * 180°), L) → J''
Polygon(L'', N'', O'', P'', Q'', R'', S'', T'', J'') → poly1'', l'', n'', o'', p'', q'', r'', s'', t'', j''
Rotate(J'_1, (d3 * 180°), L) → A_4
Rotate(T'_1, (d3 * 180°), L) → B_4
Rotate(I_3, (d3 * 180°), L) → C_4
Polygon(A_4, B_4, C_4) → poly3'', c_4, a_4, b_4
Rotate(W', (d3 * 180°), L) → W''
Rotate(Z', (d3 * 180°), L) → Z''
Rotate(O_1, (d3 * 180°), L) → D_4
Rotate(P_1, (d3 * 180°), L) → E_4
Rotate(Q_1, (d3 * 180°), L) → F_4
Rotate(R_1, (d3 * 180°), L) → G_4
Rotate(S_1, (d3 * 180°), L) → H_4
Rotate(T_1, (d3 * 180°), L) → I_4
Rotate(U_1, (d3 * 180°), L) → J_4
Rotate(V_1, (d3 * 180°), L) → K_4
Rotate(W_1, (d3 * 180°), L) → L_4
Rotate(Z_1, (d3 * 180°), L) → M_4
Rotate(A_2, (d3 * 180°), L) → N_4
Rotate(B_2, (d3 * 180°), L) → O_4
Rotate(C_2, (d3 * 180°), L) → P_4
Rotate(D_2, (d3 * 180°), L) → Q_4
Rotate(I', (d3 * 180°), L) → I''
Polygon(W'', Z'', L_4, M_4, N_4, O_4, P_4, Q_4, I'', D_4, E_4, F_4, G_4, H_4, I_4, J_4, K_4) → poly2, w'', k_4, l_4, m_4, n_4, o_4, p_4, q_4, i'', z'', d_4, e_5, f_4, g_4, h_4, i_4, j_4
Rotate(W_2, (d3 * 180°), L) → R_4
Rotate(Z_2, (d3 * 180°), L) → S_4
Rotate(A_3, (d3 * 180°), L) → T_4
Rotate(B_3, (d3 * 180°), L) → U_4
Rotate(C_3, (d3 * 180°), L) → V_4
Rotate(D_3, (d3 * 180°), L) → W_4
Rotate(E_3, (d3 * 180°), L) → Z_4
Rotate(F_3, (d3 * 180°), L) → A_5
Rotate(G_3, (d3 * 180°), L) → B_5
Polygon(R_4, S_4, T_4, U_4, V_4, W_4, Z_4, A_5, B_5) → poly2'', r_4, s_4, t_4, u_5, v_5, w_4, z_4, a_5, b_5
Rotate(M_2, (d3 * 180°), L) → C_5
Rotate(N_2, (d3 * 180°), L) → D_5
Rotate(O_2, (d3 * 180°), L) → E_5
Rotate(P_2, (d3 * 180°), L) → F_5
Rotate(Q_2, (d3 * 180°), L) → G_5
Rotate(R_2, (d3 * 180°), L) → H_5
Rotate(S_2, (d3 * 180°), L) → I_5
Rotate(T_2, (d3 * 180°), L) → J_5
Polygon(C_5, D_5, E_5, F_5, G_5, H_5, I_5, J_5) → poly3, c_5, d_5, e_6, f_5, g_5, h_5, i_5, j_5
Rotate(M', (d3 * 180°), L) → M''
Rotate(U', (d3 * 180°), L) → U''
Rotate(V', (d3 * 180°), L) → V''
Polygon(M'', U'', V'') → poly4, v'', m'', u''
Rotate(W'_1, (d3 * 180°), L) → K_5
Rotate(Z'_1, (d3 * 180°), L) → L_5
Rotate(H_3, (d3 * 180°), L) → M_5
Polygon(K_5, L_5, M_5) → poly5, m_5, k_5, l_5
Rotate(E, (d4 * 180°), M) → E'_1
Rotate(L, (d4 * 180°), M) → L'_2
Rotate(N, (d4 * 180°), M) → N'_2
Rotate(O, (d4 * 180°), M) → O'_2
Rotate(P, (d4 * 180°), M) → P'_2
Rotate(Q, (d4 * 180°), M) → Q'_2
Rotate(R, (d4 * 180°), M) → R'_2
Rotate(S, (d4 * 180°), M) → S'_2
Rotate(T, (d4 * 180°), M) → T'_3
Rotate(V_2, (d4 * 180°), M) → N_5
Rotate(E_2, (d4 * 180°), M) → O_5
Rotate(L_2, (d4 * 180°), M) → P_5
Rotate(K_2, (d4 * 180°), M) → Q_5
Rotate(J_2, (d4 * 180°), M) → R_5
Rotate(I_2, (d4 * 180°), M) → S_5
Rotate(H_2, (d4 * 180°), M) → T_5
Rotate(G_2, (d4 * 180°), M) → U_5
Rotate(F_2, (d4 * 180°), M) → V_5
Rotate(K, (d4 * 180°), M) → K'_1
Rotate(V, (d4 * 180°), M) → V'_2
Rotate(U, (d4 * 180°), M) → U'_2
Rotate(M, (d4 * 180°), M) → M'_2
Rotate(E_1, (d4 * 180°), M) → W_5
Rotate(D_1, (d4 * 180°), M) → Z_5
Rotate(C_1, (d4 * 180°), M) → A_6
Rotate(B_1, (d4 * 180°), M) → B_6
Rotate(A_1, (d4 * 180°), M) → C_6
Rotate(Z, (d4 * 180°), M) → Z'_3
Rotate(U_2, (d4 * 180°), M) → D_6
Polygon(E'_1, L'_2, O_5, P_5, Q_5, R_5, S_5, T_5, U_5, V_5, K'_1, V'_2, N'_2, U'_2, M'_2, W_5, Z_5, A_6, B_6, C_6, Z'_3, D_6, O'_2, P'_2, Q'_2, R'_2, S'_2, T'_3, N_5) → poly1'_6, e'_1, n_5, o_5, p_5, q_5, r_5, s_5, t_5, u_6, v_6, k'_1, l'_2, v'_2, u'_2, m'_2, w_5, z_5, a_6, b_6, c_6, z'_3, d_6, n'_2, o'_2, p'_2, q'_2, r'_2, s'_2, t'_3
Rotate(L', (d4 * 180°), M) → L''_1
Rotate(N', (d4 * 180°), M) → N''_1
Rotate(O', (d4 * 180°), M) → O''_1
Rotate(P', (d4 * 180°), M) → P''_1
Rotate(Q', (d4 * 180°), M) → Q''_1
Rotate(R', (d4 * 180°), M) → R''_1
Rotate(S', (d4 * 180°), M) → S''_1
Rotate(T', (d4 * 180°), M) → T''_1
Rotate(J', (d4 * 180°), M) → J''_1
Polygon(L''_1, N''_1, O''_1, P''_1, Q''_1, R''_1, S''_1, T''_1, J''_1) → poly1''_1, l''_1, n''_1, o''_1, p''_1, q''_1, r''_1, s''_1, t''_1, j''_1
