Escher's "Lizards" Tessellation
Author: Duke
Date: 11/01/06

M.C. Escher was the master of transforming polygonal tessellations into non-polygonal works of art.  The connection between the symmetries of the underlying polygonal tessellation, and the symmetries of the transformed tessellation can be traced back to the transformations used to create the non-polygonal  tile.

     Before moving any of the sliders, examine Escher’s "Lizards" tessellation below and answer the following questions:

1.       Describe the symmetries of the “Lizards” tessellation.

2.       What is the tessellation’s underlying polygonal structure

Move Sliders Alpha and Beta:

3.       What shape is the tile formed from?  What specific transformation could be used to move the tile into the spot of another lizard?  How was the tile formed?

A = (-10.266666666666666, -5.5)
B = (26.2, -5.466666666666667)
a = Segment(A, B)
C = (14.799999999999999, 15.566666666666666)
D = (9.855555555555554, 18.566666666666666)
E = (4.833333333333333, 15.666666666666666)
F = (4.866666666666666, 9.733333333333333)
G = (9.8, 6.933333333333334)
H = (14.655555555555553, 9.833333333333334)
I = (16.82222222222222, 13.5)
J = (16.82222222222222, 12.8)
K = (14.822222222222221, 11.333333333333334)
P, c, i, j, k = Polygon(C, I, J, K)
L = (11.155555555555555, 17.633333333333333)
M = (13.1, 19.3)
N = (12.722222222222221, 19.933333333333334)
O = (11.155555555555555, 20.5)
Q = (10.855555555555554, 19.9)
R = (11.02222222222222, 19.133333333333333)
S, d, l, m, n, o, q, r = Polygon(D, L, M, N, O, Q, R)
T = (7.8888888888888875, 17.433333333333334)
U = (7.088888888888888, 18.233333333333334)
V = (5.588888888888888, 17.6)
W = (4.355555555555554, 17.866666666666667)
Y = (3.4555555555555544, 16.966666666666665)
Z, t, u, v, w, y, e = Polygon(T, U, V, W, Y, E)
A_1 = (4.833333333333333, 12.1)
B_1 = (2.9555555555555544, 12.266666666666666)
C_1 = (1.422222222222221, 13.733333333333333)
D_1 = (2.2888888888888874, 11.433333333333334)
E_1 = (4.855555555555554, 10.433333333333334)
P_1, a_1, b_1, c_1, d_1, e_1 = Polygon(A_1, B_1, C_1, D_1, E_1)
F_1 = (7.922222222222221, 7.833333333333333)
G_1 = (5.955555555555554, 5.566666666666666)
H_1 = (7.322222222222221, 4.033333333333333)
I_1 = (8.222222222222221, 5.7)
Q_1, f_1, g_1, h_1, i_1, g = Polygon(F_1, G_1, H_1, I_1, G)
