Alhambra Star Pattern Construction: p4g Symmetry Design

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2023-03-22 23:17

In collections geometriadinamica.es

This example demonstrates how to construct the classic Alhambra star pattern (Estrellas) with p4g symmetry using GeoGebra. The core mathematical concepts include planar tessellation, symmetry transformations (mirror, rotation, translation), and polygon construction. Construction highlights: Using commands such as Midpoint, Line, OrthogonalLine, Point, Mirror, Intersect, Vector, Circle, Polygon, Segment, Translate, and Rotate to create complex star patterns with p4g group symmetry. Suitable for high school and above students to explore the mathematical principles in Islamic geometric decoration, and as a vivid case study for coordinate geometry and transformational geometry teaching.

GeoGebra Commands & Parameters

Midpoint(C, D) → G
Line(D, C) → b
OrthogonalLine(G, b) → e
OrthogonalLine(D, b) → d
Point(d) → E
Midpoint(E, D) → F
Midpoint(G, F) → H
Mirror(H, e) → H'
OrthogonalLine(F, d) → g
Mirror(H, g) → H'_1
Mirror(H'_1, d) → K
OrthogonalLine(E, d) → h
OrthogonalLine(C, b) → f
Mirror(H', f) → H''
Mirror(H'', g) → H'''
Line(K, H''') → k_1
Intersect(f, g) → N
Intersect(f, h) → O
Line(O, N) → n_1
Mirror(H'_1, h) → J
Mirror(H', g) → H''_1
Mirror(H''_1, h) → I
Line(I, J) → p
Intersect(f, p) → R_3
Line(H'', H') → n
Intersect(n_1, k_1) → P_5
Vector(R_3, P_5) → u
Length(u) → d1
If(a < 2.3, 0, If[a < 3.3, a - 2.3, 1]) → d3
If(a < 3.4, 0, If[a < 4.4, a - 3.4, 1]) → d4
If(a < 4.5, 0, If[a < 5.5, a - 4.5, 1]) → d5
If(a < 5.6, 0, If[a < 6.6, a - 5.6, 1]) → d6
If(a < 6.7, 0, If[a < 7.7, a - 6.7, 1]) → d7
If(a < 7.8, 0, If[a < 8.8, a - 7.8, 1]) → d8
OrthogonalLine(H, b) → i
Mirror(H, d) → H'_2
Line(H'_2, K) → j
Line(H', H''_1) → k
Line(H'', H''') → l
Line(H''', H''_1) → m
Mirror(H, b) → H'_3
Mirror(H', b) → H''_2
Intersect(e, g) → M
Intersect(e, h) → P
Intersect(j, p) → Q
Point(e) → T
Circle(M, T) → q
Intersect(q, g, 2) → V
OrthogonalLine(V, g) → a_1
Mirror(T, i) → T'
Mirror(U, i) → U'
Mirror(U, i) → U'_1
Mirror(V, i) → V'
Mirror(T, i) → T'_1
Mirror(V, i) → V'_1
Mirror(T', m) → T''
Mirror(U', m) → U''
Mirror(U'_1, m) → A_1
Mirror(V', m) → V''
Mirror(V'_1, m) → D_1
Mirror(T'_1, m) → G_1
Mirror(T'', i) → T'''
Mirror(U'', i) → U'''
Mirror(A_1, i) → H_1
Mirror(V'', i) → V'''
Mirror(D_1, i) → K_1
Mirror(G_1, i) → N_1
Polygon(H, H'_1, H''_1) → poly1, h''_1, h_1, h'_1
Point(h''_1) → R
Point(h'_1) → W
Circle(M, W) → r
Intersect(r, h'_1, 2) → S
Line(S, m) → s
Intersect(r, s, 2) → Z
Point(s) → B_1
Segment(R, H) → t
Circle(H'_1, t) → c_1
Intersect(c_1, h_1) → C_1,
OrthogonalLine(S, s) → b_1
Point(b_1) → E_1
Polygon(H'_1, C_1, E_1, S, B_1, R) → poly2, h'_2, c_2, e_1, s_1, b_2, r_1
Polygon(Z, W, M) → poly3, m_1, z, w
