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Octagon Loops Exploration

Octagon Loops Exploration
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2014-07-14 23:20
PolygonVectorGeometric Construction
This GeoGebra applet investigates patterns in tiling polygons. By constructing and rotating polygons, students can discover the patterns in octagon loops. Key mathematical concepts include polygons, vectors, and rotation. The applet uses commands like Polygon, Segment, Point, and Rotate. Suitable for middle school and above students for geometric construction and exploration activities.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 8) → poly1, a, D, E, F, G, H, b, c, d, e, f, g, h, C
  2. Segment(B, C) → i
  3. Segment(C, D) → j
  4. Segment(D, E) → k
  5. Segment(E, F) → l
  6. Segment(F, G) → m
  7. Segment(G, H) → n
  8. Segment(H, A) → p
  9. Point(Circle[I, a]) → J
  10. Rotate(J + (b, 0), Angle[C - B] + Angle[J - I] - Angle[B - A], J) → K
  11. Rotate(K + (c, 0), Angle[D - C] + Angle[K - J] - Angle[C - B], K) → L
  12. Rotate(L + (d, 0), Angle[E - D] + Angle[L - K] - Angle[D - C], L) → M
  13. Rotate(M + (e, 0), Angle[F - E] + Angle[M - L] - Angle[E - D], M) → N
  14. Rotate(N + (f, 0), Angle[G - F] + Angle[N - M] - Angle[F - E], N) → O
  15. Rotate(O + (g, 0), Angle[H - G] + Angle[O - N] - Angle[G - F], O) → P
  16. Polygon(I, J, K, L, M, N, O, P) → poly2, i_1, j_1, k_1, l_1, m_1, n_1, o, p_1
  17. Point(Circle[Q, a]) → R
  18. Rotate(R + (b, 0), Angle[C - B] + Angle[R - Q] - Angle[B - A], R) → S
  19. Rotate(S + (c, 0), Angle[D - C] + Angle[S - R] - Angle[C - B], S) → T
  20. Rotate(T + (d, 0), Angle[E - D] + Angle[T - S] - Angle[D - C], T) → U
  21. Rotate(U + (e, 0), Angle[F - E] + Angle[U - T] - Angle[E - D], U) → V
  22. Rotate(V + (f, 0), Angle[G - F] + Angle[V - U] - Angle[F - E], V) → W
  23. Rotate(W + (g, 0), Angle[H - G] + Angle[W - V] - Angle[G - F], W) → Z
  24. Polygon(Q, R, S, T, U, V, W, Z) → poly3, q, r, s, t, u, v, w, z
  25. Point(Circle[A_1, a]) → B_1
  26. Rotate(B_1 + (b, 0), Angle[C - B] + Angle[B_1 - A_1] - Angle[B - A], B_1) → C_1
  27. Rotate(C_1 + (c, 0), Angle[D - C] + Angle[C_1 - B_1] - Angle[C - B], C_1) → D_1
  28. Rotate(D_1 + (d, 0), Angle[E - D] + Angle[D_1 - C_1] - Angle[D - C], D_1) → E_1
  29. Rotate(E_1 + (e, 0), Angle[F - E] + Angle[E_1 - D_1] - Angle[E - D], E_1) → F_1
  30. Rotate(F_1 + (f, 0), Angle[G - F] + Angle[F_1 - E_1] - Angle[F - E], F_1) → G_1
  31. Rotate(G_1 + (g, 0), Angle[H - G] + Angle[G_1 - F_1] - Angle[G - F], G_1) → H_1
  32. Polygon(A_1, B_1, C_1, D_1, E_1, F_1, G_1, H_1) → poly4, a_1, b_1, c_1, d_1, e_1, f_1, g_1, h_1