Rotate(J'_1, (d4 * 180°), M) → E_6
Rotate(T'_1, (d4 * 180°), M) → F_6
Rotate(I_3, (d4 * 180°), M) → G_6
Polygon(E_6, F_6, G_6) → poly3''_1, g_6, e_7, f_6
Rotate(M_2, (d4 * 180°), M) → H_6
Rotate(N_2, (d4 * 180°), M) → I_6
Rotate(O_2, (d4 * 180°), M) → J_6
Rotate(P_2, (d4 * 180°), M) → K_6
Rotate(Q_2, (d4 * 180°), M) → L_6
Rotate(R_2, (d4 * 180°), M) → M_6
Rotate(S_2, (d4 * 180°), M) → N_6
Rotate(T_2, (d4 * 180°), M) → O_6
Polygon(H_6, I_6, J_6, K_6, L_6, M_6, N_6, O_6) → poly6, h_6, i_6, j_6, k_6, l_6, m_6, n_6, o_6
Rotate(W', (d4 * 180°), M) → W''_1
Rotate(Z', (d4 * 180°), M) → Z''_1
Rotate(O_1, (d4 * 180°), M) → P_6
Rotate(P_1, (d4 * 180°), M) → Q_6
Rotate(Q_1, (d4 * 180°), M) → R_6
Rotate(R_1, (d4 * 180°), M) → S_6
Rotate(S_1, (d4 * 180°), M) → T_6
Rotate(T_1, (d4 * 180°), M) → U_6
Rotate(U_1, (d4 * 180°), M) → V_6
Rotate(V_1, (d4 * 180°), M) → W_6
Rotate(W_1, (d4 * 180°), M) → Z_6
Rotate(Z_1, (d4 * 180°), M) → A_7
Rotate(A_2, (d4 * 180°), M) → B_7
Rotate(B_2, (d4 * 180°), M) → C_7
Rotate(C_2, (d4 * 180°), M) → D_7
Rotate(D_2, (d4 * 180°), M) → E_7
Rotate(I', (d4 * 180°), M) → I''_1
Polygon(W''_1, Z''_1, Z_6, A_7, B_7, C_7, D_7, E_7, I''_1, P_6, Q_6, R_6, S_6, T_6, U_6, V_6, W_6) → poly7, w''_1, w_6, z_6, a_7, b_7, c_7, d_7, e_8, i''_1, z''_1, p_6, q_6, r_6, s_6, t_6, u_7, v_7
Rotate(W_2, (d4 * 180°), M) → F_7
Rotate(Z_2, (d4 * 180°), M) → G_7
Rotate(A_3, (d4 * 180°), M) → H_7
Rotate(B_3, (d4 * 180°), M) → I_7
Rotate(C_3, (d4 * 180°), M) → J_7
Rotate(D_3, (d4 * 180°), M) → K_7
Rotate(E_3, (d4 * 180°), M) → L_7
Rotate(F_3, (d4 * 180°), M) → M_7
Rotate(G_3, (d4 * 180°), M) → N_7
Polygon(F_7, G_7, H_7, I_7, J_7, K_7, L_7, M_7, N_7) → poly2''_1, f_7, g_7, h_7, i_7, j_7, k_7, l_7, m_7, n_7
Rotate(M', (d4 * 180°), M) → M''_1
Rotate(U', (d4 * 180°), M) → U''_1
Rotate(V', (d4 * 180°), M) → V''_1
Polygon(M''_1, U''_1, V''_1) → poly8, v''_1, m''_1, u''_1
Rotate(W'_1, (d4 * 180°), M) → O_7
Rotate(Z'_1, (d4 * 180°), M) → P_7
Rotate(H_3, (d4 * 180°), M) → Q_7
Polygon(O_7, P_7, Q_7) → poly9, q_7, o_7, p_7
Translate(E', w) → E''
Translate(L'_1, w) → R_7
Translate(N'_1, w) → S_7
Translate(O'_1, w) → T_7
Translate(P'_1, w) → U_7
Translate(Q'_1, w) → V_7
Translate(R'_1, w) → W_7
Translate(S'_1, w) → Z_7
Translate(T'_2, w) → A_8
Translate(J_3, w) → B_8
Translate(K_3, w) → C_8
Translate(L_3, w) → D_8
Translate(M_3, w) → E_8
Translate(N_3, w) → F_8
Translate(O_3, w) → G_8
Translate(P_3, w) → H_8
Translate(Q_3, w) → I_8
Translate(R_3, w) → J_8
Translate(K', w) → K''
Translate(V'_1, w) → K_8
Translate(U'_1, w) → L_8
Translate(M'_1, w) → M_8
Translate(S_3, w) → N_8
Translate(T_3, w) → O_8
Translate(U_3, w) → P_8
Translate(V_3, w) → Q_8
Translate(W_3, w) → R_8
Translate(Z'_2, w) → S_8
Translate(Z_3, w) → T_8
Polygon(E'', R_7, C_8, D_8, E_8, F_8, G_8, H_8, I_8, J_8, K'', K_8, S_7, L_8, M_8, N_8, O_8, P_8, Q_8, R_8, S_8, T_8, T_7, U_7, V_7, W_7, Z_7, A_8, B_8) → poly10, e'', b_8, c_8, d_8, e_9, f_8, g_8, h_8, i_8, j_8, k'', r_7, k_8, l_8, m_8, n_8, o_8, p_8, q_8, r_8, s_8, t_8, s_7, t_7, u_8, v_8, w_7, z_7, a_8
Translate(L'', w) → L'''
Translate(N'', w) → N'''
Translate(O'', w) → O'''
Translate(P'', w) → P'''
Translate(Q'', w) → Q'''
Translate(R'', w) → R'''
Translate(S'', w) → S'''
Translate(T'', w) → T'''
Translate(J'', w) → J'''
Polygon(L''', N''', O''', P''', Q''', R''', S''', T''', J''') → poly1''', l''', n''', o''', p''', q''', r''', s''', t''', j'''
Translate(A_4, w) → U_8
Translate(B_4, w) → V_8
Segment(U_8, V_8) → h
Translate(A_4, w) → W_8
Translate(B_4, w) → Z_8
Translate(C_4, w) → A_9
Polygon(W_8, Z_8, A_9) → poly3''', a_9, w_8, z_8
Translate(W'', w) → W'''
Translate(Z'', w) → Z'''
Translate(D_4, w) → B_9
Translate(E_4, w) → C_9
Translate(F_4, w) → D_9
Translate(G_4, w) → E_9
Translate(H_4, w) → F_9
Translate(I_4, w) → G_9
Translate(J_4, w) → H_9
Translate(K_4, w) → I_9
Translate(L_4, w) → J_9
Translate(M_4, w) → K_9
Translate(N_4, w) → L_9
