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带对角杯状融合的立方体

带对角杯状融合的立方体
几何画板及绘图内容加载中，请稍等……
2015-12-31 17:00
多边形立体几何变换几何作图
① 该范例演示了一个立方体在对角线方向上加入杯状融合后的三维几何模型。② 涉及立体几何、多面体构造、空间变换与对称性等核心概念。③ 作图使用了 Cube、Vertex、OrthogonalLine、IntersectConic、Intersect、Rotate、Polygon 等命令，创建顶点 A、B、C… 及边、面对象，通过旋转与相交生成融合结构。④ 适合高中立体几何教学、大学几何建模课程及 GeoGebra 进阶作图练习。

GeoGebra 命令及参数

  1. Cube(C, B, A) → a, D, A3, A6, krawędźCD, krawędźBC, krawędźAB, krawędźAD, krawędźCE, krawędźDH, krawędźEH, krawędźEF, E, krawędźBF, krawędźFG, krawędźAG, krawędźGH, F, G, H, A1, A5, A4, A2
  2. Vertex(A1, 1) → B1
  3. Vertex(A1, 2) → C1
  4. Vertex(A1, 3) → D1
  5. Vertex(A1, 4) → E1
  6. OrthogonalLine((B1 + D1) / 2, Plane[A1]) → F1
  7. IntersectConic(Sphere[C1, 2], Sphere[D1, 2]) → G1
  8. IntersectConic(Sphere[C1, 2], Sphere[B1, (2 * sqrt(2))]) → H1
  9. Intersect
  10. Intersect(G1, H1, 2) → I1
  11. Rotate(I1, 90°, $F1) → J1
  12. Rotate(J1, 90°, $F1) → K1
  13. Rotate(K1, 90°, $F1) → L1
  14. Polygon(B1, E1, K1) → N1, O1, P1, Q1
  15. Polygon(B1, C1, L1) → R1, S1, T1, U1
  16. Polygon(C1, D1, I1) → V1, W1, X1, Y1
  17. Polygon(B1, K1, M1) → AD1, AE1, AF1, AG1
  18. Polygon(B1, L1, M1) → AH1, AI1, AJ1, AK1
  19. Polygon(C1, M1, L1) → AL1, AM1, AN1, AO1
  20. Polygon(C1, M1, I1) → AP1, AQ1, AR1, AS1
  21. Polygon(D1, M1, I1) → AT1, AU1, AV1, AW1
  22. Polygon(D1, M1, J1) → AX1, AY1, AZ1, BA1
  23. Polygon(E1, M1, J1) → BB1, BC1, BD1, BE1
  24. Polygon(E1, M1, K1) → BF1, BG1, BH1, BI1
  25. Vertex(A2, 1) → B2
  26. Vertex(A2, 2) → C2
  27. Vertex(A2, 3) → D2
  28. Vertex(A2, 4) → E2
  29. OrthogonalLine((B2 + D2) / 2, Plane[A2]) → F2
  30. IntersectConic(Sphere[C2, 2], Sphere[D2, 2]) → G2
  31. IntersectConic(Sphere[C2, 2], Sphere[B2, (2 * sqrt(2))]) → H2
  32. Intersect
  33. Intersect(G2, H2, 2) → I2
  34. Rotate(I2, 90°, $F2) → J2
  35. Rotate(J2, 90°, $F2) → K2
  36. Rotate(K2, 90°, $F2) → L2
  37. Vertex(A3, 1) → B3
  38. Vertex(A3, 2) → C3
  39. Vertex(A3, 3) → D3
  40. Vertex(A3, 4) → E3
  41. OrthogonalLine((B3 + D3) / 2, Plane[A3]) → F3
  42. IntersectConic(Sphere[C3, 2], Sphere[D3, 2]) → G3
  43. IntersectConic(Sphere[C3, 2], Sphere[B3, (2 * sqrt(2))]) → H3
  44. Intersect
