Possible Tessellations with Pentagrins
Loading the math board and drawing, please wait…
In collections
Tessellation with Pentagrins
This example demonstrates the possibilities of tessellations with pentagons. It involves combinatorial geometry and uses commands like Pentagrin1, Pentagrin2 to construct various pentagon tessellations. Suitable for high school and above, this example is for exploring geometric transformations and tiling theory.
GeoGebra Commands & Parameters
Pentagrin1(A, B) → poly1, a, b, c, d, e, C, D, EPentagrin1(E, D) → poly2, f, g, h, i, j, F, G, HPentagrin1(H, G) → poly3, k, l, m, n, p, I, J, KPentagrin1(K, J) → poly4, q, r, s, t, a_1, L, M, NPentagrin1(N, M) → poly5, b_1, c_1, d_1, e_1, f_1, O, P, QPentagrin1(Q, P) → poly6, g_1, h_1, i_1, j_1, k_1, R, S, TPentagrin1(T, S) → poly7, l_1, m_1, n_1, p_1, q_1, U, V, WPentagrin1(W, V) → poly8, r_1, s_1, t_1, a_2, b_2, Z, A_1, B_1Pentagrin1(B_1, A_1) → poly9, c_2, d_2, e_2, f_2, g_2, C_1, D_1, E_1Pentagrin1(E_1, D_1) → poly10, h_2, i_2, j_2, k_2, l_2, F_1, G_1, H_1Pentagrin2(G, D) → poly11, m_2, n_2, p_2, q_2, r_2, I_1, J_1, K_1Pentagrin2(G, K_1) → poly12, s_2, t_2, a_3, b_3, c_3, L_1, M_1, N_1Pentagrin2(G, N_1) → poly13, d_3, e_3, f_3, g_3, h_3, O_1, P_1, Q_1Pentagrin2(J, G) → poly14, i_3, j_3, k_3, l_3, m_3, R_1, S_1, T_1Pentagrin2(J, T_1) → poly15, n_3, p_3, q_3, r_3, s_3, U_1, V_1, W_1Pentagrin2(J, W_1) → poly16, t_3, a_4, b_4, c_4, d_4, Z_1, A_2, B_2Pentagrin2(M, J) → poly17, e_4, f_4, g_4, h_4, i_4, C_2, D_2, E_2Pentagrin2(M, E_2) → poly18, j_4, k_4, l_4, m_4, n_4, F_2, G_2, H_2Pentagrin2(M, H_2) → poly19, p_4, q_4, r_4, s_4, t_4, I_2, J_2, K_2Pentagrin2(P, M) → poly20, a_5, b_5, c_5, d_5, e_5, L_2, M_2, N_2Pentagrin2(P, N_2) → poly21, f_5, g_5, h_5, i_5, j_5, O_2, P_2, Q_2Pentagrin2(P, Q_2) → poly22, k_5, l_5, m_5, n_5, p_5, R_2, S_2, T_2Pentagrin2(S, P) → poly23, q_5, r_5, s_5, t_5, a_6, U_2, V_2, W_2Pentagrin2(S, W_2) → poly24, b_6, c_6, d_6, e_6, f_6, Z_2, A_3, B_3Pentagrin2(S, B_3) → poly25, g_6, h_6, i_6, j_6, k_6, C_3, D_3, E_3Pentagrin2(V, S) → poly26, l_6, m_6, n_6, p_6, q_6, F_3, G_3, H_3Pentagrin2(V, H_3) → poly27, r_6, s_6, t_6, a_7, b_7, I_3, J_3, K_3Pentagrin2(V, K_3) → poly28, c_7, d_7, e_7, f_7, g_7, L_3, M_3, N_3Pentagrin2(A_1, V) → poly29, h_7, i_7, j_7, k_7, l_7, O_3, P_3, Q_3Pentagrin2(A_1, Q_3) → poly30, m_7, n_7, p_7, q_7, r_7, R_3, S_3, T_3Pentagrin2(A_1, T_3) → poly31, s_7, t_7, a_8, b_8, c_8, U_3, V_3, W_3Pentagrin2(D_1, A_1) → poly32, d_8, e_8, f_8, g_8, h_8, Z_3, A_4, B_4Pentagrin2(D_1, B_4) → poly33, i_8, j_8, k_8, l_8, m_8, C_4, D_4, E_4Pentagrin2(D_1, E_4) → poly34, n_8, p_8, q_8, r_8, s_8, F_4, G_4, H_4Pentagrin2(B, D_1) → poly35, t_8, a_9, b_9, c_9, d_9, I_4, J_4, K_4Pentagrin2(B, K_4) → poly36, e_9, f_9, g_9, h_9, i_9, L_4, M_4, N_4Pentagrin2(B, N_4) → poly37, j_9, k_9, l_9, m_9, n_9, O_4, P_4, Q_4Pentagrin2(D, B) → poly38, p_9, q_9, r_9, s_9, t_9, R_4, S_4, T_4Pentagrin2(D, T_4) → poly39, a_{10}, b_{10}, c_{10}, d_{10}, e_{10}, U_4, V_4, W_4Pentagrin2(D, W_4) → poly40, f_{10}, g_{10}, h_{10}, i_{10}, j_{10}, Z_4, A_5, B_5Pentagrin2(Z_1, U_1) → poly41, k_{10}, l_{10}, m_{10}, n_{10}, p_{10}, C_5, D_5, E_5Pentagrin2(Z_1, E_5) → poly42, q_{10}, r_{10}, s_{10}, t_{10}, a_{11}, F_5, G_5, H_5Pentagrin2(F_2, Z_1) → poly43, b_{11}, c_{11}, d_{11}, e_{11}, f_{11}, I_5, J_5, K_5Pentagrin2(F_2, K_5) → poly44, g_{11}, h_{11}, i_{11}, j_{11}, k_{11}, L_5, M_5, N_5Pentagrin2(F_2, N_5) → poly45, l_{11}, m_{11}, n_{11}, p_{11}, q_{11}, O_5, P_5, Q_5Pentagrin2(I_2, F_2) → poly46, r_{11}, s_{11}, t_{11}, a_{12}, b_{12}, R_5, S_5, T_5Pentagrin2(I_2, T_5) → poly47, c_{12}, d_{12}, e_{12}, f_{12}, g_{12}, U_5, V_5, W_5Pentagrin2(O_2, I_2) → poly48, h_{12}, i_{12}, j_{12}, k_{12}, l_{12}, Z_5, A_6, B_6Pentagrin2(O_2, B_6) → poly49, m_{12}, n_{12}, p_{12}, q_{12}, r_{12}, C_6, D_6, E_6Pentagrin2(O_2, E_6) → poly50, s_{12}, t_{12}, a_{13}, b_{13}, c_{13}, F_6, G_6, H_6Pentagrin2(R_2, O_2) → poly51, d_{13}, e_{13}, f_{13}, g_{13}, h_{13}, I_6, J_6, K_6Pentagrin2(R_2, K_6) → poly52, i_{13}, j_{13}, k_{13}, l_{13}, m_{13}, L_6, M_6, N_6Pentagrin2(Z_2, R_2) → poly53, n_{13}, p_{13}, q_{13}, r_{13}, s_{13}, O_6, P_6, Q_6Pentagrin2(Z_2, Q_6) → poly54, t_{13}, a_{14}, b_{14}, c_{14}, d_{14}, R_6, S_6, T_6Pentagrin2(Z_2, T_6) → poly55, e_{14}, f_{14}, g_{14}, h_{14}, i_{14}, U_6, V_6, W_6Pentagrin2(C_3, Z_2) → poly56, j_{14}, k_{14}, l_{14}, m_{14}, n_{14}, Z_6, A_7, B_7Pentagrin2(C_3, B_7) → poly57, p_{14}, q_{14}, r_{14}, s_{14}, t_{14}, C_7, D_7, E_7Pentagrin2(I_3, C_3) → poly58, a_{15}, b_{15}, c_{15}, d_{15}, e_{15}, F_7, G_7, H_7Pentagrin2(I_3, H_7) → poly59, f_{15}, g_{15}, h_{15}, i_{15}, j_{15}, I_7, J_7, K_7Pentagrin2(I_3, K_7) → poly60, k_{15}, l_{15}, m_{15}, n_{15}, p_{15}, L_7, M_7, N_7Pentagrin2(L_3, I_3) → poly61, q_{15}, r_{15}, s_{15}, t_{15}, a_{16}, O_7, P_7, Q_7Pentagrin2(L_3, Q_7) → poly62, b_{16}, c_{16}, d_{16}, e_{16}, f_{16}, R_7, S_7, T_7Pentagrin2(R_3, L_3) → poly63, g_{16}, h_{16}, i_{16}, j_{16}, k_{16}, U_7, V_7, W_7Pentagrin2(R_3, W_7) → poly64, l_{16}, m_{16}, n_{16}, p_{16}, q_{16}, Z_7, A_8, B_8Pentagrin2(R_3, B_8) → poly65, r_{16}, s_{16}, t_{16}, a_{17}, b_{17}, C_8, D_8, E_8Pentagrin2(U_3, R_3) → poly66, c_{17}, d_{17}, e_{17}, f_{17}, g_{17}, F_8, G_8, H_8Pentagrin2(U_3, H_8) → poly67, h_{17}, i_{17}, j_{17}, k_{17}, l_{17}, I_8, J_8, K_8Pentagrin2(C_4, U_3) → poly68, m_{17}, n_{17}, p_{17}, q_{17}, r_{17}, L_8, M_8, N_8Pentagrin2(C_4, N_8) → poly69, s_{17}, t_{17}, a_{18}, b_{18}, c_{18}, O_8, P_8, Q_8Pentagrin2(C_4, Q_8) → poly70, d_{18}, e_{18}, f_{18}, g_{18}, h_{18}, R_8, S_8, T_8Pentagrin2(F_4, C_4) → poly71, i_{18}, j_{18}, k_{18}, l_{18}, m_{18}, U_8, V_8, W_8Pentagrin2(F_4, W_8) → poly72, n_{18}, p_{18}, q_{18}, r_{18}, s_{18}, Z_8, A_9, B_9Pentagrin2(L_4, F_4) → poly73, t_{18}, a_{19}, b_{19}, c_{19}, d_{19}, C_9, D_9, E_9Pentagrin2(L_4, E_9) → poly74, e_{19}, f_{19}, g_{19}, h_{19}, i_{19}, F_9, G_9, H_9Pentagrin2(L_4, H_9) → poly75, j_{19}, k_{19}, l_{19}, m_{19}, n_{19}, I_9, J_9, K_9Pentagrin2(O_4, L_4) → poly76, p_{19}, q_{19}, r_{19}, s_{19}, t_{19}, L_9, M_9, N_9Pentagrin2(O_4, N_9) → poly77, a_{20}, b_{20}, c_{20}, d_{20}, e_{20}, O_9, P_9, Q_9Pentagrin2(U_4, O_4) → poly78, f_{20}, g_{20}, h_{20}, i_{20}, j_{20}, R_9, S_9, T_9Pentagrin2(U_4, T_9) → poly79, k_{20}, l_{20}, m_{20}, n_{20}, p_{20}, U_9, V_9, W_9Pentagrin2(U_4, W_9) → poly80, q_{20}, r_{20}, s_{20}, t_{20}, a_{21}, Z_9, A_{10}, B_{10}Pentagrin2(I_1, U_4) → poly81, b_{21}, c_{21}, d_{21}, e_{21}, f_{21}, C_{10}, D_{10}, E_{10}Pentagrin2(I_1, E_{10}) → poly82, g_{21}, h_{21}, i_{21}, j_{21}, k_{21}, F_{10}, G_{10}, H_{10}Pentagrin2(L_1, I_1) → poly83, l_{21}, m_{21}, n_{21}, p_{21}, q_{21}, I_{10}, J_{10}, K_{10}Pentagrin2(L_1, K_{10}) → poly84, r_{21}, s_{21}, t_{21}, a_{22}, b_{22}, L_{10}, M_{10}, N_{10}Pentagrin2(L_1, N_{10}) → poly85, c_{22}, d_{22}, e_{22}, f_{22}, g_{22}, O_{10}, P_{10}, Q_{10}Pentagrin2(O_1, L_1) → poly86, h_{22}, i_{22}, j_{22}, k_{22}, l_{22}, R_{10}, S_{10}, T_{10}Pentagrin2(O_1, T_{10}) → poly87, m_{22}, n_{22}, p_{22}, q_{22}, r_{22}, U_{10}, V_{10}, W_{10}Pentagrin2(U_1, O_1) → poly88, s_{22}, t_{22}, a_{23}, b_{23}, c_{23}, Z_{10}, A_{11}, B_{11}Pentagrin2(U_1, B_{11}) → poly89, d_{23}, e_{23}, f_{23}, g_{23}, h_{23}, C_{11}, D_{11}, E_{11}Pentagrin2(U_1, E_{11}) → poly90, i_{23}, j_{23}, k_{23}, l_{23}, m_{23}, F_{11}, G_{11}, H_{11}
AI Drawing Prompt Reference
Create a tiling pattern made of multiple pentagons using the Pentagrin1 and Pentagrin2 commands, starting from point A and B, and sequentially constructing multiple pentagons where each pentagon's vertices connect to the vertices of the previous pentagon, forming a complex tiling pattern.
The prompt above was compiled from the original drawing commands and is for reference only.