Translate(O_4, w) → M_9
Translate(P_4, w) → N_9
Translate(Q_4, w) → O_9
Translate(I'', w) → I'''
Polygon(W''', Z''', J_9, K_9, L_9, M_9, N_9, O_9, I''', B_9, C_9, D_9, E_9, F_9, G_9, H_9, I_9) → poly2'_1, w''', i_9, j_9, k_9, l_9, m_9, n_9, o_9, i''', z''', b_9, c_9, d_9, e_{10}, f_9, g_9, h_9
Translate(C_5, w) → P_9
Translate(D_5, w) → Q_9
Translate(E_5, w) → R_9
Translate(F_5, w) → S_9
Translate(G_5, w) → T_9
Translate(H_5, w) → U_9
Translate(I_5, w) → V_9
Translate(J_5, w) → W_9
Polygon(P_9, Q_9, R_9, S_9, T_9, U_9, V_9, W_9) → poly3'_1, p_9, q_9, r_9, s_9, t_9, u_9, v_9, w_9
Translate(R_4, w) → Z_9
Translate(S_4, w) → A_{10}
Translate(T_4, w) → B_{10}
Translate(U_4, w) → C_{10}
Translate(V_4, w) → D_{10}
Translate(W_4, w) → E_{10}
Translate(Z_4, w) → F_{10}
Translate(A_5, w) → G_{10}
Translate(B_5, w) → H_{10}
Polygon(Z_9, A_{10}, B_{10}, C_{10}, D_{10}, E_{10}, F_{10}, G_{10}, H_{10}) → poly2''', z_9, a_{10}, b_{10}, c_{10}, d_{10}, e_{11}, f_{10}, g_{10}, h_{10}
Translate(M'', w) → M'''
Translate(U'', w) → U'''
Translate(V'', w) → V'''
Polygon(M''', U''', V''') → poly4', v''', m''', u'''
Translate(L', w) → L''_2
Translate(N', w) → N''_2
Translate(O', w) → O''_2
Translate(P', w) → P''_2
Translate(Q', w) → Q''_2
Translate(R', w) → R''_2
Translate(S', w) → S''_2
Translate(T', w) → T''_2
Translate(J', w) → J''_2
Polygon(L''_2, N''_2, O''_2, P''_2, Q''_2, R''_2, S''_2, T''_2, J''_2) → poly1''_2, l''_2, n''_2, o''_2, p''_2, q''_2, r''_2, s''_2, t''_2, j''_2
Translate(J'_1, w) → I_{10}
Translate(T'_1, w) → J_{10}
Translate(I_3, w) → K_{10}
Polygon(I_{10}, J_{10}, K_{10}) → poly3''_2, k_{10}, i_{10}, j_{10}
Translate(E, w) → E'_2
Translate(L, w) → L'_3
Translate(N, w) → N'_3
Translate(O, w) → O'_3
Translate(P, w) → P'_3
Translate(Q, w) → Q'_3
Translate(R, w) → R'_3
Translate(S, w) → S'_3
Translate(T, w) → T'_4
Translate(V_2, w) → L_{10}
Translate(E_2, w) → M_{10}
Translate(L_2, w) → N_{10}
Translate(K_2, w) → O_{10}
Translate(J_2, w) → P_{10}
Translate(I_2, w) → Q_{10}
Translate(H_2, w) → R_{10}
Translate(G_2, w) → S_{10}
Translate(F_2, w) → T_{10}
Translate(K, w) → K'_2
Translate(V, w) → V'_3
Translate(U, w) → U'_3
Translate(M, w) → M'_3
Translate(E_1, w) → U_{10}
Translate(D_1, w) → V_{10}
Translate(C_1, w) → W_{10}
Translate(B_1, w) → Z_{10}
Translate(A_1, w) → A_{11}
Translate(Z, w) → Z'_4
Translate(U_2, w) → B_{11}
Polygon(E'_2, L'_3, M_{10}, N_{10}, O_{10}, P_{10}, Q_{10}, R_{10}, S_{10}, T_{10}, K'_2, V'_3, N'_3, U'_3, M'_3, U_{10}, V_{10}, W_{10}, Z_{10}, A_{11}, Z'_4, B_{11}, O'_3, P'_3, Q'_3, R'_3, S'_3, T'_4, L_{10}) → poly1'_7, e'_2, l_{10}, m_{10}, n_{10}, o_{10}, p_{10}, q_{10}, r_{10}, s_{10}, t_{10}, k'_2, l'_3, v'_3, u'_3, m'_3, u_{10}, v_{10}, w_{10}, z_{10}, a_{11}, z'_4, b_{11}, n'_3, o'_3, p'_3, q'_3, r'_3, s'_3, t'_4
Translate(W'_1, w) → C_{11}
Translate(Z'_1, w) → D_{11}
Translate(H_3, w) → E_{11}
Polygon(C_{11}, D_{11}, E_{11}) → poly11, e_{12}, c_{11}, d_{11}
Translate(W', w) → W''_2
Translate(Z', w) → Z''_2
Translate(O_1, w) → F_{11}
Translate(P_1, w) → G_{11}
Translate(Q_1, w) → H_{11}
Translate(R_1, w) → I_{11}
Translate(S_1, w) → J_{11}
Translate(T_1, w) → K_{11}
Translate(U_1, w) → L_{11}
Translate(V_1, w) → M_{11}
Translate(W_1, w) → N_{11}
Translate(Z_1, w) → O_{11}
Translate(A_2, w) → P_{11}
Translate(B_2, w) → Q_{11}
Translate(C_2, w) → R_{11}
Translate(D_2, w) → S_{11}
Translate(I', w) → I''_2
Polygon(W''_2, Z''_2, N_{11}, O_{11}, P_{11}, Q_{11}, R_{11}, S_{11}, I''_2, F_{11}, G_{11}, H_{11}, I_{11}, J_{11}, K_{11}, L_{11}, M_{11}) → poly12, w''_2, m_{11}, n_{11}, o_{11}, p_{11}, q_{11}, r_{11}, s_{11}, i''_2, z''_2, f_{11}, g_{11}, h_{11}, i_{11}, j_{11}, k_{11}, l_{11}
Translate(W_2, w) → T_{11}
Translate(Z_2, w) → U_{11}
Translate(A_3, w) → V_{11}
Translate(B_3, w) → W_{11}
Translate(C_3, w) → Z_{11}
Translate(D_3, w) → A_{12}
Translate(E_3, w) → B_{12}
Translate(F_3, w) → C_{12}