  33. Point(Circle[I_1, a]) → J_1
  34. Rotate(J_1 + (b, 0), Angle[C - B] + Angle[J_1 - I_1] - Angle[B - A], J_1) → K_1
  35. Rotate(K_1 + (c, 0), Angle[D - C] + Angle[K_1 - J_1] - Angle[C - B], K_1) → L_1
  36. Rotate(L_1 + (d, 0), Angle[E - D] + Angle[L_1 - K_1] - Angle[D - C], L_1) → M_1
  37. Rotate(M_1 + (e, 0), Angle[F - E] + Angle[M_1 - L_1] - Angle[E - D], M_1) → N_1
  38. Rotate(N_1 + (f, 0), Angle[G - F] + Angle[N_1 - M_1] - Angle[F - E], N_1) → O_1
  39. Rotate(O_1 + (g, 0), Angle[H - G] + Angle[O_1 - N_1] - Angle[G - F], O_1) → P_1
  40. Polygon(I_1, J_1, K_1, L_1, M_1, N_1, O_1, P_1) → poly5, i_2, j_2, k_2, l_2, m_2, n_2, o_1, p_2
  41. Point(Circle[Q_1, a]) → R_1
  42. Rotate(R_1 + (b, 0), Angle[C - B] + Angle[R_1 - Q_1] - Angle[B - A], R_1) → S_1
  43. Rotate(S_1 + (c, 0), Angle[D - C] + Angle[S_1 - R_1] - Angle[C - B], S_1) → T_1
  44. Rotate(T_1 + (d, 0), Angle[E - D] + Angle[T_1 - S_1] - Angle[D - C], T_1) → U_1
  45. Rotate(U_1 + (e, 0), Angle[F - E] + Angle[U_1 - T_1] - Angle[E - D], U_1) → V_1
  46. Rotate(V_1 + (f, 0), Angle[G - F] + Angle[V_1 - U_1] - Angle[F - E], V_1) → W_1
  47. Rotate(W_1 + (g, 0), Angle[H - G] + Angle[W_1 - V_1] - Angle[G - F], W_1) → Z_1
  48. Polygon(Q_1, R_1, S_1, T_1, U_1, V_1, W_1, Z_1) → poly6, q_1, r_1, s_1, t_1, u_1, v_1, w_1, z_1
  49. Point(Circle[A_2, a]) → B_2
  50. Rotate(B_2 + (b, 0), Angle[C - B] + Angle[B_2 - A_2] - Angle[B - A], B_2) → C_2
  51. Rotate(C_2 + (c, 0), Angle[D - C] + Angle[C_2 - B_2] - Angle[C - B], C_2) → D_2
  52. Rotate(D_2 + (d, 0), Angle[E - D] + Angle[D_2 - C_2] - Angle[D - C], D_2) → E_2
  53. Rotate(E_2 + (e, 0), Angle[F - E] + Angle[E_2 - D_2] - Angle[E - D], E_2) → F_2
  54. Rotate(F_2 + (f, 0), Angle[G - F] + Angle[F_2 - E_2] - Angle[F - E], F_2) → G_2
  55. Rotate(G_2 + (g, 0), Angle[H - G] + Angle[G_2 - F_2] - Angle[G - F], G_2) → H_2
  56. Polygon(A_2, B_2, C_2, D_2, E_2, F_2, G_2, H_2) → poly7, a_2, b_2, c_2, d_2, e_2, f_2, g_2, h_2
  57. Point(Circle[I_2, a]) → J_2
  58. Rotate(J_2 + (b, 0), Angle[C - B] + Angle[J_2 - I_2] - Angle[B - A], J_2) → K_2
  59. Rotate(K_2 + (c, 0), Angle[D - C] + Angle[K_2 - J_2] - Angle[C - B], K_2) → L_2
  60. Rotate(L_2 + (d, 0), Angle[E - D] + Angle[L_2 - K_2] - Angle[D - C], L_2) → M_2
  61. Rotate(M_2 + (e, 0), Angle[F - E] + Angle[M_2 - L_2] - Angle[E - D], M_2) → N_2
  62. Rotate(N_2 + (f, 0), Angle[G - F] + Angle[N_2 - M_2] - Angle[F - E], N_2) → O_2
  63. Rotate(O_2 + (g, 0), Angle[H - G] + Angle[O_2 - N_2] - Angle[G - F], O_2) → P_2