Polygon(S, H''_1, C_1, E_1) → poly4, s_2, h''_2, c_3, e_2
Polygon(Z, W, H, R, B_1) → poly5, z_1, w_1, h_2, r_2, b_3
Polygon(Z, M, S) → poly6, s_3, z_2, m_2
Mirror(Z, i) → Z'
Mirror(W, i) → W'
Mirror(H, i) → H'_4
Mirror(R, i) → R'
Mirror(B_1, i) → F_1
Polygon(Z', W', H'_4, R', F_1) → poly5', z', w', h'_4, r', f_1
Mirror(Z, i) → Z'_1
Mirror(W, i) → W'_1
Mirror(M, i) → M'
Polygon(Z'_1, W'_1, M') → poly3', m', z'_1, w'_1
Mirror(Z, i) → Z'_2
Mirror(M, i) → M'_1
Mirror(S, i) → S'
Polygon(Z'_2, M'_1, S') → poly6', s', z'_2, m'_1
Mirror(H'_1, i) → I_1
Mirror(C_1, i) → J_1
Mirror(E_1, i) → L_1
Mirror(S, i) → S'_1
Mirror(B_1, i) → M_1
Mirror(R, i) → R'_1
Polygon(I_1, J_1, L_1, S'_1, M_1, R'_1) → poly2', i_1, j_1, l_1, s'_1, m_3, r'_1
Mirror(S, i) → S'_2
Mirror(H''_1, i) → O_1
Mirror(C_1, i) → P_1
Mirror(E_1, i) → Q_1
Polygon(S'_2, O_1, P_1, Q_1) → poly4', s'_2, o_1, p_1, q_1
Mirror(Z', m) → Z''
Mirror(W', m) → W''
Mirror(H'_4, m) → R_1
Mirror(R', m) → R''
Mirror(F_1, m) → S_1
Polygon(Z'', W'', R_1, R'', S_1) → poly5'', z'', w'', r_3, r'', s_4
Mirror(I_1, m) → T_1
Mirror(J_1, m) → U_1
Mirror(L_1, m) → V_1
Mirror(S'_1, m) → W_1
Mirror(M_1, m) → Z_1
Mirror(R'_1, m) → A_2
Polygon(T_1, U_1, V_1, W_1, Z_1, A_2) → poly2'', t_1, u_1, v_1, w_2, z_3, a_2
Mirror(S'_2, m) → B_2
Mirror(O_1, m) → C_2
Mirror(P_1, m) → D_2
Mirror(Q_1, m) → E_2
Polygon(B_2, C_2, D_2, E_2) → poly4'', b_4, c_4, d_2, e_3
Mirror(Z'_2, m) → F_2
Mirror(M'_1, m) → G_2
Mirror(S', m) → S''
Polygon(F_2, G_2, S'') → poly6'', s'', f_2, g_2
Mirror(Z'_1, m) → H_2
Mirror(W'_1, m) → I_2
Mirror(M', m) → M''
Polygon(H_2, I_2, M'') → poly3'', m'', h_3, i_2
Mirror(Z'', i) → Z'''
Mirror(W'', i) → W'''
Mirror(R_1, i) → J_2
Mirror(R'', i) → R'''
Mirror(S_1, i) → K_2
Polygon(Z''', W''', J_2, R''', K_2) → poly5''', z''', w''', j_2, r''', k_2
Mirror(T_1, i) → L_2
Mirror(U_1, i) → M_2
Mirror(V_1, i) → N_2
Mirror(W_1, i) → O_2
Mirror(Z_1, i) → P_2
Mirror(A_2, i) → Q_2
Polygon(L_2, M_2, N_2, O_2, P_2, Q_2) → poly2''', l_2, m_4, n_2, o_2, p_2, q_2
Mirror(B_2, i) → R_2
Mirror(C_2, i) → S_2
Mirror(D_2, i) → T_2
Mirror(E_2, i) → U_2
Polygon(R_2, S_2, T_2, U_2) → poly4''', r_4, s_5, t_2, u_2
Mirror(F_2, i) → V_2
Mirror(G_2, i) → W_2
Mirror(S'', i) → S'''
Polygon(V_2, W_2, S''') → poly6''', s''', v_2, w_3
Mirror(H_2, i) → Z_2
Mirror(I_2, i) → A_3
Mirror(M'', i) → M'''
Polygon(Z_2, A_3, M''') → poly3''', m''', z_4, a_3
Mirror(Z, e) → Z'_3
Mirror(W, e) → W'_2
Mirror(H, e) → H'_5
Mirror(R, e) → R'_2
Mirror(B_1, e) → B_3
Polygon(Z'_3, W'_2, H'_5, R'_2, B_3) → poly5'_1, z'_3, w'_2, h'_5, r'_2, b_5
Mirror(Z', e) → Z''_1
Mirror(W', e) → W''_1
Mirror(H'_4, e) → C_3
Mirror(R', e) → R''_1
Mirror(F_1, e) → D_3
Polygon(Z''_1, W''_1, C_3, R''_1, D_3) → poly5''_1, z''_1, w''_1, c_5, r''_1, d_3
Mirror(Z, e) → Z'_4
Mirror(W, e) → W'_3
Mirror(M, e) → M'_2