Translate(G_3, w) → D_{12}
Polygon(T_{11}, U_{11}, V_{11}, W_{11}, Z_{11}, A_{12}, B_{12}, C_{12}, D_{12}) → poly2''_2, t_{11}, u_{11}, v_{11}, w_{11}, z_{11}, a_{12}, b_{12}, c_{12}, d_{12}
Translate(M_2, w) → E_{12}
Translate(N_2, w) → F_{12}
Translate(O_2, w) → G_{12}
Translate(P_2, w) → H_{12}
Translate(Q_2, w) → I_{12}
Translate(R_2, w) → J_{12}
Translate(S_2, w) → K_{12}
Translate(T_2, w) → L_{12}
Polygon(E_{12}, F_{12}, G_{12}, H_{12}, I_{12}, J_{12}, K_{12}, L_{12}) → poly13, e_{13}, f_{12}, g_{12}, h_{12}, i_{12}, j_{12}, k_{12}, l_{12}
Translate(F_7, w) → M_{12}
Translate(G_7, w) → N_{12}
Translate(H_7, w) → O_{12}
Translate(I_7, w) → P_{12}
Translate(J_7, w) → Q_{12}
Translate(K_7, w) → R_{12}
Translate(L_7, w) → S_{12}
Translate(M_7, w) → T_{12}
Translate(N_7, w) → U_{12}
Polygon(M_{12}, N_{12}, O_{12}, P_{12}, Q_{12}, R_{12}, S_{12}, T_{12}, U_{12}) → poly14, m_{12}, n_{12}, o_{12}, p_{12}, q_{12}, r_{12}, s_{12}, t_{12}, u_{12}
Translate(H_6, w) → V_{12}
Translate(I_6, w) → W_{12}
Translate(J_6, w) → Z_{12}
Translate(K_6, w) → A_{13}
Translate(L_6, w) → B_{13}
Translate(M_6, w) → C_{13}
Translate(N_6, w) → D_{13}
Translate(O_6, w) → E_{13}
Polygon(V_{12}, W_{12}, Z_{12}, A_{13}, B_{13}, C_{13}, D_{13}, E_{13}) → poly6', v_{12}, w_{12}, z_{12}, a_{13}, b_{13}, c_{13}, d_{13}, e_{14}
Translate(W''_1, w) → F_{13}
Translate(Z''_1, w) → G_{13}
Translate(P_6, w) → H_{13}
Translate(Q_6, w) → I_{13}
Translate(R_6, w) → J_{13}
Translate(S_6, w) → K_{13}
Translate(T_6, w) → L_{13}
Translate(U_6, w) → M_{13}
Translate(V_6, w) → N_{13}
Translate(W_6, w) → O_{13}
Translate(Z_6, w) → P_{13}
Translate(A_7, w) → Q_{13}
Translate(B_7, w) → R_{13}
Translate(C_7, w) → S_{13}
Translate(D_7, w) → T_{13}
Translate(E_7, w) → U_{13}
Translate(I''_1, w) → V_{13}
Polygon(F_{13}, G_{13}, P_{13}, Q_{13}, R_{13}, S_{13}, T_{13}, U_{13}, V_{13}, H_{13}, I_{13}, J_{13}, K_{13}, L_{13}, M_{13}, N_{13}, O_{13}) → poly7', f_{13}, o_{13}, p_{13}, q_{13}, r_{13}, s_{13}, t_{13}, u_{13}, v_{13}, g_{13}, h_{13}, i_{13}, j_{13}, k_{13}, l_{13}, m_{13}, n_{13}
Translate(E'_1, w) → W_{13}
Translate(L'_2, w) → Z_{13}
Translate(N'_2, w) → A_{14}
Translate(O'_2, w) → B_{14}
Translate(P'_2, w) → C_{14}
Translate(Q'_2, w) → D_{14}
Translate(R'_2, w) → E_{14}
Translate(S'_2, w) → F_{14}
Translate(T'_3, w) → G_{14}
Translate(N_5, w) → H_{14}
Translate(O_5, w) → I_{14}
Translate(P_5, w) → J_{14}
Translate(Q_5, w) → K_{14}
Translate(R_5, w) → L_{14}
Translate(S_5, w) → M_{14}
Translate(T_5, w) → N_{14}
Translate(U_5, w) → O_{14}
Translate(V_5, w) → P_{14}
Translate(K'_1, w) → Q_{14}
Translate(V'_2, w) → R_{14}
Translate(U'_2, w) → S_{14}
Translate(M'_2, w) → T_{14}
Translate(W_5, w) → U_{14}
Translate(Z_5, w) → V_{14}
Translate(A_6, w) → W_{14}
Translate(B_6, w) → Z_{14}
Translate(C_6, w) → A_{15}
Translate(Z'_3, w) → B_{15}
Translate(D_6, w) → C_{15}
Polygon(W_{13}, Z_{13}, I_{14}, J_{14}, K_{14}, L_{14}, M_{14}, N_{14}, O_{14}, P_{14}, Q_{14}, R_{14}, A_{14}, S_{14}, T_{14}, U_{14}, V_{14}, W_{14}, Z_{14}, A_{15}, B_{15}, C_{15}, B_{14}, C_{14}, D_{14}, E_{14}, F_{14}, G_{14}, H_{14}) → poly15, w_{13}, h_{14}, i_{14}, j_{14}, k_{14}, l_{14}, m_{14}, n_{14}, o_{14}, p_{14}, q_{14}, z_{13}, r_{14}, s_{14}, t_{14}, u_{14}, v_{14}, w_{14}, z_{14}, a_{15}, b_{15}, c_{15}, a_{14}, b_{14}, c_{14}, d_{14}, e_{15}, f_{14}, g_{14}
Translate(O_7, w) → D_{15}
Translate(P_7, w) → E_{15}
Translate(Q_7, w) → F_{15}
Polygon(D_{15}, E_{15}, F_{15}) → poly9', f_{15}, d_{15}, e_{16}
Translate(L''_1, w) → G_{15}
Translate(N''_1, w) → H_{15}
Translate(O''_1, w) → I_{15}
Translate(P''_1, w) → J_{15}
Translate(Q''_1, w) → K_{15}
Translate(R''_1, w) → L_{15}
Translate(S''_1, w) → M_{15}
Translate(T''_1, w) → N_{15}
Translate(J''_1, w) → O_{15}
Polygon(G_{15}, H_{15}, I_{15}, J_{15}, K_{15}, L_{15}, M_{15}, N_{15}, O_{15}) → poly16, g_{15}, h_{15}, i_{15}, j_{15}, k_{15}, l_{15}, m_{15}, n_{15}, o_{15}
