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COSMOS Challenge - Building Model

COSMOS Challenge - Building Model
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2020-06-05 22:31
PolygonVectorSolid GeometryTransformationGeometric Construction
This example demonstrates the construction of a building model through geometric construction. Key mathematical concepts include vectors, polygons, and solid geometry. Using GeoGebra commands such as Intersect, Polygon, Midpoint, and Segment, the framework and details of the building can be constructed. Suitable for high school or university students and educators.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Polygon(A, B, 4) → poly_{frame}, f_2, g_2, h_2, i_2, C, D
  3. Midpoint(A, B) → E
  4. Midpoint(B, C) → F
  5. Midpoint(C, D) → G
  6. Midpoint(D, A) → H
  7. Midpoint(A, E) → I
  8. Midpoint(E, B) → J
  9. Midpoint(B, F) → K
  10. Midpoint(F, C) → L
  11. Midpoint(C, G) → M
  12. Midpoint(G, D) → N
  13. Midpoint(D, H) → O
  14. Midpoint(H, A) → P
  15. Segment(N, I) → j_2
  16. Segment(G, E) → k_2
  17. Segment(M, J) → l_1
  18. Segment(O, L) → m_1
  19. Segment(H, F) → n_1
  20. Segment(P, K) → p_1
  21. Polygon(Q, R, 4) → poly1, q, r, s, t, S, T
  22. Vector(D, N) → u
  23. Vector(D, O) → v
  24. Translate(poly1, u) → poly2
  25. Translate(poly2, u) → poly3
  26. Translate(poly3, u) → poly4
  27. Translate(poly1, v) → poly5
  28. Translate(poly5, v) → poly9
  29. Translate(poly9, v) → poly13
  30. Translate(poly2, v) → poly6
  31. Translate(poly6, v) → poly10
  32. Translate(poly10, v) → poly14
  33. Translate(poly3, v) → poly7
  34. Translate(poly7, v) → poly11
  35. Translate(poly11, v) → poly15
  36. Translate(poly4, v) → poly8
  37. Translate(poly8, v) → poly12
  38. Translate(poly12, v) → poly16
  39. Prism(poly1, (0.6 * a_1)) → a, U, edgeQU, edgeRV, edgeSW, edgeTZ, edgeUV, edgeVW, edgeWZ, edgeUZ, V, W, Z, face1_a, face3_a, face4_a, face2_a, face5_a
  40. Segment(G, E) → e_1
  41. Segment(N, I) → f_1
  42. Segment(M, J) → g_1
  43. Segment(O, L) → h_1
  44. Segment(H, F) → i_1
  45. Segment(P, K) → j_1
  46. Prism(poly2, (0.6 * a_2)) → b, A_1, edge1, edge2, edge3, edge4, edge5, edge7, edge8, edge6, B_1, C_1, D_1, face1_b, face3_b, face4_b, face2_b, face5_b
  47. Prism(poly3, (0.6 * a_3)) → c, E_1, edge9, edge10, edge11, edge12, edge13, edge15, edge16, edge14, F_1, G_1, H_1, face1_c, face3_c, face4_c, face2_c, face5_c
  48. Prism(poly4, (0.6 * a_4)) → d, K_1, edge17, edge18, edge19, edge20, edge21, edge23, edge24, edge22, L_1, M_1, N_{17}, face1_d, face2_d, face4_d, face3_d, face5_d
  49. Translate(N_5, u) → N_6
  50. Translate(N_6, u) → N_7
  51. Translate(N_7, u) → N_8
  52. Translate(N_1, v') → N_2
  53. Translate(N_2, v') → N_3
  54. Translate(N_3, v') → N_4
  55. Translate(N_9, v) → N_{10}
  56. Translate(N_{10}, v) → N_{11}
  57. Translate(N_{16}, u) → N_{15}