Polygon(Z'_4, W'_3, M'_2) → poly3'_1, m'_2, z'_4, w'_3
Mirror(Z, e) → Z'_5
Mirror(M, e) → M'_3
Mirror(S, e) → S'_3
Polygon(Z'_5, M'_3, S'_3) → poly6'_1, s'_3, z'_5, m'_3
Mirror(S, e) → S'_4
Mirror(H''_1, e) → E_3
Mirror(C_1, e) → F_3
Mirror(E_1, e) → G_3
Polygon(S'_4, E_3, F_3, G_3) → poly4'_1, s'_4, e_4, f_3, g_3
Mirror(Z_2, e) → H_3
Mirror(A_3, e) → I_3
Mirror(M''', e) → J_3
Polygon(H_3, I_3, J_3) → poly7, j_3, h_4, i_3
Mirror(Z''', e) → K_3
Mirror(W''', e) → L_3
Mirror(J_2, e) → M_3
Mirror(R''', e) → N_3
Mirror(K_2, e) → O_3
Polygon(K_3, L_3, M_3, N_3, O_3) → poly8, k_3, l_3, m_5, n_3, o_3
Mirror(Z'', e) → Z'''_1
Mirror(W'', e) → W'''_1
Mirror(R_1, e) → P_3
Mirror(R'', e) → R'''_1
Mirror(S_1, e) → Q_3
Polygon(Z'''_1, W'''_1, P_3, R'''_1, Q_3) → poly5'''_1, z'''_1, w'''_1, p_3, r'''_1, q_3
Mirror(L_2, e) → S_3
Mirror(M_2, e) → T_3
Mirror(N_2, e) → U_3
Mirror(O_2, e) → V_3
Mirror(P_2, e) → W_3
Mirror(Q_2, e) → Z_3
Polygon(S_3, T_3, U_3, V_3, W_3, Z_3) → poly9, s_6, t_3, u_3, v_3, w_4, z_5
Mirror(H'_1, e) → A_4
Mirror(C_1, e) → B_4
Mirror(E_1, e) → C_4
Mirror(S, e) → S'_5
Mirror(B_1, e) → D_4
Mirror(R, e) → R'_3
Polygon(A_4, B_4, C_4, S'_5, D_4, R'_3) → poly2'_1, a_4, b_6, c_6, s'_5, d_4, r'_3
Mirror(I_1, e) → E_4
Mirror(J_1, e) → F_4
Mirror(L_1, e) → G_4
Mirror(S'_1, e) → H_4
Mirror(M_1, e) → I_4
Mirror(R'_1, e) → J_4
Polygon(E_4, F_4, G_4, H_4, I_4, J_4) → poly2''_1, e_5, f_4, g_4, h_5, i_4, j_4
Mirror(T_1, e) → K_4
Mirror(U_1, e) → L_4
Mirror(V_1, e) → M_4
Mirror(W_1, e) → N_4
Mirror(Z_1, e) → O_4
Mirror(A_2, e) → P_4
Polygon(K_4, L_4, M_4, N_4, O_4, P_4) → poly2'''_1, k_4, l_4, m_6, n_4, o_4, p_4
Mirror(Z'_1, e) → Q_4
Mirror(W'_1, e) → R_4
Mirror(M', e) → M''_1
Polygon(Q_4, R_4, M''_1) → poly3''_1, m''_1, q_4, r_5
Mirror(Z'_2, e) → S_4
Mirror(M'_1, e) → T_4
Mirror(S', e) → S''_1
Polygon(S_4, T_4, S''_1) → poly6''_1, s''_1, s_7, t_4
Mirror(S'_2, e) → U_4
Mirror(O_1, e) → V_4
Mirror(P_1, e) → W_4
Mirror(Q_1, e) → Z_4
Polygon(U_4, V_4, W_4, Z_4) → poly4''_1, u_4, v_4, w_5, z_6
Mirror(B_2, e) → A_5
Mirror(C_2, e) → B_5
Mirror(D_2, e) → C_5
Mirror(E_2, e) → D_5
Polygon(A_5, B_5, C_5, D_5) → poly4'''_1, a_5, b_7, c_7, d_5
Mirror(F_2, e) → E_5
Mirror(G_2, e) → F_5
Mirror(S'', e) → S'''_1
Polygon(E_5, F_5, S'''_1) → poly6'''_1, s'''_1, e_6, f_5
Mirror(H_2, e) → G_5
Mirror(I_2, e) → H_5
Mirror(M'', e) → M'''_1
Polygon(G_5, H_5, M'''_1) → poly3'''_1, m'''_1, g_5, h_6
Mirror(R_2, e) → I_5
Mirror(S_2, e) → J_5
Mirror(T_2, e) → K_5
Mirror(U_2, e) → L_5
Polygon(I_5, J_5, K_5, L_5) → poly10, i_5, j_5, k_5, l_5
Mirror(V_2, e) → M_5
Mirror(W_2, e) → N_5
Mirror(S''', e) → O_5
Polygon(M_5, N_5, O_5) → poly11, o_5, m_7, n_5
Min(d1, ((a - 3.5) * d1)) → d2
Circle(R_3, d2) → d_1
Intersect(d_1, f) → L, Q_5
Vector(R_3, Q_5) → g_1
Translate(Z'_3, g_1) → R_5
Translate(W'_2, g_1) → S_5