J_1 = (15.255555555555555, 9.5)
K_1 = (14.455555555555554, 8.266666666666666)
L_1 = (11.555555555555554, 8.166666666666666)
R_1, h, j_1, k_1, l_1 = Polygon(H, J_1, K_1, L_1)
M_1 = (12, 14.866666666666667)
N_1 = (11.4, 15.222222222222223)
O_1 = (9.4, 18.266666666666666)
S_1 = (9.766666666666666, 15.6)
T_1 = (8.2, 13.666666666666666)
U_1 = (8.733333333333333, 15.733333333333333)
V_1 = (6.666666666666667, 16.2)
W_1 = (7, 15)
Y_1 = (6.133333333333333, 14.033333333333333)
Z_1 = (5.933333333333334, 12.4)
A_2 = (5.288888888888888, 12.233333333333333)
B_2 = (6.333333333333333, 10.266666666666666)
C_2 = (7.266666666666667, 8.833333333333334)
D_2 = (9.5, 8.933333333333334)
E_2 = (8.5, 10.533333333333333)
F_2 = (10.533333333333333, 10.933333333333334)
G_2 = (13.566666666666666, 10.5)
H_2 = (13, 10)
I_2 = (12.366666666666667, 9.933333333333334)
J_2 = (12.066666666666666, 11.6)
K_2 = (12.422222222222222, 12.266666666666667)
P_2, j_2, k_2, k_3, c_2, m_1, n_1, l_2, d_2, o_1, s_1, t_1, u_1, t_2, e_2, v_1, w_1, y_1, z_1, a_2, a_3, e_3, b_2, c_3, f_2, g_2, d_3, e_4, f_3, l_3, h_2, g_3, h_3, i_2 = Polygon(J_2, K_2, K, C, M_1, N_1, L, D, O_1, S_1, T_1, U_1, T, E, V_1, W_1, Y_1, Z_1, A_2, A_1, E_1, B_2, C_2, F_1, G, D_2, E_2, F_2, L_1, H, G_2, H_2, I_2)
α = 0 rad (slider from 0 to 4.1887902047863905, step 0.017453292519943295)
F_1' = Rotate(F_1, α, G)
G_1' = Rotate(G_1, α, G)
H_1' = Rotate(H_1, α, G)
I_1' = Rotate(I_1, α, G)
G' = Rotate(G, α, G)
Q_1', f_1', g_1', h_1', i_1', g' = Polygon(F_1', G_1', H_1', I_1', G')
C' = Rotate(C, α, C)
I' = Rotate(I, α, C)
J' = Rotate(J, α, C)
K' = Rotate(K, α, C)
P', c', i', j', k' = Polygon(C', I', J', K')
β = 0 rad (slider from 0 to 2.0943951023931953, step 0.017453292519943295)
T' = Rotate(T, α, E)
U' = Rotate(U, α, E)
V' = Rotate(V, α, E)
W' = Rotate(W, α, E)
Y' = Rotate(Y, α, E)
E' = Rotate(E, α, E)
Z', t', u', v', w', y', e' = Polygon(T', U', V', W', Y', E')
A_1' = Rotate(A_1, β, E)
B_1' = Rotate(B_1, β, E)
C_1' = Rotate(C_1, β, E)
D_1' = Rotate(D_1, β, E)
E_1' = Rotate(E_1, β, E)
P_1', a_1', b_1', c_1', d_1', e_1' = Polygon(A_1', B_1', C_1', D_1', E_1')
H' = Rotate(H, β, G)
J_1' = Rotate(J_1, β, G)
K_1' = Rotate(K_1, β, G)
L_1' = Rotate(L_1, β, G)
R_1', h', j_1', k_1', l_1' = Polygon(H', J_1', K_1', L_1')
D' = Rotate(D, β, C)
L' = Rotate(L, β, C)
M' = Rotate(M, β, C)
N' = Rotate(N, β, C)