  45. Intersect(G3, H3, 2) → I3
  46. Rotate(I3, 90°, $F3) → J3
  47. Rotate(J3, 90°, $F3) → K3
  48. Rotate(K3, 90°, $F3) → L3
  49. Vertex(A4, 1) → B4
  50. Vertex(A4, 2) → C4
  51. Vertex(A4, 3) → D4
  52. Vertex(A4, 4) → E4
  53. OrthogonalLine((B4 + D4) / 2, Plane[A4]) → F4
  54. IntersectConic(Sphere[C4, 2], Sphere[D4, 2]) → G4
  55. IntersectConic(Sphere[C4, 2], Sphere[B4, (2 * sqrt(2))]) → H4
  56. Intersect
  57. Intersect(G4, H4, 2) → I4
  58. Rotate(I4, 90°, $F4) → J4
  59. Rotate(J4, 90°, $F4) → K4
  60. Rotate(K4, 90°, $F4) → L4
  61. Vertex(A5, 1) → B5
  62. Vertex(A5, 2) → C5
  63. Vertex(A5, 3) → D5
  64. Vertex(A5, 4) → E5
  65. OrthogonalLine((B5 + D5) / 2, Plane[A5]) → F5
  66. IntersectConic(Sphere[C5, 2], Sphere[D5, 2]) → G5
  67. IntersectConic(Sphere[C5, 2], Sphere[B5, (2 * sqrt(2))]) → H5
  68. Intersect
  69. Intersect(G5, H5, 2) → I5
  70. Rotate(I5, 90°, $F5) → J5
  71. Rotate(J5, 90°, $F5) → K5
  72. Rotate(K5, 90°, $F5) → L5
  73. Vertex(A6, 1) → B6
  74. Vertex(A6, 2) → C6
  75. Vertex(A6, 3) → D6
  76. Vertex(A6, 4) → E6
  77. OrthogonalLine((B6 + D6) / 2, Plane[A6]) → F6
  78. IntersectConic(Sphere[C6, 2], Sphere[D6, 2]) → G6
  79. IntersectConic(Sphere[C6, 2], Sphere[B6, (2 * sqrt(2))]) → H6
  80. Intersect
  81. Intersect(G6, H6, 2) → I6
  82. Rotate(I6, 90°, $F6) → J6
  83. Rotate(J6, 90°, $F6) → K6
  84. Rotate(K6, 90°, $F6) → L6
  85. Polygon(B2, E2, K2) → N2, O2, P2, Q2
  86. Polygon(B3, E3, K3) → N3, O3, P3, Q3
  87. Polygon(B4, E4, K4) → N4, O4, P4, Q4
  88. Polygon(B5, E5, K5) → N5, O5, P5, Q5
  89. Polygon(B6, E6, K6) → N6, O6, P6, Q6
  90. Polygon(B2, C2, L2) → R2, S2, T2, U2
  91. Polygon(B3, C3, L3) → R3, S3, T3, U3
  92. Polygon(B4, C4, L4) → R4, S4, T4, U4
  93. Polygon(B5, C5, L5) → R5, S5, T5, U5
  94. Polygon(B6, C6, L6) → R6, S6, T6, U6
  95. Polygon(C2, D2, I2) → V2, W2, X2, Y2
  96. Polygon(C3, D3, I3) → V3, W3, X3, Y3
  97. Polygon(C4, D4, I4) → V4, W4, X4, Y4
  98. Polygon(C5, D5, I5) → V5, W5, X5, Y5
  99. Polygon(C6, D6, I6) → V6, W6, X6, Y6
  100. Polygon(D2, E2, J2) → Z2, AA2, AB2, AC2
  101. Polygon(D3, E3, J3) → Z3, AA3, AB3, AC3
  102. Polygon(D4, E4, J4) → Z4, AA4, AB4, AC4