Translate(H'_5, g_1) → T_5
Translate(R'_2, g_1) → U_5
Translate(B_3, g_1) → V_5
Polygon(R_5, S_5, T_5, U_5, V_5) → poly12, r_6, s_8, t_5, u_5, v_5
Translate(Z''_1, g_1) → W_5
Translate(W''_1, g_1) → Z_5
Translate(C_3, g_1) → A_6
Translate(R''_1, g_1) → B_6
Translate(D_3, g_1) → C_6
Polygon(W_5, Z_5, A_6, B_6, C_6) → poly13, w_6, z_7, a_6, b_8, c_8
Translate(Q_4, g_1) → D_6
Translate(R_4, g_1) → E_6
Translate(M''_1, g_1) → F_6
Polygon(D_6, E_6, F_6) → poly14, f_6, d_6, e_7
Translate(E_4, g_1) → G_6
Translate(F_4, g_1) → H_6
Translate(G_4, g_1) → I_6
Translate(H_4, g_1) → J_6
Translate(I_4, g_1) → K_6
Translate(J_4, g_1) → L_6
Polygon(G_6, H_6, I_6, J_6, K_6, L_6) → poly15, g_6, h_7, i_6, j_6, k_6, l_6
Translate(S_4, g_1) → M_6
Translate(T_4, g_1) → N_6
Translate(S''_1, g_1) → O_6
Polygon(M_6, N_6, O_6) → poly16, o_6, m_8, n_6
Translate(U_4, g_1) → P_6
Translate(V_4, g_1) → Q_6
Translate(W_4, g_1) → R_6
Translate(Z_4, g_1) → S_6
Polygon(P_6, Q_6, R_6, S_6) → poly17, p_6, q_6, r_7, s_9
Translate(A_5, g_1) → T_6
Translate(B_5, g_1) → U_6
Translate(C_5, g_1) → V_6
Translate(D_5, g_1) → W_6
Polygon(T_6, U_6, V_6, W_6) → poly18, t_6, u_6, v_6, w_7
Translate(K_4, g_1) → Z_6
Translate(L_4, g_1) → A_7
Translate(M_4, g_1) → B_7
Translate(N_4, g_1) → C_7
Translate(O_4, g_1) → D_7
Translate(P_4, g_1) → E_7
Polygon(Z_6, A_7, B_7, C_7, D_7, E_7) → poly19, z_8, a_7, b_9, c_9, d_7, e_8
Translate(S_3, g_1) → F_7
Translate(T_3, g_1) → G_7
Translate(U_3, g_1) → H_7
Translate(V_3, g_1) → I_7
Translate(W_3, g_1) → J_7
Translate(Z_3, g_1) → K_7
Polygon(F_7, G_7, H_7, I_7, J_7, K_7) → poly9', f_7, g_7, h_8, i_7, j_7, k_7
Translate(A_4, g_1) → L_7
Translate(B_4, g_1) → M_7
Translate(C_4, g_1) → N_7
Translate(S'_5, g_1) → O_7
Translate(D_4, g_1) → P_7
Translate(R'_3, g_1) → Q_7
Polygon(L_7, M_7, N_7, O_7, P_7, Q_7) → poly20, l_7, m_9, n_7, o_7, p_7, q_7
Translate(Z'_4, g_1) → R_7
Translate(W'_3, g_1) → S_7
Translate(M'_2, g_1) → T_7
Polygon(R_7, S_7, T_7) → poly21, t_7, r_8, s_{10}
Translate(Z'_5, g_1) → U_7
Translate(M'_3, g_1) → V_7
Translate(S'_3, g_1) → W_7
Polygon(U_7, V_7, W_7) → poly22, w_8, u_7, v_7
Translate(S'_4, g_1) → Z_7
Translate(E_3, g_1) → A_8
Translate(F_3, g_1) → B_8
Translate(G_3, g_1) → C_8
Polygon(Z_7, A_8, B_8, C_8) → poly23, z_9, a_8, b_{10}, c_{10}
Translate(I_5, g_1) → D_8
Translate(J_5, g_1) → E_8
Translate(K_5, g_1) → F_8
Translate(L_5, g_1) → G_8
Polygon(D_8, E_8, F_8, G_8) → poly10', d_8, e_9, f_8, g_8
Translate(M_5, g_1) → H_8
Translate(N_5, g_1) → I_8
Translate(O_5, g_1) → J_8
Polygon(H_8, I_8, J_8) → poly11', j_8, h_9, i_8
Translate(K_3, g_1) → K_8
Translate(L_3, g_1) → L_8
Translate(M_3, g_1) → M_8
Translate(N_3, g_1) → N_8
Translate(O_3, g_1) → O_8
Polygon(K_8, L_8, M_8, N_8, O_8) → poly8', k_8, l_8, m_{10}, n_8, o_8
Translate(Z'''_1, g_1) → P_8