O' = Rotate(O, β, C)
Q' = Rotate(Q, β, C)
R' = Rotate(R, β, C)
S', d', l', m', n', o', q', r' = Polygon(D', L', M', N', O', Q', R')
Q_2, k_4, j_3, i_3, c_4, m_2, n_2, l_4, m_3, n_3, o_2, q_1, r_1, o_3, s_2, t_3, u_2, t_4, u_3, v_2, w_2, y_2, e_5, v_3, w_3, y_3, z_2, a_4, a_5, b_3, c_5, d_4, e_6, b_4, c_6, f_4, g_4, h_4, i_4, g_5, d_5, e_7, f_5, l_5, k_5, j_4, g_6, h_5, i_5, j_5, k_6 = Polygon(K, J, I, C, M_1, N_1, L, M, N, O, Q, R, O_1, S_1, T_1, U_1, T, U, V, W, Y, E, V_1, W_1, Y_1, Z_1, A_2, A_1, B_1, C_1, D_1, E_1, B_2, C_2, F_1, G_1, H_1, I_1, G, D_2, E_2, F_2, L_1, K_1, J_1, G_2, H_2, I_2, J_2, K_2)
γ = 0 rad (slider from 0 to 4.1887902047863905, step 0.017453292519943295)
K'_1 = Rotate(K, γ, C)
J'_1 = Rotate(J, γ, C)
I'_1 = Rotate(I, γ, C)
C'_1 = Rotate(C, γ, C)
M_1' = Rotate(M_1, γ, C)
N_1' = Rotate(N_1, γ, C)
L'_1 = Rotate(L, γ, C)
M'_1 = Rotate(M, γ, C)
N'_1 = Rotate(N, γ, C)
O'_1 = Rotate(O, γ, C)
Q'_1 = Rotate(Q, γ, C)
R'_1 = Rotate(R, γ, C)
O_1' = Rotate(O_1, γ, C)
S_1' = Rotate(S_1, γ, C)
T_1' = Rotate(T_1, γ, C)
U_1' = Rotate(U_1, γ, C)
T'_1 = Rotate(T, γ, C)
U'_1 = Rotate(U, γ, C)
V'_1 = Rotate(V, γ, C)
W'_1 = Rotate(W, γ, C)
Y'_1 = Rotate(Y, γ, C)
E'_1 = Rotate(E, γ, C)
V_1' = Rotate(V_1, γ, C)
W_1' = Rotate(W_1, γ, C)
Y_1' = Rotate(Y_1, γ, C)
Z_1' = Rotate(Z_1, γ, C)
A_2' = Rotate(A_2, γ, C)
A_3 = Rotate(A_1, γ, C)
B_3 = Rotate(B_1, γ, C)
C_3 = Rotate(C_1, γ, C)
D_3 = Rotate(D_1, γ, C)
E_3 = Rotate(E_1, γ, C)
B_2' = Rotate(B_2, γ, C)
C_2' = Rotate(C_2, γ, C)
F_3 = Rotate(F_1, γ, C)
G_3 = Rotate(G_1, γ, C)
H_3 = Rotate(H_1, γ, C)
I_3 = Rotate(I_1, γ, C)
G'_1 = Rotate(G, γ, C)
D_2' = Rotate(D_2, γ, C)
E_2' = Rotate(E_2, γ, C)
F_2' = Rotate(F_2, γ, C)
L_2 = Rotate(L_1, γ, C)
K_3 = Rotate(K_1, γ, C)
J_3 = Rotate(J_1, γ, C)
G_2' = Rotate(G_2, γ, C)
H_2' = Rotate(H_2, γ, C)
I_2' = Rotate(I_2, γ, C)
J_2' = Rotate(J_2, γ, C)
K_2' = Rotate(K_2, γ, C)
Q_2', k'_1, j'_1, i'_1, c'_1, m_1', n_1', l'_1, m'_1, n'_1, o'_1, q'_1, r'_1, o_1', s_1', t_1', u_1', t'_1, u'_1, v'_1, w'_1, y'_1, e'_1, v_1', w_1', y_1', z_1', a_2', a_6, b_5, c_7, d_6, e_8, b_2', c_2', f_6, g_7, h_6, i_6, g'_1, d_2', e_2', f_2', l_6, k_7, j_6, g_2', h_2', i_2', j_2', k_2' = Polygon(K'_1, J'_1, I'_1, C'_1, M_1', N_1', L'_1, M'_1, N'_1, O'_1, Q'_1, R'_1, O_1', S_1', T_1', U_1', T'_1, U'_1, V'_1, W'_1, Y'_1, E'_1, V_1', W_1', Y_1', Z_1', A_2', A_3, B_3, C_3, D_3, E_3, B_2', C_2', F_3, G_3, H_3, I_3, G'_1, D_2', E_2', F_2', L_2, K_3, J_3, G_2', H_2', I_2', J_2', K_2')