  64. Polygon(I_2, J_2, K_2, L_2, M_2, N_2, O_2, P_2) → poly8, i_3, j_3, k_3, l_3, m_3, n_3, o_2, p_3
  65. Point(Circle[Q_2, a]) → R_2
  66. Rotate(R_2 + (b, 0), Angle[C - B] + Angle[R_2 - Q_2] - Angle[B - A], R_2) → S_2
  67. Rotate(S_2 + (c, 0), Angle[D - C] + Angle[S_2 - R_2] - Angle[C - B], S_2) → T_2
  68. Rotate(T_2 + (d, 0), Angle[E - D] + Angle[T_2 - S_2] - Angle[D - C], T_2) → U_2
  69. Rotate(U_2 + (e, 0), Angle[F - E] + Angle[U_2 - T_2] - Angle[E - D], U_2) → V_2
  70. Rotate(V_2 + (f, 0), Angle[G - F] + Angle[V_2 - U_2] - Angle[F - E], V_2) → W_2
  71. Rotate(W_2 + (g, 0), Angle[H - G] + Angle[W_2 - V_2] - Angle[G - F], W_2) → Z_2
  72. Polygon(Q_2, R_2, S_2, T_2, U_2, V_2, W_2, Z_2) → poly9, q_2, r_2, s_2, t_2, u_2, v_2, w_2, z_2
  73. Point(Circle[A_3, a]) → B_3
  74. Rotate(B_3 + (b, 0), Angle[C - B] + Angle[B_3 - A_3] - Angle[B - A], B_3) → C_3
  75. Rotate(C_3 + (c, 0), Angle[D - C] + Angle[C_3 - B_3] - Angle[C - B], C_3) → D_3
  76. Rotate(D_3 + (d, 0), Angle[E - D] + Angle[D_3 - C_3] - Angle[D - C], D_3) → E_3
  77. Rotate(E_3 + (e, 0), Angle[F - E] + Angle[E_3 - D_3] - Angle[E - D], E_3) → F_3
  78. Rotate(F_3 + (f, 0), Angle[G - F] + Angle[F_3 - E_3] - Angle[F - E], F_3) → G_3
  79. Rotate(G_3 + (g, 0), Angle[H - G] + Angle[G_3 - F_3] - Angle[G - F], G_3) → H_3
  80. Polygon(A_3, B_3, C_3, D_3, E_3, F_3, G_3, H_3) → poly10, a_3, b_3, c_3, d_3, e_3, f_3, g_3, h_3
  81. Point(Circle[I_3, a]) → J_3
  82. Rotate(J_3 + (b, 0), Angle[C - B] + Angle[J_3 - I_3] - Angle[B - A], J_3) → K_3
  83. Rotate(K_3 + (c, 0), Angle[D - C] + Angle[K_3 - J_3] - Angle[C - B], K_3) → L_3
  84. Rotate(L_3 + (d, 0), Angle[E - D] + Angle[L_3 - K_3] - Angle[D - C], L_3) → M_3
  85. Rotate(M_3 + (e, 0), Angle[F - E] + Angle[M_3 - L_3] - Angle[E - D], M_3) → N_3
  86. Rotate(N_3 + (f, 0), Angle[G - F] + Angle[N_3 - M_3] - Angle[F - E], N_3) → O_3
  87. Rotate(O_3 + (g, 0), Angle[H - G] + Angle[O_3 - N_3] - Angle[G - F], O_3) → P_3
  88. Polygon(I_3, J_3, K_3, L_3, M_3, N_3, O_3, P_3) → poly11, i_4, j_4, k_4, l_4, m_4, n_4, o_3, p_4
  89. Point(Circle[Q_3, a]) → R_3
  90. Rotate(R_3 + (b, 0), Angle[C - B] + Angle[R_3 - Q_3] - Angle[B - A], R_3) → S_3
  91. Rotate(S_3 + (c, 0), Angle[D - C] + Angle[S_3 - R_3] - Angle[C - B], S_3) → T_3
  92. Rotate(T_3 + (d, 0), Angle[E - D] + Angle[T_3 - S_3] - Angle[D - C], T_3) → U_3
  93. Rotate(U_3 + (e, 0), Angle[F - E] + Angle[U_3 - T_3] - Angle[E - D], U_3) → V_3
  94. Rotate(V_3 + (f, 0), Angle[G - F] + Angle[V_3 - U_3] - Angle[F - E], V_3) → W_3
  95. Rotate(W_3 + (g, 0), Angle[H - G] + Angle[W_3 - V_3] - Angle[G - F], W_3) → Z_3