Translate(W'''_1, g_1) → Q_8
Translate(P_3, g_1) → R_8
Translate(R'''_1, g_1) → S_8
Translate(Q_3, g_1) → T_8
Polygon(P_8, Q_8, R_8, S_8, T_8) → poly24, p_8, q_8, r_9, s_{11}, t_8
Translate(K_3, g_1) → U_8
Translate(L_3, g_1) → V_8
Translate(M_3, g_1) → W_8
Translate(N_3, g_1) → Z_8
Translate(O_3, g_1) → A_9
Polygon(U_8, V_8, W_8, Z_8, A_9) → poly8'_1, u_8, v_8, w_9, z_{10}, a_9
Translate(G_5, g_1) → B_9
Translate(H_5, g_1) → C_9
Translate(M'''_1, g_1) → D_9
Polygon(B_9, C_9, D_9) → poly25, d_9, b_{11}, c_{11}
Translate(E_5, g_1) → E_9
Translate(F_5, g_1) → F_9
Translate(S'''_1, g_1) → G_9
Polygon(E_9, F_9, G_9) → poly26, g_9, e_{10}, f_9
Mirror(Z_2, e) → H_9
Mirror(A_3, e) → I_9
Mirror(M''', e) → J_9
Polygon(H_9, I_9, J_9) → poly27, j_9, h_{10}, i_9
Translate(H_9, g_1) → K_9
Translate(I_9, g_1) → L_9
Translate(J_9, g_1) → M_9
Polygon(K_9, L_9, M_9) → poly27', m_{11}, k_9, l_9
Min(180, ((a - 5) * 180)) → r1
Rotate(R_5, r1°, G) → N_9
Rotate(S_5, r1°, G) → O_9
Rotate(T_5, r1°, G) → P_9
Rotate(U_5, r1°, G) → Q_9
Rotate(V_5, r1°, G) → R_9
Polygon(N_9, O_9, P_9, Q_9, R_9) → poly12', n_9, o_9, p_9, q_9, r_{10}
Rotate(R_7, r1°, G) → S_9
Rotate(S_7, r1°, G) → T_9
Rotate(T_7, r1°, G) → U_9
Polygon(S_9, T_9, U_9) → poly21', u_9, s_{12}, t_9
Rotate(U_7, r1°, G) → V_9
Rotate(V_7, r1°, G) → W_9
Rotate(W_7, r1°, G) → Z_9
Polygon(V_9, W_9, Z_9) → poly22', z_{11}, v_9, w_{10}
Rotate(Z_7, r1°, G) → A_{10}
Rotate(A_8, r1°, G) → B_{10}
Rotate(B_8, r1°, G) → C_{10}
Rotate(C_8, r1°, G) → D_{10}
Polygon(A_{10}, B_{10}, C_{10}, D_{10}) → poly23', a_{10}, b_{12}, c_{12}, d_{10}
Rotate(L_7, r1°, G) → E_{10}
Rotate(M_7, r1°, G) → F_{10}
Rotate(N_7, r1°, G) → G_{10}
Rotate(O_7, r1°, G) → H_{10}
Rotate(P_7, r1°, G) → I_{10}
Rotate(Q_7, r1°, G) → J_{10}
Polygon(E_{10}, F_{10}, G_{10}, H_{10}, I_{10}, J_{10}) → poly20', e_{11}, f_{10}, g_{10}, h_{11}, i_{10}, j_{10}
Rotate(W_5, r1°, G) → K_{10}
Rotate(Z_5, r1°, G) → L_{10}
Rotate(A_6, r1°, G) → M_{10}
Rotate(B_6, r1°, G) → N_{10}
Rotate(C_6, r1°, G) → O_{10}
Polygon(K_{10}, L_{10}, M_{10}, N_{10}, O_{10}) → poly13', k_{10}, l_{10}, m_{12}, n_{10}, o_{10}
Rotate(D_6, r1°, G) → P_{10}
Rotate(E_6, r1°, G) → Q_{10}
Rotate(F_6, r1°, G) → R_{10}
Polygon(P_{10}, Q_{10}, R_{10}) → poly14', r_{11}, p_{10}, q_{10}
Rotate(M_6, r1°, G) → S_{10}
Rotate(N_6, r1°, G) → T_{10}
Rotate(O_6, r1°, G) → U_{10}
Polygon(S_{10}, T_{10}, U_{10}) → poly16', u_{10}, s_{13}, t_{10}
Rotate(G_6, r1°, G) → V_{10}
Rotate(H_6, r1°, G) → W_{10}
Rotate(I_6, r1°, G) → Z_{10}
Rotate(J_6, r1°, G) → A_{11}
Rotate(K_6, r1°, G) → B_{11}
Rotate(L_6, r1°, G) → C_{11}
Polygon(V_{10}, W_{10}, Z_{10}, A_{11}, B_{11}, C_{11}) → poly15', v_{10}, w_{11}, z_{12}, a_{11}, b_{13}, c_{13}
Rotate(P_6, r1°, G) → D_{11}
Rotate(Q_6, r1°, G) → E_{11}
Rotate(R_6, r1°, G) → F_{11}
Rotate(S_6, r1°, G) → G_{11}