K'_2 = Rotate(K, γ, E)
J'_2 = Rotate(J, γ, E)
I'_2 = Rotate(I, γ, E)
C'_2 = Rotate(C, γ, E)
M_2 = Rotate(M_1, γ, E)
N_2 = Rotate(N_1, γ, E)
L'_2 = Rotate(L, γ, E)
M'_2 = Rotate(M, γ, E)
N'_2 = Rotate(N, γ, E)
O'_2 = Rotate(O, γ, E)
Q'_2 = Rotate(Q, γ, E)
R'_2 = Rotate(R, γ, E)
O_2 = Rotate(O_1, γ, E)
S_2 = Rotate(S_1, γ, E)
T_2 = Rotate(T_1, γ, E)
U_2 = Rotate(U_1, γ, E)
T'_2 = Rotate(T, γ, E)
U'_2 = Rotate(U, γ, E)
V'_2 = Rotate(V, γ, E)
W'_2 = Rotate(W, γ, E)
Y'_2 = Rotate(Y, γ, E)
E'_2 = Rotate(E, γ, E)
V_2 = Rotate(V_1, γ, E)
W_2 = Rotate(W_1, γ, E)
Y_2 = Rotate(Y_1, γ, E)
Z_2 = Rotate(Z_1, γ, E)
A_4 = Rotate(A_2, γ, E)
A_5 = Rotate(A_1, γ, E)
B_4 = Rotate(B_1, γ, E)
C_4 = Rotate(C_1, γ, E)
D_4 = Rotate(D_1, γ, E)
E_4 = Rotate(E_1, γ, E)
B_5 = Rotate(B_2, γ, E)
C_5 = Rotate(C_2, γ, E)
F_4 = Rotate(F_1, γ, E)
G_4 = Rotate(G_1, γ, E)
H_4 = Rotate(H_1, γ, E)
I_4 = Rotate(I_1, γ, E)
G'_2 = Rotate(G, γ, E)
D_5 = Rotate(D_2, γ, E)
E_5 = Rotate(E_2, γ, E)
F_5 = Rotate(F_2, γ, E)
L_3 = Rotate(L_1, γ, E)
K_4 = Rotate(K_1, γ, E)
J_4 = Rotate(J_1, γ, E)
G_5 = Rotate(G_2, γ, E)
H_5 = Rotate(H_2, γ, E)
I_5 = Rotate(I_2, γ, E)
J_5 = Rotate(J_2, γ, E)
K_5 = Rotate(K_2, γ, E)
Q_3, k'_2, j'_2, i'_2, c'_2, m_4, n_4, l'_2, m'_2, n'_2, o'_2, q'_2, r'_2, o_4, s_3, t_5, u_4, t'_2, u'_2, v'_2, w'_2, y'_2, e'_2, v_4, w_4, y_4, z_3, a_7, a_8, b_6, c_8, d_7, e_9, b_7, c_9, f_7, g_8, h_7, i_7, g'_2, d_8, e_{10}, f_8, l_7, k_8, j_7, g_9, h_8, i_8, j_8, k_9 = Polygon(K'_2, J'_2, I'_2, C'_2, M_2, N_2, L'_2, M'_2, N'_2, O'_2, Q'_2, R'_2, O_2, S_2, T_2, U_2, T'_2, U'_2, V'_2, W'_2, Y'_2, E'_2, V_2, W_2, Y_2, Z_2, A_4, A_5, B_4, C_4, D_4, E_4, B_5, C_5, F_4, G_4, H_4, I_4, G'_2, D_5, E_5, F_5, L_3, K_4, J_4, G_5, H_5, I_5, J_5, K_5)
K'_3 = Rotate(K, γ, G)
J'_3 = Rotate(J, γ, G)
I'_3 = Rotate(I, γ, G)
C'_3 = Rotate(C, γ, G)
M_3 = Rotate(M_1, γ, G)
N_3 = Rotate(N_1, γ, G)
L'_3 = Rotate(L, γ, G)
M'_3 = Rotate(M, γ, G)
N'_3 = Rotate(N, γ, G)
O'_3 = Rotate(O, γ, G)
Q'_3 = Rotate(Q, γ, G)
R'_3 = Rotate(R, γ, G)
O_3 = Rotate(O_1, γ, G)
S_3 = Rotate(S_1, γ, G)
T_3 = Rotate(T_1, γ, G)
U_3 = Rotate(U_1, γ, G)
T'_3 = Rotate(T, γ, G)
U'_3 = Rotate(U, γ, G)
V'_3 = Rotate(V, γ, G)
W'_3 = Rotate(W, γ, G)
Y'_3 = Rotate(Y, γ, G)