Translate(E_6, w) → P_{15}
Translate(F_6, w) → Q_{15}
Translate(G_6, w) → R_{15}
Polygon(P_{15}, Q_{15}, R_{15}) → poly17, r_{15}, p_{15}, q_{15}
Translate(M''_1, w) → S_{15}
Translate(U''_1, w) → T_{15}
Translate(V''_1, w) → U_{15}
Polygon(S_{15}, T_{15}, U_{15}) → poly8', u_{15}, s_{15}, t_{15}
Translate(M', w) → M''_2
Translate(U', w) → U''_2
Translate(V', w) → V''_2
Polygon(M''_2, U''_2, V''_2) → poly18, v''_2, m''_2, u''_2
Rotate(E', (d6 * 180°), J) → E''_1
Rotate(L'_1, (d6 * 180°), J) → V_{15}
Rotate(N'_1, (d6 * 180°), J) → W_{15}
Rotate(O'_1, (d6 * 180°), J) → Z_{15}
Rotate(P'_1, (d6 * 180°), J) → A_{16}
Rotate(Q'_1, (d6 * 180°), J) → B_{16}
Rotate(R'_1, (d6 * 180°), J) → C_{16}
Rotate(S'_1, (d6 * 180°), J) → D_{16}
Rotate(T'_2, (d6 * 180°), J) → E_{16}
Rotate(J_3, (d6 * 180°), J) → F_{16}
Rotate(K_3, (d6 * 180°), J) → G_{16}
Rotate(L_3, (d6 * 180°), J) → H_{16}
Rotate(M_3, (d6 * 180°), J) → I_{16}
Rotate(N_3, (d6 * 180°), J) → J_{16}
Rotate(O_3, (d6 * 180°), J) → K_{16}
Rotate(P_3, (d6 * 180°), J) → L_{16}
Rotate(Q_3, (d6 * 180°), J) → M_{16}
Rotate(R_3, (d6 * 180°), J) → N_{16}
Rotate(K', (d6 * 180°), J) → K''_1
Rotate(V'_1, (d6 * 180°), J) → O_{16}
Rotate(U'_1, (d6 * 180°), J) → P_{16}
Rotate(M'_1, (d6 * 180°), J) → Q_{16}
Rotate(S_3, (d6 * 180°), J) → R_{16}
Rotate(T_3, (d6 * 180°), J) → S_{16}
Rotate(U_3, (d6 * 180°), J) → T_{16}
Rotate(V_3, (d6 * 180°), J) → U_{16}
Rotate(W_3, (d6 * 180°), J) → V_{16}
Rotate(Z'_2, (d6 * 180°), J) → W_{16}
Rotate(Z_3, (d6 * 180°), J) → Z_{16}
Polygon(E''_1, V_{15}, G_{16}, H_{16}, I_{16}, J_{16}, K_{16}, L_{16}, M_{16}, N_{16}, K''_1, O_{16}, W_{15}, P_{16}, Q_{16}, R_{16}, S_{16}, T_{16}, U_{16}, V_{16}, W_{16}, Z_{16}, Z_{15}, A_{16}, B_{16}, C_{16}, D_{16}, E_{16}, F_{16}) → poly19, e''_1, f_{16}, g_{16}, h_{16}, i_{16}, j_{16}, k_{16}, l_{16}, m_{16}, n_{16}, k''_1, v_{15}, o_{16}, p_{16}, q_{16}, r_{16}, s_{16}, t_{16}, u_{16}, v_{16}, w_{16}, z_{16}, w_{15}, z_{15}, a_{16}, b_{16}, c_{16}, d_{16}, e_{17}
Rotate(A_4, (d6 * 180°), J) → A_{17}
Rotate(B_4, (d6 * 180°), J) → B_{17}
Rotate(C_4, (d6 * 180°), J) → C_{17}
Polygon(A_{17}, B_{17}, C_{17}) → poly3'''_1, c_{17}, a_{17}, b_{17}
Rotate(L'', (d6 * 180°), J) → L'''_1
Rotate(N'', (d6 * 180°), J) → N'''_1
Rotate(O'', (d6 * 180°), J) → O'''_1
Rotate(P'', (d6 * 180°), J) → P'''_1
Rotate(Q'', (d6 * 180°), J) → Q'''_1
Rotate(R'', (d6 * 180°), J) → R'''_1
Rotate(S'', (d6 * 180°), J) → S'''_1
Rotate(T'', (d6 * 180°), J) → T'''_1
Rotate(J'', (d6 * 180°), J) → J'''_1
Polygon(L'''_1, N'''_1, O'''_1, P'''_1, Q'''_1, R'''_1, S'''_1, T'''_1, J'''_1) → poly1'''_1, l'''_1, n'''_1, o'''_1, p'''_1, q'''_1, r'''_1, s'''_1, t'''_1, j'''_1
Rotate(W'', (d6 * 180°), J) → W'''_1
Rotate(Z'', (d6 * 180°), J) → Z'''_1
Rotate(D_4, (d6 * 180°), J) → D_{17}
Rotate(E_4, (d6 * 180°), J) → E_{17}
Rotate(F_4, (d6 * 180°), J) → F_{17}
Rotate(G_4, (d6 * 180°), J) → G_{17}
Rotate(H_4, (d6 * 180°), J) → H_{17}
Rotate(I_4, (d6 * 180°), J) → I_{17}
Rotate(J_4, (d6 * 180°), J) → J_{17}
Rotate(K_4, (d6 * 180°), J) → K_{17}
Rotate(L_4, (d6 * 180°), J) → L_{17}
Rotate(M_4, (d6 * 180°), J) → M_{17}
Rotate(N_4, (d6 * 180°), J) → N_{17}
Rotate(O_4, (d6 * 180°), J) → O_{17}
Rotate(P_4, (d6 * 180°), J) → P_{17}
Rotate(Q_4, (d6 * 180°), J) → Q_{17}
Rotate(I'', (d6 * 180°), J) → I'''_1
Polygon(W'''_1, Z'''_1, L_{17}, M_{17}, N_{17}, O_{17}, P_{17}, Q_{17}, I'''_1, D_{17}, E_{17}, F_{17}, G_{17}, H_{17}, I_{17}, J_{17}, K_{17}) → poly2'_2, w'''_1, k_{17}, l_{17}, m_{17}, n_{17}, o_{17}, p_{17}, q_{17}, i'''_1, z'''_1, d_{17}, e_{18}, f_{17}, g_{17}, h_{17}, i_{17}, j_{17}
Rotate(C_5, (d6 * 180°), J) → R_{17}
Rotate(D_5, (d6 * 180°), J) → S_{17}
Rotate(E_5, (d6 * 180°), J) → T_{17}
Rotate(F_5, (d6 * 180°), J) → U_{17}
Rotate(G_5, (d6 * 180°), J) → V_{17}
Rotate(H_5, (d6 * 180°), J) → W_{17}
Rotate(I_5, (d6 * 180°), J) → Z_{17}
Rotate(J_5, (d6 * 180°), J) → A_{18}