Polygon(D_{11}, E_{11}, F_{11}, G_{11}) → poly17', d_{11}, e_{12}, f_{11}, g_{11}
Rotate(T_6, r1°, G) → H_{11}
Rotate(U_6, r1°, G) → I_{11}
Rotate(V_6, r1°, G) → J_{11}
Rotate(W_6, r1°, G) → K_{11}
Polygon(H_{11}, I_{11}, J_{11}, K_{11}) → poly18', h_{12}, i_{11}, j_{11}, k_{11}
Rotate(E_9, r1°, G) → L_{11}
Rotate(F_9, r1°, G) → M_{11}
Rotate(G_9, r1°, G) → N_{11}
Polygon(L_{11}, M_{11}, N_{11}) → poly26', n_{11}, l_{11}, m_{13}
Rotate(B_9, r1°, G) → O_{11}
Rotate(C_9, r1°, G) → P_{11}
Rotate(D_9, r1°, G) → Q_{11}
Polygon(O_{11}, P_{11}, Q_{11}) → poly25', q_{11}, o_{11}, p_{11}
Rotate(P_8, r1°, G) → R_{11}
Rotate(Q_8, r1°, G) → S_{11}
Rotate(R_8, r1°, G) → T_{11}
Rotate(S_8, r1°, G) → U_{11}
Rotate(T_8, r1°, G) → V_{11}
Polygon(R_{11}, S_{11}, T_{11}, U_{11}, V_{11}) → poly24', r_{12}, s_{14}, t_{11}, u_{11}, v_{11}
Rotate(U_8, r1°, G) → W_{11}
Rotate(V_8, r1°, G) → Z_{11}
Rotate(W_8, r1°, G) → A_{12}
Rotate(Z_8, r1°, G) → B_{12}
Rotate(A_9, r1°, G) → C_{12}
Polygon(W_{11}, Z_{11}, A_{12}, B_{12}, C_{12}) → poly28, w_{12}, z_{13}, a_{12}, b_{14}, c_{14}
Rotate(K_9, r1°, G) → D_{12}
Rotate(L_9, r1°, G) → E_{12}
Rotate(M_9, r1°, G) → F_{12}
Polygon(D_{12}, E_{12}, F_{12}) → poly27'', f_{12}, d_{12}, e_{13}
Rotate(H_8, r1°, G) → G_{12}
Rotate(I_8, r1°, G) → H_{12}
Rotate(J_8, r1°, G) → I_{12}
Polygon(G_{12}, H_{12}, I_{12}) → poly11'', i_{12}, g_{12}, h_{13}
Rotate(D_8, r1°, G) → J_{12}
Rotate(E_8, r1°, G) → K_{12}
Rotate(F_8, r1°, G) → L_{12}
Rotate(G_8, r1°, G) → M_{12}
Polygon(J_{12}, K_{12}, L_{12}, M_{12}) → poly10'', j_{12}, k_{12}, l_{12}, m_{14}
Rotate(Z_6, r1°, G) → N_{12}
Rotate(A_7, r1°, G) → O_{12}
Rotate(B_7, r1°, G) → P_{12}
Rotate(C_7, r1°, G) → Q_{12}
Rotate(D_7, r1°, G) → R_{12}
Rotate(E_7, r1°, G) → S_{12}
Polygon(N_{12}, O_{12}, P_{12}, Q_{12}, R_{12}, S_{12}) → poly19', n_{12}, o_{12}, p_{12}, q_{12}, r_{13}, s_{15}
Rotate(F_7, r1°, G) → T_{12}
Rotate(G_7, r1°, G) → U_{12}
Rotate(H_7, r1°, G) → V_{12}
Rotate(I_7, r1°, G) → W_{12}
Rotate(J_7, r1°, G) → Z_{12}
Rotate(K_7, r1°, G) → A_{13}
Polygon(T_{12}, U_{12}, V_{12}, W_{12}, Z_{12}, A_{13}) → poly9'', t_{12}, u_{12}, v_{12}, w_{13}, z_{14}, a_{13}
Min(180, ((a - 6.5) * 180)) → r5
Mirror(H'_1, J) → B_{13}
Vector(Q, B_{13}) → p_5
Vector(Q, I) → q_5
Rotate(S'_2, (-(r5°)), H) → C_{13}
Rotate(O_1, (-(r5°)), H) → D_{13}
Rotate(P_1, (-(r5°)), H) → E_{13}
Rotate(Q_1, (-(r5°)), H) → F_{13}
Rotate(G_6, (-(r5°)), N) → G_{13}
Rotate(H_6, (-(r5°)), N) → H_{13}
Rotate(I_6, (-(r5°)), N) → I_{13}
Rotate(J_6, (-(r5°)), N) → J_{13}
Rotate(K_6, (-(r5°)), N) → K_{13}
Rotate(L_6, (-(r5°)), N) → L_{13}
Polygon(G_{13}, H_{13}, I_{13}, J_{13}, K_{13}, L_{13}) → poly15'_1, g_{13}, h_{14}, i_{13}, j_{13}, k_{13}, l_{13}
Rotate(L_7, (-(r5°)), N) → M_{13}
Rotate(M_7, (-(r5°)), N) → N_{13}
Rotate(N_7, (-(r5°)), N) → O_{13}