E'_3 = Rotate(E, γ, G)
V_3 = Rotate(V_1, γ, G)
W_3 = Rotate(W_1, γ, G)
Y_3 = Rotate(Y_1, γ, G)
Z_3 = Rotate(Z_1, γ, G)
A_6 = Rotate(A_2, γ, G)
A_7 = Rotate(A_1, γ, G)
B_6 = Rotate(B_1, γ, G)
C_6 = Rotate(C_1, γ, G)
D_6 = Rotate(D_1, γ, G)
E_6 = Rotate(E_1, γ, G)
B_7 = Rotate(B_2, γ, G)
C_7 = Rotate(C_2, γ, G)
F_6 = Rotate(F_1, γ, G)
G_6 = Rotate(G_1, γ, G)
H_6 = Rotate(H_1, γ, G)
I_6 = Rotate(I_1, γ, G)
G'_3 = Rotate(G, γ, G)
D_7 = Rotate(D_2, γ, G)
E_7 = Rotate(E_2, γ, G)
F_7 = Rotate(F_2, γ, G)
L_4 = Rotate(L_1, γ, G)
K_6 = Rotate(K_1, γ, G)
J_6 = Rotate(J_1, γ, G)
G_7 = Rotate(G_2, γ, G)
H_7 = Rotate(H_2, γ, G)
I_7 = Rotate(I_2, γ, G)
J_7 = Rotate(J_2, γ, G)
K_7 = Rotate(K_2, γ, G)
Q_4, k'_3, j'_3, i'_3, c'_3, m_5, n_5, l'_3, m'_3, n'_3, o'_3, q'_3, r'_3, o_5, s_4, t_6, u_5, t'_3, u'_3, v'_3, w'_3, y'_3, e'_3, v_5, w_5, y_5, z_4, a_9, a_{10}, b_8, c_{10}, d_9, e_{11}, b_9, c_{11}, f_9, g_{10}, h_9, i_9, g'_3, d_{10}, e_{12}, f_{10}, l_8, k_{10}, j_9, g_{11}, h_{10}, i_{10}, j_{10}, k_{11} = Polygon(K'_3, J'_3, I'_3, C'_3, M_3, N_3, L'_3, M'_3, N'_3, O'_3, Q'_3, R'_3, O_3, S_3, T_3, U_3, T'_3, U'_3, V'_3, W'_3, Y'_3, E'_3, V_3, W_3, Y_3, Z_3, A_6, A_7, B_6, C_6, D_6, E_6, B_7, C_7, F_6, G_6, H_6, I_6, G'_3, D_7, E_7, F_7, L_4, K_6, J_6, G_7, H_7, I_7, J_7, K_7)
δ = 0 rad (slider from 0 to 2.0943951023931953, step 0.017453292519943295)
K'_4 = Rotate(K, δ, C)
J'_4 = Rotate(J, δ, C)
I'_4 = Rotate(I, δ, C)
C'_4 = Rotate(C, δ, C)
M_4 = Rotate(M_1, δ, C)
N_4 = Rotate(N_1, δ, C)
L'_4 = Rotate(L, δ, C)
M'_4 = Rotate(M, δ, C)
N'_4 = Rotate(N, δ, C)
O'_4 = Rotate(O, δ, C)
Q'_4 = Rotate(Q, δ, C)
R'_4 = Rotate(R, δ, C)
O_4 = Rotate(O_1, δ, C)
S_4 = Rotate(S_1, δ, C)
T_4 = Rotate(T_1, δ, C)
U_4 = Rotate(U_1, δ, C)
T'_4 = Rotate(T, δ, C)
U'_4 = Rotate(U, δ, C)
V'_4 = Rotate(V, δ, C)
W'_4 = Rotate(W, δ, C)
Y'_4 = Rotate(Y, δ, C)
E'_4 = Rotate(E, δ, C)
V_4 = Rotate(V_1, δ, C)
W_4 = Rotate(W_1, δ, C)
Y_4 = Rotate(Y_1, δ, C)
Z_4 = Rotate(Z_1, δ, C)
A_8 = Rotate(A_2, δ, C)
A_9 = Rotate(A_1, δ, C)
B_8 = Rotate(B_1, δ, C)
C_8 = Rotate(C_1, δ, C)
D_8 = Rotate(D_1, δ, C)
E_8 = Rotate(E_1, δ, C)
B_9 = Rotate(B_2, δ, C)
C_9 = Rotate(C_2, δ, C)
F_8 = Rotate(F_1, δ, C)
G_8 = Rotate(G_1, δ, C)
H_8 = Rotate(H_1, δ, C)
I_8 = Rotate(I_1, δ, C)
G'_4 = Rotate(G, δ, C)
D_9 = Rotate(D_2, δ, C)
E_9 = Rotate(E_2, δ, C)