  103. Polygon(D5, E5, J5) → Z5, AA5, AB5, AC5
  104. Polygon(D6, E6, J6) → Z6, AA6, AB6, AC6
  105. Polygon(D1, E1, J1) → Z1, AA1, AB1, AC1
  106. Polygon(B2, K2, M2) → AD2, AE2, AF2, AG2
  107. Polygon(B3, K3, M3) → AD3, AE3, AF3, AG3
  108. Polygon(B4, K4, M4) → AD4, AE4, AF4, AG4
  109. Polygon(B5, K5, M5) → AD5, AE5, AF5, AG5
  110. Polygon(B6, K6, M6) → AD6, AE6, AF6, AG6
  111. Polygon(B2, L2, M2) → AH2, AI2, AJ2, AK2
  112. Polygon(B3, L3, M3) → AH3, AI3, AJ3, AK3
  113. Polygon(B4, L4, M4) → AH4, AI4, AJ4, AK4
  114. Polygon(B5, L5, M5) → AH5, AI5, AJ5, AK5
  115. Polygon(B6, L6, M6) → AH6, AI6, AJ6, AK6
  116. Polygon(C2, M2, L2) → AL2, AM2, AN2, AO2
  117. Polygon(C3, M3, L3) → AL3, AM3, AN3, AO3
  118. Polygon(C4, M4, L4) → AL4, AM4, AN4, AO4
  119. Polygon(C5, M5, L5) → AL5, AM5, AN5, AO5
  120. Polygon(C6, M6, L6) → AL6, AM6, AN6, AO6
  121. Polygon(C2, M2, I2) → AP2, AQ2, AR2, AS2
  122. Polygon(C3, M3, I3) → AP3, AQ3, AR3, AS3
  123. Polygon(C4, M4, I4) → AP4, AQ4, AR4, AS4
  124. Polygon(C5, M5, I5) → AP5, AQ5, AR5, AS5
  125. Polygon(C6, M6, I6) → AP6, AQ6, AR6, AS6
  126. Polygon(D2, M2, I2) → AT2, AU2, AV2, AW2
  127. Polygon(D3, M3, I3) → AT3, AU3, AV3, AW3
  128. Polygon(D4, M4, I4) → AT4, AU4, AV4, AW4
  129. Polygon(D5, M5, I5) → AT5, AU5, AV5, AW5
  130. Polygon(D6, M6, I6) → AT6, AU6, AV6, AW6
  131. Polygon(D2, M2, J2) → AX2, AY2, AZ2, BA2
  132. Polygon(D3, M3, J3) → AX3, AY3, AZ3, BA3
  133. Polygon(D4, M4, J4) → AX4, AY4, AZ4, BA4
  134. Polygon(D5, M5, J5) → AX5, AY5, AZ5, BA5
  135. Polygon(D6, M6, J6) → AX6, AY6, AZ6, BA6
  136. Polygon(E2, M2, J2) → BB2, BC2, BD2, BE2
  137. Polygon(E3, M3, J3) → BB3, BC3, BD3, BE3
  138. Polygon(E4, M4, J4) → BB4, BC4, BD4, BE4
  139. Polygon(E5, M5, J5) → BB5, BC5, BD5, BE5
  140. Polygon(E6, M6, J6) → BB6, BC6, BD6, BE6
  141. Polygon(E2, M2, K2) → BF2, BG2, BH2, BI2
  142. Polygon(E3, M3, K3) → BF3, BG3, BH3, BI3
  143. Polygon(E4, M4, K4) → BF4, BG4, BH4, BI4
  144. Polygon(E5, M5, K5) → BF5, BG5, BH5, BI5
  145. Polygon(E6, M6, K6) → BF6, BG6, BH6, BI6

AI 绘图提示语参考

绘制一个立方体，并在其上添加对角棱柱融合结构。首先绘制一个立方体，然后在立方体的每个顶点处创建一个圆，通过圆的交点构造新的顶点，再通过旋转这些顶点来构建融合结构。最后，连接这些顶点形成新的多边形，完成整个立方体的对角棱柱融合结构。
以上提示语为根据原始绘图命令整理而来，仅供参考。