Rotate(O_7, (-(r5°)), N) → P_{13}
Rotate(P_7, (-(r5°)), N) → Q_{13}
Rotate(Q_7, (-(r5°)), N) → R_{13}
Polygon(M_{13}, N_{13}, O_{13}, P_{13}, Q_{13}, R_{13}) → poly20'_1, m_{15}, n_{13}, o_{13}, p_{13}, q_{13}, r_{14}
Rotate(F_7, (-(r5°)), N) → S_{13}
Rotate(G_7, (-(r5°)), N) → T_{13}
Rotate(H_7, (-(r5°)), N) → U_{13}
Rotate(I_7, (-(r5°)), N) → V_{13}
Rotate(J_7, (-(r5°)), N) → W_{13}
Rotate(K_7, (-(r5°)), N) → Z_{13}
Polygon(S_{13}, T_{13}, U_{13}, V_{13}, W_{13}, Z_{13}) → poly9''_1, s_{16}, t_{13}, u_{13}, v_{13}, w_{14}, z_{15}
Rotate(Z_6, (-(r5°)), N) → A_{14}
Rotate(A_7, (-(r5°)), N) → B_{14}
Rotate(B_7, (-(r5°)), N) → C_{14}
Rotate(C_7, (-(r5°)), N) → D_{14}
Rotate(D_7, (-(r5°)), N) → E_{14}
Rotate(E_7, (-(r5°)), N) → F_{14}
Polygon(A_{14}, B_{14}, C_{14}, D_{14}, E_{14}, F_{14}) → poly19'_1, a_{14}, b_{15}, c_{15}, d_{14}, e_{14}, f_{14}
Rotate(H'_1, (-(r5°)), P) → G_{14}
Rotate(C_1, (-(r5°)), P) → H_{14}
Rotate(E_1, (-(r5°)), P) → I_{14}
Rotate(S, (-(r5°)), P) → S'_6
Rotate(B_1, (-(r5°)), P) → J_{14}
Rotate(R, (-(r5°)), P) → R'_4
Polygon(G_{14}, H_{14}, I_{14}, S'_6, J_{14}, R'_4) → poly2'_2, g_{14}, h_{15}, i_{14}, s'_6, j_{14}, r'_4
Rotate(I_1, (-(r5°)), P) → K_{14}
Rotate(J_1, (-(r5°)), P) → L_{14}
Rotate(L_1, (-(r5°)), P) → M_{14}
Rotate(S'_1, (-(r5°)), P) → N_{14}
Rotate(M_1, (-(r5°)), P) → O_{14}
Rotate(R'_1, (-(r5°)), P) → P_{14}
Polygon(K_{14}, L_{14}, M_{14}, N_{14}, O_{14}, P_{14}) → poly2''_2, k_{14}, l_{14}, m_{16}, n_{14}, o_{14}, p_{14}
Rotate(T_1, (-(r5°)), P) → Q_{14}
Rotate(U_1, (-(r5°)), P) → R_{14}
Rotate(V_1, (-(r5°)), P) → S_{14}
Rotate(W_1, (-(r5°)), P) → T_{14}
Rotate(Z_1, (-(r5°)), P) → U_{14}
Rotate(A_2, (-(r5°)), P) → V_{14}
Polygon(Q_{14}, R_{14}, S_{14}, T_{14}, U_{14}, V_{14}) → poly2'''_2, q_{14}, r_{15}, s_{17}, t_{14}, u_{14}, v_{14}
Rotate(L_2, (-(r5°)), P) → W_{14}
Rotate(M_2, (-(r5°)), P) → Z_{14}
Rotate(N_2, (-(r5°)), P) → A_{15}
Rotate(O_2, (-(r5°)), P) → B_{15}
Rotate(P_2, (-(r5°)), P) → C_{15}
Rotate(Q_2, (-(r5°)), P) → D_{15}
Polygon(W_{14}, Z_{14}, A_{15}, B_{15}, C_{15}, D_{15}) → poly29, w_{15}, z_{16}, a_{15}, b_{16}, c_{16}, d_{15}
Rotate(I_1, (-(r5°)), E) → E_{15}
Rotate(J_1, (-(r5°)), E) → F_{15}
Rotate(L_1, (-(r5°)), E) → G_{15}
Rotate(S'_1, (-(r5°)), E) → H_{15}
Rotate(M_1, (-(r5°)), E) → I_{15}
Rotate(R'_1, (-(r5°)), E) → J_{15}
Polygon(E_{15}, F_{15}, G_{15}, H_{15}, I_{15}, J_{15}) → poly2''_3, e_{15}, f_{15}, g_{15}, h_{16}, i_{15}, j_{15}
Rotate(H'_1, (-(r5°)), E) → K_{15}
Rotate(C_1, (-(r5°)), E) → L_{15}
Rotate(E_1, (-(r5°)), E) → M_{15}
Rotate(S, (-(r5°)), E) → S'_7
Rotate(B_1, (-(r5°)), E) → N_{15}
Rotate(R, (-(r5°)), E) → R'_5
Polygon(K_{15}, L_{15}, M_{15}, S'_7, N_{15}, R'_5) → poly2'_3, k_{15}, l_{15}, m_{17}, s'_7, n_{15}, r'_5
Rotate(L_2, (-(r5°)), E) → O_{15}
