MathPlotAI Logo MathPlotAI

Baravelle Pentagon Dodecahedron Basis

Baravelle Pentagon Dodecahedron Basis
Loading the math board and drawing, please wait…
2019-03-06 20:42
PolygonCoordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the construction of a Baravelle pentagon with interactive elements, showcasing its role as a basis for a dodecahedron. Key mathematical concepts include polygon construction, similarity transformation, coordinate geometry, and geometric transformations. The construction emphasizes commands and objects like Intersect, Polygon, Point, Distance, and Circle in GeoGebra. Suitable for high school and above, focusing on solid geometry and geometric construction.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Polygon(A, B, 5) → poly1, f, g, h, i, j, C, D, E
  3. Point(f) → F
  4. Distance(A, F) → AF
  5. Distance(A, B) → AB
  6. Circle(B, AF) → c
  7. Circle(C, AF) → d
  8. Circle(D, AF) → e
  9. Circle(E, AF) → k
  10. Intersect(c, g, 1) → G
  11. Intersect(d, h, 1) → H
  12. Intersect(e, i, 1) → I
  13. Intersect(k, j, 1) → J
  14. Polygon(F, B, G) → t1, g_1, f_1, b
  15. Polygon(G, C, H) → t2, h_1, g_2, c_1
  16. Polygon(H, D, I) → t3, i_1, h_2, d_1
  17. Polygon(I, E, J) → t4, j_1, i_2, e_1
  18. Polygon(J, A, F) → t5, f_2, j_2, a
  19. Circle(J, (r * a)) → p
  20. Intersect(p, a, 1) → K
  21. Circle(I, (r * a)) → q
  22. Circle(H, (r * a)) → s
  23. Circle(G, (r * a)) → t
  24. Circle(F, (r * a)) → k_1
  25. Intersect(q, e_1, 1) → L
  26. Intersect(k_1, b, 1) → P
  27. Intersect(s, d_1, 1) → Q
  28. Intersect(t, c_1, 1) → M
  29. Polygon(K, L, J) → t6, j_3, k_2, l
  30. Polygon(L, Q, I) → t7, i_3, l_1, q_1
  31. Polygon(Q, M, H) → t8, h_3, q_2, m
  32. Polygon(M, P, G) → t9, g_3, m_1, p_1
  33. Polygon(K, P, F) → t10, f_3, k_3, p_2
  34. Circle(K, (r * f_3)) → r_1
  35. Circle(L, (r * f_3)) → s_1
  36. Circle(Q, (r * f_3)) → t_1
  37. Circle(M, (r * f_3)) → c_2
  38. Circle(P, (r * f_3)) → d_2
  39. Intersect(r_1, f_3, 1) → N
  40. Intersect(s_1, j_3, 1) → O
  41. Intersect(t_1, i_3, 1) → R
  42. Intersect(c_2, h_3, 1) → S
  43. Intersect(d_2, g_3, 1) → T
  44. Polygon(N, K, O) → t11, o, n, k_4
  45. Polygon(O, L, R) → t12, r_2, o_1, l_2
  46. Polygon(R, Q, S) → t13, s_2, r_3, q_3
  47. Polygon(S, M, T) → t14, t_2, s_3, m_2
  48. Polygon(T, P, N) → t15, n_1, t_3, p_3
  49. Circle(N, (r * p_3)) → e_2
  50. Circle(O, (r * p_3)) → c_3
  51. Circle(R, (r * p_3)) → d_3
  52. Circle(S, (r * p_3)) → e_3
  53. Circle(T, (r * p_3)) → c_4
  54. Intersect(d_3, l_2, 1) → W
  55. Intersect(c_3, k_4, 1) → Z
  56. Polygon(O, Z, W) → t16, w, o_2, z_1
  57. Intersect(e_3, q_3, 1) → U
  58. Polygon(W, U, R) → t17, r_4, w_1, u
  59. Intersect(c_4, m_2, 1) → A_1
  60. Intersect(e_2, p_3, 1) → B_1
  61. Polygon(Z, B_1, N) → t18, n_2, z_2, b_1
  62. Polygon(U, S, A_1) → t19, a_1, u_1, s_4
  63. Polygon(A_1, B_1, T) → t20, t_4, a_2, b_2
  64. Circle(Z, (r * n_2)) → d_4
  65. Circle(W, (r * n_2)) → e_4
  66. Circle(U, (r * n_2)) → f_4
  67. Circle(A_1, (r * n_2)) → g_4
  68. Circle(B_1, (r * n_2)) → h_4
  69. Intersect(d_4, n_2, 1) → V
  70. Intersect(e_4, o_2, 1) → C_1
  71. Intersect(f_4, r_4, 1) → D_1
  72. Intersect(g_4, s_4, 1) → E_1