Polygon(R_{17}, S_{17}, T_{17}, U_{17}, V_{17}, W_{17}, Z_{17}, A_{18}) → poly3'_2, r_{17}, s_{17}, t_{17}, u_{17}, v_{17}, w_{17}, z_{17}, a_{18}
Rotate(R_4, (d6 * 180°), J) → B_{18}
Rotate(S_4, (d6 * 180°), J) → C_{18}
Rotate(T_4, (d6 * 180°), J) → D_{18}
Rotate(U_4, (d6 * 180°), J) → E_{18}
Rotate(V_4, (d6 * 180°), J) → F_{18}
Rotate(W_4, (d6 * 180°), J) → G_{18}
Rotate(Z_4, (d6 * 180°), J) → H_{18}
Rotate(A_5, (d6 * 180°), J) → I_{18}
Rotate(B_5, (d6 * 180°), J) → J_{18}
Polygon(B_{18}, C_{18}, D_{18}, E_{18}, F_{18}, G_{18}, H_{18}, I_{18}, J_{18}) → poly2'''_1, b_{18}, c_{18}, d_{18}, e_{19}, f_{18}, g_{18}, h_{18}, i_{18}, j_{18}
Rotate(M'', (d6 * 180°), J) → M'''_1
Rotate(U'', (d6 * 180°), J) → U'''_1
Rotate(V'', (d6 * 180°), J) → V'''_1
Polygon(M'''_1, U'''_1, V'''_1) → poly4'_1, v'''_1, m'''_1, u'''_1
Rotate(K_5, (d6 * 180°), J) → K_{18}
Rotate(L_5, (d6 * 180°), J) → L_{18}
Rotate(M_5, (d6 * 180°), J) → M_{18}
Polygon(K_{18}, L_{18}, M_{18}) → poly5', m_{18}, k_{18}, l_{18}
Rotate(E, (d6 * 180°), J) → E'_3
Rotate(L, (d6 * 180°), J) → L'_4
Rotate(N, (d6 * 180°), J) → N'_4
Rotate(O, (d6 * 180°), J) → O'_4
Rotate(P, (d6 * 180°), J) → P'_4
Rotate(Q, (d6 * 180°), J) → Q'_4
Rotate(R, (d6 * 180°), J) → R'_4
Rotate(S, (d6 * 180°), J) → S'_4
Rotate(T, (d6 * 180°), J) → T'_5
Rotate(V_2, (d6 * 180°), J) → N_{18}
Rotate(E_2, (d6 * 180°), J) → O_{18}
Rotate(L_2, (d6 * 180°), J) → P_{18}
Rotate(K_2, (d6 * 180°), J) → Q_{18}
Rotate(J_2, (d6 * 180°), J) → R_{18}
Rotate(I_2, (d6 * 180°), J) → S_{18}
Rotate(H_2, (d6 * 180°), J) → T_{18}
Rotate(G_2, (d6 * 180°), J) → U_{18}
Rotate(F_2, (d6 * 180°), J) → V_{18}
Rotate(K, (d6 * 180°), J) → K'_3
Rotate(V, (d6 * 180°), J) → V'_4
Rotate(U, (d6 * 180°), J) → U'_4
Rotate(M, (d6 * 180°), J) → M'_4
Rotate(E_1, (d6 * 180°), J) → W_{18}
Rotate(D_1, (d6 * 180°), J) → Z_{18}
Rotate(C_1, (d6 * 180°), J) → A_{19}
Rotate(B_1, (d6 * 180°), J) → B_{19}
Rotate(A_1, (d6 * 180°), J) → C_{19}
Rotate(Z, (d6 * 180°), J) → Z'_5
Rotate(U_2, (d6 * 180°), J) → D_{19}
Polygon(E'_3, L'_4, O_{18}, P_{18}, Q_{18}, R_{18}, S_{18}, T_{18}, U_{18}, V_{18}, K'_3, V'_4, N'_4, U'_4, M'_4, W_{18}, Z_{18}, A_{19}, B_{19}, C_{19}, Z'_5, D_{19}, O'_4, P'_4, Q'_4, R'_4, S'_4, T'_5, N_{18}) → poly1'_8, e'_3, n_{18}, o_{18}, p_{18}, q_{18}, r_{18}, s_{18}, t_{18}, u_{18}, v_{18}, k'_3, l'_4, v'_4, u'_4, m'_4, w_{18}, z_{18}, a_{19}, b_{19}, c_{19}, z'_5, d_{19}, n'_4, o'_4, p'_4, q'_4, r'_4, s'_4, t'_5
Rotate(L', (d6 * 180°), J) → L''_3
Rotate(N', (d6 * 180°), J) → N''_3
Rotate(O', (d6 * 180°), J) → O''_3
Rotate(P', (d6 * 180°), J) → P''_3
Rotate(Q', (d6 * 180°), J) → Q''_3
Rotate(R', (d6 * 180°), J) → R''_3
Rotate(S', (d6 * 180°), J) → S''_3
Rotate(T', (d6 * 180°), J) → T''_3
Rotate(J', (d6 * 180°), J) → J''_3
Polygon(L''_3, N''_3, O''_3, P''_3, Q''_3, R''_3, S''_3, T''_3, J''_3) → poly1''_3, l''_3, n''_3, o''_3, p''_3, q''_3, r''_3, s''_3, t''_3, j''_3
Rotate(J'_1, (d6 * 180°), J) → E_{19}
Rotate(T'_1, (d6 * 180°), J) → F_{19}
Rotate(I_3, (d6 * 180°), J) → G_{19}
Polygon(E_{19}, F_{19}, G_{19}) → poly3''_3, g_{19}, e_{20}, f_{19}
Rotate(M', (d6 * 180°), J) → M''_3
Rotate(U', (d6 * 180°), J) → U''_3
Rotate(V', (d6 * 180°), J) → V''_3
Polygon(M''_3, U''_3, V''_3) → poly20, v''_3, m''_3, u''_3
Rotate(W', (d6 * 180°), J) → W''_3
Rotate(Z', (d6 * 180°), J) → Z''_3
Rotate(O_1, (d6 * 180°), J) → H_{19}
Rotate(P_1, (d6 * 180°), J) → I_{19}
Rotate(Q_1, (d6 * 180°), J) → J_{19}
Rotate(R_1, (d6 * 180°), J) → K_{19}
Rotate(S_1, (d6 * 180°), J) → L_{19}
Rotate(T_1, (d6 * 180°), J) → M_{19}
Rotate(U_1, (d6 * 180°), J) → N_{19}
Rotate(V_1, (d6 * 180°), J) → O_{19}
Rotate(W_1, (d6 * 180°), J) → P_{19}
Rotate(Z_1, (d6 * 180°), J) → Q_{19}
Rotate(A_2, (d6 * 180°), J) → R_{19}
Rotate(B_2, (d6 * 180°), J) → S_{19}
Rotate(C_2, (d6 * 180°), J) → T_{19}
Rotate(D_2, (d6 * 180°), J) → U_{19}
Rotate(I', (d6 * 180°), J) → I''_3