  96. Polygon(Q_3, R_3, S_3, T_3, U_3, V_3, W_3, Z_3) → poly12, q_3, r_3, s_3, t_3, u_3, v_3, w_3, z_3
  97. Point(Circle[A_4, a]) → B_4
  98. Rotate(B_4 + (b, 0), Angle[C - B] + Angle[B_4 - A_4] - Angle[B - A], B_4) → C_4
  99. Rotate(C_4 + (c, 0), Angle[D - C] + Angle[C_4 - B_4] - Angle[C - B], C_4) → D_4
  100. Rotate(D_4 + (d, 0), Angle[E - D] + Angle[D_4 - C_4] - Angle[D - C], D_4) → E_4
  101. Rotate(E_4 + (e, 0), Angle[F - E] + Angle[E_4 - D_4] - Angle[E - D], E_4) → F_4
  102. Rotate(F_4 + (f, 0), Angle[G - F] + Angle[F_4 - E_4] - Angle[F - E], F_4) → G_4
  103. Rotate(G_4 + (g, 0), Angle[H - G] + Angle[G_4 - F_4] - Angle[G - F], G_4) → H_4
  104. Polygon(A_4, B_4, C_4, D_4, E_4, F_4, G_4, H_4) → poly13, a_4, b_4, c_4, d_4, e_4, f_4, g_4, h_4
  105. Point(Circle[I_4, a]) → J_4
  106. Rotate(J_4 + (b, 0), Angle[C - B] + Angle[J_4 - I_4] - Angle[B - A], J_4) → K_4
  107. Rotate(K_4 + (c, 0), Angle[D - C] + Angle[K_4 - J_4] - Angle[C - B], K_4) → L_4
  108. Rotate(L_4 + (d, 0), Angle[E - D] + Angle[L_4 - K_4] - Angle[D - C], L_4) → M_4
  109. Rotate(M_4 + (e, 0), Angle[F - E] + Angle[M_4 - L_4] - Angle[E - D], M_4) → N_4
  110. Rotate(N_4 + (f, 0), Angle[G - F] + Angle[N_4 - M_4] - Angle[F - E], N_4) → O_4
  111. Rotate(O_4 + (g, 0), Angle[H - G] + Angle[O_4 - N_4] - Angle[G - F], O_4) → P_4
  112. Polygon(I_4, J_4, K_4, L_4, M_4, N_4, O_4, P_4) → poly14, i_5, j_5, k_5, l_5, m_5, n_5, o_4, p_5
  113. Point(Circle[Q_4, a]) → R_4
  114. Rotate(R_4 + (b, 0), Angle[C - B] + Angle[R_4 - Q_4] - Angle[B - A], R_4) → S_4
  115. Rotate(S_4 + (c, 0), Angle[D - C] + Angle[S_4 - R_4] - Angle[C - B], S_4) → T_4
  116. Rotate(T_4 + (d, 0), Angle[E - D] + Angle[T_4 - S_4] - Angle[D - C], T_4) → U_4
  117. Rotate(U_4 + (e, 0), Angle[F - E] + Angle[U_4 - T_4] - Angle[E - D], U_4) → V_4
  118. Rotate(V_4 + (f, 0), Angle[G - F] + Angle[V_4 - U_4] - Angle[F - E], V_4) → W_4
  119. Rotate(W_4 + (g, 0), Angle[H - G] + Angle[W_4 - V_4] - Angle[G - F], W_4) → Z_4
  120. Polygon(Q_4, R_4, S_4, T_4, U_4, V_4, W_4, Z_4) → poly15, q_4, r_4, s_4, t_4, u_4, v_4, w_4, z_4
  121. Point(Circle[A_5, q]) → B_5
  122. Rotate(B_5 + (r, 0), Angle[S - R] + Angle[B_5 - A_5] - Angle[R - Q], B_5) → C_5
  123. Rotate(C_5 + (s, 0), Angle[T - S] + Angle[C_5 - B_5] - Angle[S - R], C_5) → D_5
  124. Rotate(D_5 + (t, 0), Angle[U - T] + Angle[D_5 - C_5] - Angle[T - S], D_5) → E_5
  125. Rotate(E_5 + (u, 0), Angle[V - U] + Angle[E_5 - D_5] - Angle[U - T], E_5) → F_5
  126. Rotate(F_5 + (v, 0), Angle[W - V] + Angle[F_5 - E_5] - Angle[V - U], F_5) → G_5
  127. Rotate(G_5 + (w, 0), Angle[Z - W] + Angle[G_5 - F_5] - Angle[W - V], G_5) → H_5