  58. Translate(N_{15}, u) → N_{14}
  59. Translate(N_{14}, u) → N_{13}
  60. Translate(N_{11}, v) → N_{12}
  61. Line(O_1, h_1) → k_1
  62. Prism(poly5, (0.6 * a_5)) → e, P_1, edge25, edge26, edge27, edge28, edge29, edge31, edge32, edge30, Q_1, R_1, S_1, face4_e, face2_e, face3_e, face1_e, face5_e
  63. Prism(poly6, (0.6 * a_6)) → f, T_1, edge33, edge34, edge35, edge36, edge37, edge39, edge40, edge38, U_1, V_1, W_1, face4_f, face2_f, face3_f, face1_f, face5_f
  64. Prism(poly7, (0.6 * a_7)) → g, Z_1, edge41, edge42, edge43, edge44, edge45, edge47, edge48, edge46, A_2, B_2, C_2, face1_g, face3_g, face4_g, face2_g, face5_g
  65. Prism(poly9, (0.6 * a_9)) → i, D_2, edge49, edge50, edge51, edge52, edge53, edge55, edge56, edge54, E_2, F_2, G_2, face1_i, face3_i, face4_i, face2_i, face5_i
  66. Prism(poly8, (0.6 * a_8)) → h, H_2, edge57, edge58, edge59, edge60, edge61, edge63, edge64, edge62, I_2, J_2, K_2, face1_h, face3_h, face4_h, face2_h, face5_h
  67. Prism(poly10, (0.6 * a_{10})) → j, L_2, edge65, edge66, edge67, edge68, edge69, edge71, edge72, edge70, M_2, O_2, P_2, face1_j, face3, face4, face2_j, face5_j
  68. Prism(poly11, (0.6 * a_{11})) → k, Q_2, edge73, edge74, edge75, edge76, edge77, edge79, edge80, edge78, R_2, S_2, T_2, face4_k, face2_k, face3_k, face1_k, face5_k
  69. Prism(poly12, (0.6 * a_{12})) → l, U_2, edge81, edge82, edge83, edge84, edge85, edge87, edge88, edge86, V_2, W_2, Z_2, face1, face1_l, face2_l, face2, face5_l
  70. Prism(poly13, (0.6 * a_{13})) → m, A_3, edge89, edge90, edge91, edge92, edge93, edge95, edge96, edge94, B_3, C_3, D_3, face2_m, face3_m, face4_m, face1_m, face5_m
  71. Prism(poly14, (0.6 * a_{14})) → n, E_3, edge97, edge98, edge99, edge100, edge101, edge103, edge104, edge102, F_3, G_3, H_3, face1_n, face3_n, face4_n, face2_n, face5_n
  72. Prism(poly15, (0.6 * a_{15})) → o, I_3, edge105, edge106, edge107, edge108, edge109, edge111, edge112, edge110, J_3, K_3, L_3, face4_o, face2_o, face3_o, face1_o, face5_o
  73. Prism(poly16, (0.6 * a_{16})) → p, M_3, edge113, edge114, edge115, edge116, edge117, edge119, edge120, edge118, O_3, P_3, Q_3, face1_p, face3_p, face4_p, face2_p, face5_p
  74. Polygon(A, B, 4) → poly17, q_1, r_1, s_1, t_1, R_3, S_3
  75. Polygon(A_4, V_3, W_3, Z_3) → q1, a_{17}, v_3, w_3, z_3
  76. Polygon(B_4, A_4, V_3, C_4) → q2, b_4, a_{18}, v_1, c_4
  77. Polygon(B_4, D_4, Z_3, A_4) → q3, b_1, d_4, z_1, a_{19}
  78. Polygon(A_4, V_3, W_3, Z_3) → q4, c_1, d_1, l_2, m_2

AI Drawing Prompt Reference

Draw a building model with four rectangular frames, each connected by midpoints to form a quadrilateral. Then, use vector translation to generate multiple parallel rectangular frames. Finally, construct prisms using these rectangular frames to form the building's solid structure.
The prompt above was compiled from the original drawing commands and is for reference only.