Polygon(W''_3, Z''_3, P_{19}, Q_{19}, R_{19}, S_{19}, T_{19}, U_{19}, I''_3, H_{19}, I_{19}, J_{19}, K_{19}, L_{19}, M_{19}, N_{19}, O_{19}) → poly21, w''_3, o_{19}, p_{19}, q_{19}, r_{19}, s_{19}, t_{19}, u_{19}, i''_3, z''_3, h_{19}, i_{19}, j_{19}, k_{19}, l_{19}, m_{19}, n_{19}
Rotate(M_2, (d6 * 180°), J) → V_{19}
Rotate(N_2, (d6 * 180°), J) → W_{19}
Rotate(O_2, (d6 * 180°), J) → Z_{19}
Rotate(P_2, (d6 * 180°), J) → A_{20}
Rotate(Q_2, (d6 * 180°), J) → B_{20}
Rotate(R_2, (d6 * 180°), J) → C_{20}
Rotate(S_2, (d6 * 180°), J) → D_{20}
Rotate(T_2, (d6 * 180°), J) → E_{20}
Rotate(W_2, (d6 * 180°), J) → F_{20}
Rotate(Z_2, (d6 * 180°), J) → G_{20}
Rotate(A_3, (d6 * 180°), J) → H_{20}
Rotate(B_3, (d6 * 180°), J) → I_{20}
Rotate(C_3, (d6 * 180°), J) → J_{20}
Rotate(D_3, (d6 * 180°), J) → K_{20}
Rotate(E_3, (d6 * 180°), J) → L_{20}
Rotate(F_3, (d6 * 180°), J) → M_{20}
Rotate(G_3, (d6 * 180°), J) → N_{20}
Polygon(F_{20}, G_{20}, H_{20}, I_{20}, J_{20}, K_{20}, L_{20}, M_{20}, N_{20}) → poly2''_3, f_{20}, g_{20}, h_{20}, i_{20}, j_{20}, k_{20}, l_{20}, m_{20}, n_{20}
Rotate(W'_1, (d6 * 180°), J) → O_{20}
Rotate(Z'_1, (d6 * 180°), J) → P_{20}
Rotate(H_3, (d6 * 180°), J) → Q_{20}
Polygon(O_{20}, P_{20}, Q_{20}) → poly23, q_{20}, o_{20}, p_{20}
Rotate(E'_1, (d6 * 180°), J) → R_{20}
Rotate(L'_2, (d6 * 180°), J) → S_{20}
Rotate(N'_2, (d6 * 180°), J) → T_{20}
Rotate(O'_2, (d6 * 180°), J) → U_{20}
Rotate(P'_2, (d6 * 180°), J) → V_{20}
Rotate(Q'_2, (d6 * 180°), J) → W_{20}
Rotate(R'_2, (d6 * 180°), J) → Z_{20}
Rotate(S'_2, (d6 * 180°), J) → A_{21}
Rotate(T'_3, (d6 * 180°), J) → B_{21}
Rotate(N_5, (d6 * 180°), J) → C_{21}
Rotate(O_5, (d6 * 180°), J) → D_{21}
Rotate(P_5, (d6 * 180°), J) → E_{21}
Rotate(Q_5, (d6 * 180°), J) → F_{21}
Rotate(R_5, (d6 * 180°), J) → G_{21}
Rotate(S_5, (d6 * 180°), J) → H_{21}
Rotate(T_5, (d6 * 180°), J) → I_{21}
Rotate(U_5, (d6 * 180°), J) → J_{21}
Rotate(V_5, (d6 * 180°), J) → K_{21}
Rotate(K'_1, (d6 * 180°), J) → L_{21}
Rotate(V'_2, (d6 * 180°), J) → M_{21}
Rotate(U'_2, (d6 * 180°), J) → N_{21}
Rotate(M'_2, (d6 * 180°), J) → O_{21}
Rotate(W_5, (d6 * 180°), J) → P_{21}
Rotate(Z_5, (d6 * 180°), J) → Q_{21}
Rotate(A_6, (d6 * 180°), J) → R_{21}
Rotate(B_6, (d6 * 180°), J) → S_{21}
Rotate(C_6, (d6 * 180°), J) → T_{21}
Rotate(Z'_3, (d6 * 180°), J) → U_{21}
Rotate(D_6, (d6 * 180°), J) → V_{21}
Polygon(R_{20}, S_{20}, D_{21}, E_{21}, F_{21}, G_{21}, H_{21}, I_{21}, J_{21}, K_{21}, L_{21}, M_{21}, T_{20}, N_{21}, O_{21}, P_{21}, Q_{21}, R_{21}, S_{21}, T_{21}, U_{21}, V_{21}, U_{20}, V_{20}, W_{20}, Z_{20}, A_{21}, B_{21}, C_{21}) → poly24, r_{20}, c_{21}, d_{21}, e_{22}, f_{21}, g_{21}, h_{21}, i_{21}, j_{21}, k_{21}, l_{21}, s_{20}, m_{21}, n_{21}, o_{21}, p_{21}, q_{21}, r_{21}, s_{21}, t_{21}, u_{21}, v_{21}, t_{20}, u_{20}, v_{20}, w_{20}, z_{20}, a_{21}, b_{21}
Rotate(L''_1, (d6 * 180°), J) → W_{21}
Rotate(N''_1, (d6 * 180°), J) → Z_{21}
Rotate(O''_1, (d6 * 180°), J) → A_{22}
Rotate(P''_1, (d6 * 180°), J) → B_{22}
Rotate(Q''_1, (d6 * 180°), J) → C_{22}
Rotate(R''_1, (d6 * 180°), J) → D_{22}
Rotate(S''_1, (d6 * 180°), J) → E_{22}
Rotate(T''_1, (d6 * 180°), J) → F_{22}
Rotate(J''_1, (d6 * 180°), J) → G_{22}
Polygon(W_{21}, Z_{21}, A_{22}, B_{22}, C_{22}, D_{22}, E_{22}, F_{22}, G_{22}) → poly25, w_{21}, z_{21}, a_{22}, b_{22}, c_{22}, d_{22}, e_{23}, f_{22}, g_{22}
Rotate(E_6, (d6 * 180°), J) → H_{22}
Rotate(F_6, (d6 * 180°), J) → I_{22}
Rotate(G_6, (d6 * 180°), J) → J_{22}
Polygon(H_{22}, I_{22}, J_{22}) → poly26, j_{22}, h_{22}, i_{22}
Rotate(O_7, (d6 * 180°), J) → K_{22}
Rotate(P_7, (d6 * 180°), J) → L_{22}
Rotate(Q_7, (d6 * 180°), J) → M_{22}
Polygon(K_{22}, L_{22}, M_{22}) → poly9'_1, m_{22}, k_{22}, l_{22}
Rotate(M''_1, (d6 * 180°), J) → N_{22}
Rotate(U''_1, (d6 * 180°), J) → O_{22}
Rotate(V''_1, (d6 * 180°), J) → P_{22}
Polygon(N_{22}, O_{22}, P_{22}) → poly8'_1, p_{22}, n_{22}, o_{22}
Rotate(W''_1, (d6 * 180°), J) → Q_{22}