  128. Polygon(A_5, B_5, C_5, D_5, E_5, F_5, G_5, H_5) → poly16, a_5, b_5, c_5, d_5, e_5, f_5, g_5, h_5
  129. Point(Circle[I_5, q]) → J_5
  130. Rotate(J_5 + (r, 0), Angle[S - R] + Angle[J_5 - I_5] - Angle[R - Q], J_5) → K_5
  131. Rotate(K_5 + (s, 0), Angle[T - S] + Angle[K_5 - J_5] - Angle[S - R], K_5) → L_5
  132. Rotate(L_5 + (t, 0), Angle[U - T] + Angle[L_5 - K_5] - Angle[T - S], L_5) → M_5
  133. Rotate(M_5 + (u, 0), Angle[V - U] + Angle[M_5 - L_5] - Angle[U - T], M_5) → N_5
  134. Rotate(N_5 + (v, 0), Angle[W - V] + Angle[N_5 - M_5] - Angle[V - U], N_5) → O_5
  135. Rotate(O_5 + (w, 0), Angle[Z - W] + Angle[O_5 - N_5] - Angle[W - V], O_5) → P_5
  136. Polygon(I_5, J_5, K_5, L_5, M_5, N_5, O_5, P_5) → poly17, i_6, j_6, k_6, l_6, m_6, n_6, o_5, p_6
  137. Point(Circle[Q_5, q]) → R_5
  138. Rotate(R_5 + (r, 0), Angle[S - R] + Angle[R_5 - Q_5] - Angle[R - Q], R_5) → S_5
  139. Rotate(S_5 + (s, 0), Angle[T - S] + Angle[S_5 - R_5] - Angle[S - R], S_5) → T_5
  140. Rotate(T_5 + (t, 0), Angle[U - T] + Angle[T_5 - S_5] - Angle[T - S], T_5) → U_5
  141. Rotate(U_5 + (u, 0), Angle[V - U] + Angle[U_5 - T_5] - Angle[U - T], U_5) → V_5
  142. Rotate(V_5 + (v, 0), Angle[W - V] + Angle[V_5 - U_5] - Angle[V - U], V_5) → W_5
  143. Rotate(W_5 + (w, 0), Angle[Z - W] + Angle[W_5 - V_5] - Angle[W - V], W_5) → Z_5
  144. Polygon(Q_5, R_5, S_5, T_5, U_5, V_5, W_5, Z_5) → poly18, q_5, r_5, s_5, t_5, u_5, v_5, w_5, z_5
  145. Point(Circle[A_6, q]) → B_6
  146. Rotate(B_6 + (r, 0), Angle[S - R] + Angle[B_6 - A_6] - Angle[R - Q], B_6) → C_6
  147. Rotate(C_6 + (s, 0), Angle[T - S] + Angle[C_6 - B_6] - Angle[S - R], C_6) → D_6
  148. Rotate(D_6 + (t, 0), Angle[U - T] + Angle[D_6 - C_6] - Angle[T - S], D_6) → E_6
  149. Rotate(E_6 + (u, 0), Angle[V - U] + Angle[E_6 - D_6] - Angle[U - T], E_6) → F_6
  150. Rotate(F_6 + (v, 0), Angle[W - V] + Angle[F_6 - E_6] - Angle[V - U], F_6) → G_6
  151. Rotate(G_6 + (w, 0), Angle[Z - W] + Angle[G_6 - F_6] - Angle[W - V], G_6) → H_6
  152. Polygon(A_6, B_6, C_6, D_6, E_6, F_6, G_6, H_6) → poly19, a_6, b_6, c_6, d_6, e_6, f_6, g_6, h_6
  153. Point(Circle[I_6, q]) → J_6
  154. Rotate(J_6 + (r, 0), Angle[S - R] + Angle[J_6 - I_6] - Angle[R - Q], J_6) → K_6
  155. Rotate(K_6 + (s, 0), Angle[T - S] + Angle[K_6 - J_6] - Angle[S - R], K_6) → L_6
  156. Rotate(L_6 + (t, 0), Angle[U - T] + Angle[L_6 - K_6] - Angle[T - S], L_6) → M_6
  157. Rotate(M_6 + (u, 0), Angle[V - U] + Angle[M_6 - L_6] - Angle[U - T], M_6) → N_6
  158. Rotate(N_6 + (v, 0), Angle[W - V] + Angle[N_6 - M_6] - Angle[V - U], N_6) → O_6