F_9 = Rotate(F_2, δ, C)
L_5 = Rotate(L_1, δ, C)
K_8 = Rotate(K_1, δ, C)
J_8 = Rotate(J_1, δ, C)
G_9 = Rotate(G_2, δ, C)
H_9 = Rotate(H_2, δ, C)
I_9 = Rotate(I_2, δ, C)
J_9 = Rotate(J_2, δ, C)
K_9 = Rotate(K_2, δ, C)
Q_5, k'_4, j'_4, i'_4, c'_4, m_6, n_6, l'_4, m'_4, n'_4, o'_4, q'_4, r'_4, o_6, s_5, t_7, u_6, t'_4, u'_4, v'_4, w'_4, y'_4, e'_4, v_6, w_6, y_6, z_5, a_{11}, a_{12}, b_{10}, c_{12}, d_{11}, e_{13}, b_{11}, c_{13}, f_{11}, g_{12}, h_{11}, i_{11}, g'_4, d_{12}, e_{14}, f_{12}, l_9, k_{12}, j_{11}, g_{13}, h_{12}, i_{12}, j_{12}, k_{13} = Polygon(K'_4, J'_4, I'_4, C'_4, M_4, N_4, L'_4, M'_4, N'_4, O'_4, Q'_4, R'_4, O_4, S_4, T_4, U_4, T'_4, U'_4, V'_4, W'_4, Y'_4, E'_4, V_4, W_4, Y_4, Z_4, A_8, A_9, B_8, C_8, D_8, E_8, B_9, C_9, F_8, G_8, H_8, I_8, G'_4, D_9, E_9, F_9, L_5, K_8, J_8, G_9, H_9, I_9, J_9, K_9)
K'_5 = Rotate(K, δ, E)
J'_5 = Rotate(J, δ, E)
I'_5 = Rotate(I, δ, E)
C'_5 = Rotate(C, δ, E)
M_5 = Rotate(M_1, δ, E)
N_5 = Rotate(N_1, δ, E)
L'_5 = Rotate(L, δ, E)
M'_5 = Rotate(M, δ, E)
N'_5 = Rotate(N, δ, E)
O'_5 = Rotate(O, δ, E)
Q'_5 = Rotate(Q, δ, E)
R'_5 = Rotate(R, δ, E)
O_5 = Rotate(O_1, δ, E)
S_5 = Rotate(S_1, δ, E)
T_5 = Rotate(T_1, δ, E)
U_5 = Rotate(U_1, δ, E)
T'_5 = Rotate(T, δ, E)
U'_5 = Rotate(U, δ, E)
V'_5 = Rotate(V, δ, E)
W'_5 = Rotate(W, δ, E)
Y'_5 = Rotate(Y, δ, E)
E'_5 = Rotate(E, δ, E)
V_5 = Rotate(V_1, δ, E)
W_5 = Rotate(W_1, δ, E)
Y_5 = Rotate(Y_1, δ, E)
Z_5 = Rotate(Z_1, δ, E)
A_{10} = Rotate(A_2, δ, E)
A_{11} = Rotate(A_1, δ, E)
B_{10} = Rotate(B_1, δ, E)
C_{10} = Rotate(C_1, δ, E)
D_{10} = Rotate(D_1, δ, E)
E_{10} = Rotate(E_1, δ, E)
B_{11} = Rotate(B_2, δ, E)
C_{11} = Rotate(C_2, δ, E)
F_{10} = Rotate(F_1, δ, E)
G_{10} = Rotate(G_1, δ, E)
H_{10} = Rotate(H_1, δ, E)
I_{10} = Rotate(I_1, δ, E)
G'_5 = Rotate(G, δ, E)
D_{11} = Rotate(D_2, δ, E)
E_{11} = Rotate(E_2, δ, E)
F_{11} = Rotate(F_2, δ, E)
L_6 = Rotate(L_1, δ, E)
K_{10} = Rotate(K_1, δ, E)
J_{10} = Rotate(J_1, δ, E)
G_{11} = Rotate(G_2, δ, E)
H_{11} = Rotate(H_2, δ, E)
I_{11} = Rotate(I_2, δ, E)
J_{11} = Rotate(J_2, δ, E)
K_{11} = Rotate(K_2, δ, E)