Rotate(Z''_1, (d6 * 180°), J) → R_{22}
Rotate(P_6, (d6 * 180°), J) → S_{22}
Rotate(Q_6, (d6 * 180°), J) → T_{22}
Rotate(R_6, (d6 * 180°), J) → U_{22}
Rotate(S_6, (d6 * 180°), J) → V_{22}
Rotate(T_6, (d6 * 180°), J) → W_{22}
Rotate(U_6, (d6 * 180°), J) → Z_{22}
Rotate(V_6, (d6 * 180°), J) → A_{23}
Rotate(W_6, (d6 * 180°), J) → B_{23}
Rotate(Z_6, (d6 * 180°), J) → C_{23}
Rotate(A_7, (d6 * 180°), J) → D_{23}
Rotate(B_7, (d6 * 180°), J) → E_{23}
Rotate(C_7, (d6 * 180°), J) → F_{23}
Rotate(D_7, (d6 * 180°), J) → G_{23}
Rotate(E_7, (d6 * 180°), J) → H_{23}
Rotate(I''_1, (d6 * 180°), J) → I_{23}
Polygon(Q_{22}, R_{22}, C_{23}, D_{23}, E_{23}, F_{23}, G_{23}, H_{23}, I_{23}, S_{22}, T_{22}, U_{22}, V_{22}, W_{22}, Z_{22}, A_{23}, B_{23}) → poly7'_1, q_{22}, b_{23}, c_{23}, d_{23}, e_{24}, f_{23}, g_{23}, h_{23}, i_{23}, r_{22}, s_{22}, t_{22}, u_{22}, v_{22}, w_{22}, z_{22}, a_{23}
Rotate(F_7, (d6 * 180°), J) → J_{23}
Rotate(G_7, (d6 * 180°), J) → K_{23}
Rotate(H_7, (d6 * 180°), J) → L_{23}
Rotate(I_7, (d6 * 180°), J) → M_{23}
Rotate(J_7, (d6 * 180°), J) → N_{23}
Rotate(K_7, (d6 * 180°), J) → O_{23}
Rotate(L_7, (d6 * 180°), J) → P_{23}
Rotate(M_7, (d6 * 180°), J) → Q_{23}
Rotate(N_7, (d6 * 180°), J) → R_{23}
Polygon(J_{23}, K_{23}, L_{23}, M_{23}, N_{23}, O_{23}, P_{23}, Q_{23}, R_{23}) → poly27, j_{23}, k_{23}, l_{23}, m_{23}, n_{23}, o_{23}, p_{23}, q_{23}, r_{23}
Rotate(H_6, (d6 * 180°), J) → S_{23}
Rotate(I_6, (d6 * 180°), J) → T_{23}
Rotate(J_6, (d6 * 180°), J) → U_{23}
Rotate(K_6, (d6 * 180°), J) → V_{23}
Rotate(L_6, (d6 * 180°), J) → W_{23}
Rotate(M_6, (d6 * 180°), J) → Z_{23}
Rotate(N_6, (d6 * 180°), J) → A_{24}
Rotate(O_6, (d6 * 180°), J) → B_{24}
Rotate(M_2, (d6 * 180°), J) → C_{24}
Rotate(N_2, (d6 * 180°), J) → D_{24}
Rotate(O_2, (d6 * 180°), J) → E_{24}
Rotate(P_2, (d6 * 180°), J) → F_{24}
Rotate(Q_2, (d6 * 180°), J) → G_{24}
Rotate(R_2, (d6 * 180°), J) → H_{24}
Rotate(S_2, (d6 * 180°), J) → I_{24}
Rotate(T_2, (d6 * 180°), J) → J_{24}
Polygon(C_{24}, D_{24}, E_{24}, F_{24}, G_{24}, H_{24}, I_{24}, J_{24}) → poly22, c_{24}, d_{24}, e_{21}, f_{24}, g_{24}, h_{24}, i_{24}, j_{24}
Rotate(H_6, (d6 * 180°), J) → K_{24}
Rotate(I_6, (d6 * 180°), J) → L_{24}
Rotate(J_6, (d6 * 180°), J) → M_{24}
Rotate(K_6, (d6 * 180°), J) → N_{24}
Rotate(L_6, (d6 * 180°), J) → O_{24}
Rotate(M_6, (d6 * 180°), J) → P_{24}
Rotate(N_6, (d6 * 180°), J) → Q_{24}
Rotate(O_6, (d6 * 180°), J) → R_{24}
Polygon(K_{24}, L_{24}, M_{24}, N_{24}, O_{24}, P_{24}, Q_{24}, R_{24}) → poly6'_1, k_{24}, l_{24}, m_{24}, n_{24}, o_{24}, p_{24}, q_{24}, r_{24}
Midpoint(I, K) → S_{24}
Mirror(S_{24}, K) → U_{24}
Mirror(K, U_{24}) → K'_4
Mirror(S_{24}, I) → V_{24}
Mirror(I, V_{24}) → I'_1
Mirror(L, E) → L'_5
Mirror(E, L'_5) → E'_4
Mirror(L'_5, E'_4) → W_{24}
Mirror(L, J) → L'_6
Mirror(K, U_{24}) → K'_5
Mirror(K, J) → K'_6
Mirror(S_{24}, L) → Z_{24}
Mirror(E, V_{24}) → E'_5
Mirror(V_{24}, L'_5) → A_{25}
Mirror(L'_5, V_{24}) → B_{25}
Mirror(E, I) → E'_6
Mirror(L, S_{24}) → L'_7
Mirror(J, K) → J'_2
Mirror(V_{24}, B_{25}) → C_{25}
Mirror(I, E'_6) → I'_2
Mirror(S_{24}, L'_7) → D_{25}
Mirror(L'_6, U_{24}) → E_{25}
Mirror(Z_{24}, K'_6) → F_{25}
Mirror(J, L'_6) → J'_3
Mirror(U_{24}, K'_4) → G_{25}
Mirror(J'_2, E_{25}) → H_{25}
Mirror(K'_6, Z_{24}) → I_{25}
Vector(I, I_{25}) → j_1
Vector(I, K) → k_1

AI Drawing Prompt Reference

Create an Escher-style pattern featuring seahorses, transforming a basic motif into a dancing effect through rotations, translations, and reflections. Start by creating control points and auxiliary variables, then construct several lines and line segments using these points and variables. Find the intersections of these lines and segments, and use rotation and reflection operations to generate multiple seahorse patterns. Finally, assemble these patterns to form the complete design.

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