  159. Rotate(O_6 + (w, 0), Angle[Z - W] + Angle[O_6 - N_6] - Angle[W - V], O_6) → P_6
  160. Polygon(I_6, J_6, K_6, L_6, M_6, N_6, O_6, P_6) → poly20, i_7, j_7, k_7, l_7, m_7, n_7, o_6, p_7
  161. Point(Circle[Q_6, q]) → R_6
  162. Rotate(R_6 + (r, 0), Angle[S - R] + Angle[R_6 - Q_6] - Angle[R - Q], R_6) → S_6
  163. Rotate(S_6 + (s, 0), Angle[T - S] + Angle[S_6 - R_6] - Angle[S - R], S_6) → T_6
  164. Rotate(T_6 + (t, 0), Angle[U - T] + Angle[T_6 - S_6] - Angle[T - S], T_6) → U_6
  165. Rotate(U_6 + (u, 0), Angle[V - U] + Angle[U_6 - T_6] - Angle[U - T], U_6) → V_6
  166. Rotate(V_6 + (v, 0), Angle[W - V] + Angle[V_6 - U_6] - Angle[V - U], V_6) → W_6
  167. Rotate(W_6 + (w, 0), Angle[Z - W] + Angle[W_6 - V_6] - Angle[W - V], W_6) → Z_6
  168. Polygon(Q_6, R_6, S_6, T_6, U_6, V_6, W_6, Z_6) → poly21, q_6, r_6, s_6, t_6, u_6, v_6, w_6, z_6
  169. Point(Circle[A_7, q]) → B_7
  170. Rotate(B_7 + (r, 0), Angle[S - R] + Angle[B_7 - A_7] - Angle[R - Q], B_7) → C_7
  171. Rotate(C_7 + (s, 0), Angle[T - S] + Angle[C_7 - B_7] - Angle[S - R], C_7) → D_7
  172. Rotate(D_7 + (t, 0), Angle[U - T] + Angle[D_7 - C_7] - Angle[T - S], D_7) → E_7
  173. Rotate(E_7 + (u, 0), Angle[V - U] + Angle[E_7 - D_7] - Angle[U - T], E_7) → F_7
  174. Rotate(F_7 + (v, 0), Angle[W - V] + Angle[F_7 - E_7] - Angle[V - U], F_7) → G_7
  175. Rotate(G_7 + (w, 0), Angle[Z - W] + Angle[G_7 - F_7] - Angle[W - V], G_7) → H_7
  176. Polygon(A_7, B_7, C_7, D_7, E_7, F_7, G_7, H_7) → poly22, a_7, b_7, c_7, d_7, e_7, f_7, g_7, h_7
  177. Point(Circle[I_7, q]) → J_7
  178. Rotate(J_7 + (r, 0), Angle[S - R] + Angle[J_7 - I_7] - Angle[R - Q], J_7) → K_7
  179. Rotate(K_7 + (s, 0), Angle[T - S] + Angle[K_7 - J_7] - Angle[S - R], K_7) → L_7
  180. Rotate(L_7 + (t, 0), Angle[U - T] + Angle[L_7 - K_7] - Angle[T - S], L_7) → M_7
  181. Rotate(M_7 + (u, 0), Angle[V - U] + Angle[M_7 - L_7] - Angle[U - T], M_7) → N_7
  182. Rotate(N_7 + (v, 0), Angle[W - V] + Angle[N_7 - M_7] - Angle[V - U], N_7) → O_7
  183. Rotate(O_7 + (w, 0), Angle[Z - W] + Angle[O_7 - N_7] - Angle[W - V], O_7) → P_7
  184. Polygon(I_7, J_7, K_7, L_7, M_7, N_7, O_7, P_7) → poly23, i_8, j_8, k_8, l_8, m_8, n_8, o_7, p_8

AI Drawing Prompt Reference

Draw an octagon, then rotate a new octagon around each vertex of the original octagon, and repeat this process twice to form a series of nested octagons. First, create an octagon, then rotate a new octagon around each vertex of the original octagon, and repeat this process to create a second, third, and fourth octagon.
The prompt above was compiled from the original drawing commands and is for reference only.