Q_6, k'_5, j'_5, i'_5, c'_5, m_7, n_7, l'_5, m'_5, n'_5, o'_5, q'_5, r'_5, o_7, s_6, t_8, u_7, t'_5, u'_5, v'_5, w'_5, y'_5, e'_5, v_7, w_7, y_7, z_6, a_{13}, a_{14}, b_{12}, c_{14}, d_{13}, e_{15}, b_{13}, c_{15}, f_{13}, g_{14}, h_{13}, i_{13}, g'_5, d_{14}, e_{16}, f_{14}, l_{10}, k_{14}, j_{13}, g_{15}, h_{14}, i_{14}, j_{14}, k_{15} = Polygon(K'_5, J'_5, I'_5, C'_5, M_5, N_5, L'_5, M'_5, N'_5, O'_5, Q'_5, R'_5, O_5, S_5, T_5, U_5, T'_5, U'_5, V'_5, W'_5, Y'_5, E'_5, V_5, W_5, Y_5, Z_5, A_{10}, A_{11}, B_{10}, C_{10}, D_{10}, E_{10}, B_{11}, C_{11}, F_{10}, G_{10}, H_{10}, I_{10}, G'_5, D_{11}, E_{11}, F_{11}, L_6, K_{10}, J_{10}, G_{11}, H_{11}, I_{11}, J_{11}, K_{11})
K'_6 = Rotate(K, δ, G)
J'_6 = Rotate(J, δ, G)
I'_6 = Rotate(I, δ, G)
C'_6 = Rotate(C, δ, G)
M_6 = Rotate(M_1, δ, G)
N_6 = Rotate(N_1, δ, G)
L'_6 = Rotate(L, δ, G)
M'_6 = Rotate(M, δ, G)
N'_6 = Rotate(N, δ, G)
O'_6 = Rotate(O, δ, G)
Q'_6 = Rotate(Q, δ, G)
R'_6 = Rotate(R, δ, G)
O_6 = Rotate(O_1, δ, G)
S_6 = Rotate(S_1, δ, G)
T_6 = Rotate(T_1, δ, G)
U_6 = Rotate(U_1, δ, G)
T'_6 = Rotate(T, δ, G)
U'_6 = Rotate(U, δ, G)
V'_6 = Rotate(V, δ, G)
W'_6 = Rotate(W, δ, G)
Y'_6 = Rotate(Y, δ, G)
E'_6 = Rotate(E, δ, G)
V_6 = Rotate(V_1, δ, G)
W_6 = Rotate(W_1, δ, G)
Y_6 = Rotate(Y_1, δ, G)
Z_6 = Rotate(Z_1, δ, G)
A_{12} = Rotate(A_2, δ, G)
A_{13} = Rotate(A_1, δ, G)
B_{12} = Rotate(B_1, δ, G)
C_{12} = Rotate(C_1, δ, G)
D_{12} = Rotate(D_1, δ, G)
E_{12} = Rotate(E_1, δ, G)
B_{13} = Rotate(B_2, δ, G)
C_{13} = Rotate(C_2, δ, G)
F_{12} = Rotate(F_1, δ, G)
G_{12} = Rotate(G_1, δ, G)
H_{12} = Rotate(H_1, δ, G)
I_{12} = Rotate(I_1, δ, G)
G'_6 = Rotate(G, δ, G)
D_{13} = Rotate(D_2, δ, G)
E_{13} = Rotate(E_2, δ, G)
F_{13} = Rotate(F_2, δ, G)
L_7 = Rotate(L_1, δ, G)
K_{12} = Rotate(K_1, δ, G)
J_{12} = Rotate(J_1, δ, G)
G_{13} = Rotate(G_2, δ, G)
H_{13} = Rotate(H_2, δ, G)
I_{13} = Rotate(I_2, δ, G)
J_{13} = Rotate(J_2, δ, G)
K_{13} = Rotate(K_2, δ, G)
Q_7, k'_6, j'_6, i'_6, c'_6, m_8, n_8, l'_6, m'_6, n'_6, o'_6, q'_6, r'_6, o_8, s_7, t_9, u_8, t'_6, u'_6, v'_6, w'_6, y'_6, e'_6, v_8, w_8, y_8, z_7, a_{15}, a_{16}, b_{14}, c_{16}, d_{15}, e_{17}, b_{15}, c_{17}, f_{15}, g_{16}, h_{15}, i_{15}, g'_6, d_{16}, e_{18}, f_{16}, l_{11}, k_{16}, j_{15}, g_{17}, h_{16}, i_{16}, j_{16}, k_{17} = Polygon(K'_6, J'_6, I'_6, C'_6, M_6, N_6, L'_6, M'_6, N'_6, O'_6, Q'_6, R'_6, O_6, S_6, T_6, U_6, T'_6, U'_6, V'_6, W'_6, Y'_6, E'_6, V_6, W_6, Y_6, Z_6, A_{12}, A_{13}, B_{12}, C_{12}, D_{12}, E_{12}, B_{13}, C_{13}, F_{12}, G_{12}, H_{12}, I_{12}, G'_6, D_{13}, E_{13}, F_{13}, L_7, K_{12}, J_{12}, G_{13}, H_{13}, I_{13}, J_{13}, K_{13})