  73. Intersect(h_4, t_4) → F_1,
  74. Polygon(V, C_1, Z) → t21, z_3, v, c_5
  75. Polygon(C_1, D_1, W) → t22, w_2, c_6, d_5
  76. Polygon(D_1, U, E_1) → t23, e_5, d_6, u_2
  77. Polygon(E_1, A_1, F_1) → t24, f_5, e_6, a_3
  78. Polygon(V, F_1, B_1) → t25, b_3, v_1, f_6
  79. Circle(F_1, (r * a_3)) → p_4
  80. Circle(V, (r * a_3)) → q_4
  81. Circle(C_1, (r * a_3)) → g_5
  82. Circle(D_1, (r * a_3)) → h_5
  83. Circle(E_1, (r * a_3)) → k_5
  84. Intersect(q_4, b_3, 1) → G_1
  85. Intersect(g_5, z_3, 1) → H_1
  86. Intersect(h_5, w_2, 1) → I_1
  87. Intersect(k_5, u_2, 1) → J_1
  88. Intersect(p_4, a_3, 1) → K_1
  89. Polygon(G_1, H_1, V) → t26, v_2, g_6, h_6
  90. Polygon(H_1, I_1, C_1) → t27, c_7, h_7, i_4
  91. Polygon(I_1, D_1, J_1) → t28, j_4, i_5, d_7
  92. Polygon(J_1, K_1, E_1) → t29, e_7, j_5, k_6
  93. Polygon(K_1, G_1, F_1) → t30, f_7, k_7, g_7
  94. Circle(H_1, (r * v_2)) → p_5
  95. Circle(I_1, (r * v_2)) → q_5
  96. Circle(J_1, (r * v_2)) → r_5
  97. Circle(K_1, (r * v_2)) → s_5
  98. Circle(G_1, (r * v_2)) → t_5
  99. Intersect(p_5, v_2, 1) → L_1
  100. Intersect(q_5, c_7, 1) → M_1
  101. Intersect(r_5, d_7, 1) → N_1
  102. Intersect(s_5, e_7, 1) → O_1
  103. Intersect(t_5, f_7, 1) → P_1
  104. Polygon(L_1, P_1, G_1) → t31, g_8, l_3, p_6
  105. Polygon(H_1, L_1, M_1) → t32, m_3, h_8, l_4
  106. Polygon(M_1, I_1, N_1) → t33, n_3, m_4, i_6
  107. Polygon(N_1, J_1, O_1) → t34, o_3, n_4, j_6
  108. Polygon(O_1, K_1, P_1) → t35, p_7, o_4, k_8
  109. Circle(L_1, (r * g_8)) → q_6
  110. Circle(M_1, (r * g_8)) → r_6
  111. Circle(N_1, (r * g_8)) → s_6
  112. Circle(O_1, (r * g_8)) → t_6
  113. Circle(P_1, (r * g_8)) → q_7
  114. Intersect(r_6, h_8, 1) → Q_1
  115. Intersect(q_6, g_8, 1) → R_1
  116. Intersect(q_7, k_8, 1) → S_1
  117. Intersect(t_6, j_6, 1) → T_1
  118. Intersect(s_6, i_6, 1) → U_1
  119. Polygon(L_1, Q_1, R_1) → t36, r_7, l_5, q_8
  120. Polygon(Q_1, U_1, M_1) → t37, m_5, q_9, u_3
  121. Polygon(U_1, N_1, T_1) → t38, t_7, u_4, n_5
  122. Polygon(T_1, S_1, O_1) → t39, o_5, t_8, s_7
  123. Polygon(R_1, S_1, P_1) → t40, p_8, r_8, s_8
  124. Circle(Q_1, (r * l_5)) → c_8
  125. Intersect(c_8, l_5, 1) → V_1
  126. Circle(R_1, (r * l_5)) → d_8
  127. Circle(S_1, (r * l_5)) → e_8
  128. Circle(T_1, (r * l_5)) → f_8
  129. Circle(U_1, (r * l_5)) → c_9
  130. Intersect(d_8, p_8, 1) → W_1
  131. Intersect(e_8, o_5, 1) → Z_1
  132. Intersect(f_8, n_5, 1) → A_2
  133. Intersect(c_9, m_5, 1) → B_2
  134. Polygon(W_1, V_1, R_1) → t41, r_9, w_3, v_3
  135. Polygon(V_1, B_2, Q_1) → t42, q_{10}, v_4, b_4
  136. Polygon(B_2, U_1, A_2) → t43, a_4, b_5, u_5
  137. Polygon(A_2, T_1, Z_1) → t44, z_4, a_5, t_9
  138. Polygon(W_1, Z_1, S_1) → t45, s_9, w_4, z_5

AI Drawing Prompt Reference

Draw a Baravelle pentagon as the basis for a dodecahedron, starting with the intersection of coordinate axes, then construct a pentagon, draw circles centered at the pentagon's vertices, find their intersections to get new vertices, build several pentagons in sequence, and finally combine them to form a solid shape, showcasing the geometric relationship as the basis for a dodecahedron.
The prompt above was compiled from the original drawing commands and is for reference only.