Rotate(M_2, (-(r5°)), E) → P_{15}
Rotate(N_2, (-(r5°)), E) → Q_{15}
Rotate(O_2, (-(r5°)), E) → R_{15}
Rotate(P_2, (-(r5°)), E) → S_{15}
Rotate(Q_2, (-(r5°)), E) → T_{15}
Polygon(O_{15}, P_{15}, Q_{15}, R_{15}, S_{15}, T_{15}) → poly30, o_{15}, p_{15}, q_{15}, r_{16}, s_{18}, t_{15}
Rotate(T_1, (-(r5°)), E) → U_{15}
Rotate(U_1, (-(r5°)), E) → V_{15}
Rotate(V_1, (-(r5°)), E) → W_{15}
Rotate(W_1, (-(r5°)), E) → Z_{15}
Rotate(Z_1, (-(r5°)), E) → A_{16}
Rotate(A_2, (-(r5°)), E) → B_{16}
Polygon(U_{15}, V_{15}, W_{15}, Z_{15}, A_{16}, B_{16}) → poly2'''_3, u_{15}, v_{15}, w_{16}, z_{17}, a_{16}, b_{17}
Rotate(I_1, (-(r5°)), F) → C_{16}
Rotate(J_1, (-(r5°)), F) → D_{16}
Rotate(L_1, (-(r5°)), F) → E_{16}
Rotate(S'_1, (-(r5°)), F) → F_{16}
Rotate(M_1, (-(r5°)), F) → G_{16}
Rotate(R'_1, (-(r5°)), F) → H_{16}
Polygon(C_{16}, D_{16}, E_{16}, F_{16}, G_{16}, H_{16}) → poly2''_4, c_{17}, d_{16}, e_{16}, f_{16}, g_{16}, h_{17}
Rotate(H'_1, (-(r5°)), F) → I_{16}
Rotate(C_1, (-(r5°)), F) → J_{16}
Rotate(E_1, (-(r5°)), F) → K_{16}
Rotate(S, (-(r5°)), F) → S'_8
Rotate(B_1, (-(r5°)), F) → L_{16}
Rotate(R, (-(r5°)), F) → R'_6
Polygon(I_{16}, J_{16}, K_{16}, S'_8, L_{16}, R'_6) → poly2'_4, i_{16}, j_{16}, k_{16}, s'_8, l_{16}, r'_6
Rotate(T_1, (-(r5°)), F) → M_{16}
Rotate(U_1, (-(r5°)), F) → N_{16}
Rotate(V_1, (-(r5°)), F) → O_{16}
Rotate(W_1, (-(r5°)), F) → P_{16}
Rotate(Z_1, (-(r5°)), F) → Q_{16}
Rotate(A_2, (-(r5°)), F) → R_{16}
Polygon(M_{16}, N_{16}, O_{16}, P_{16}, Q_{16}, R_{16}) → poly2'''_4, m_{18}, n_{16}, o_{16}, p_{16}, q_{16}, r_{17}
Rotate(L_2, (-(r5°)), F) → S_{16}
Rotate(M_2, (-(r5°)), F) → T_{16}
Rotate(N_2, (-(r5°)), F) → U_{16}
Rotate(O_2, (-(r5°)), F) → V_{16}
Rotate(P_2, (-(r5°)), F) → W_{16}
Rotate(Q_2, (-(r5°)), F) → Z_{16}
Polygon(S_{16}, T_{16}, U_{16}, V_{16}, W_{16}, Z_{16}) → poly31, s_{19}, t_{16}, u_{16}, v_{16}, w_{17}, z_{18}
Midpoint(H''_2, H) → A_{17}
Midpoint(H, H''_1) → B_{17}
Midpoint(H''_1, H'') → C_{17}
Midpoint(H'', H''_2) → D_{17}
Midpoint(H'_3, H'_2) → E_{17}
Midpoint(H'_2, H'_1) → F_{17}
Midpoint(H'_1, I) → G_{17}
Midpoint(I, H''') → H_{17}
Midpoint(I, B_{13}) → I_{17}
Midpoint(J, K) → J_{17}
Mirror(J_{17}, K) → K_{17}
Mirror(F_{17}, K) → L_{17}
Mirror(G_{17}, J) → M_{17}
Mirror(Q, L_{17}) → Q'
Mirror(D_{17}, H''_2) → N_{17}
Mirror(D_{17}, H'') → O_{17}

AI Drawing Prompt Reference

Draw an Alhambra star pattern with p4g symmetry, featuring multiple symmetric star shapes and geometric figures. Start by constructing a basic polygon, then use midpoints and perpendicular lines to locate key points. Create symmetric star structures through mirror and rotation operations. Connect these points with line segments to form complex star patterns. Finally, add decorative arcs and lines to enrich the design.

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