积极 AI Logo 积极 AI

燕尾十二面体

燕尾十二面体
几何画板及绘图内容加载中，请稍等……
2017-11-21 15:52
向量立体几何几何作图
这个范例演示了燕尾十二面体的构造。燕尾十二面体是一种非正多面体，由12个正五边形和20个等边三角形组成。作图过程中使用了旋转、镜像、角度、向量等命令，展示了立体几何中的变换和作图技巧。适合高中数学教学和学习立体几何的学生。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A_0
  2. Circle(A_0, 1 / ((2 * sin(36°)))) → c
  3. Intersect(c, xAxis, 2) → A
  4. Rotate(A, 72°, A_0) → B
  5. Mirror(B, xAxis) → C
  6. Angle(A, A_0, D) → α
  7. Point(Circle[((A * (1 - sqrt(5))) + (B * (3 + sqrt(5)))) / 4, (Distance[A, B] * sqrt(10 + (2 * sqrt(5))) / 4), Segment[A, B]]) → E
  8. Dodecahedron(A, B, E) → e, F, O, P, Q, R, S, T, U, V, 면ABEFG, 면AGKQL, G, 면ABHML, 면BEINH, 면EFJOI, 면FGKPJ, 면KPUVQ, 면LMRVQ, 면HMRSN, 면INSTO, 면JOTUP, 면RSTUV, H, 모서리AG, 모서리AB, 모서리BE, 모서리EF, 모서리FG, 모서리AL, 모서리GK, 모서리KQ, 모서리LQ, 모서리LM, I, 모서리HM, 모서리BH, 모서리HN, 모서리IN, 모서리EI, 모서리IO, 모서리JO, 모서리FJ, 모서리JP, 모서리KP, J, 모서리PU, 모서리UV, 모서리QV, 모서리RV, 모서리MR, 모서리RS, 모서리NS, 모서리ST, 모서리OT, 모서리TU, K, L, M, N
  9. Midpoint(A, T) → W
  10. Centroid(B1) → C1
  11. Centroid(B2) → C2
  12. Centroid(B3) → C3
  13. Centroid(B4) → C4
  14. Centroid(B5) → C5
  15. Centroid(B6) → C6
  16. Centroid(B7) → C7
  17. Centroid(B8) → C8
  18. Centroid(B9) → C9
  19. Centroid(B10) → C10
  20. Centroid(B11) → C11
  21. Centroid(B12) → C12
  22. Vector(C1, D1) → E1
  23. Vector(C2, D2) → E2
  24. Vector(C3, D3) → E3
  25. Vector(C4, D4) → E4
  26. Vector(C5, D5) → E5
  27. Vector(C6, D6) → E6
  28. Vector(C7, D7) → E7
  29. Vector(C8, D8) → E8
  30. Vector(C9, D9) → E9
  31. Vector(C10, D10) → E10
  32. Vector(C11, D11) → E11
  33. Vector(C12, D12) → E12
  34. Rotate(Translate[B1, Vector[(k * E1)]], (k * α), Line[W, C1]) → F1
  35. Rotate(Translate[B2, Vector[(k * E2)]], (k * α), Line[W, C2]) → F2
  36. Rotate(Translate[B3, Vector[(k * E3)]], (k * α), Line[W, C3]) → F3
  37. Rotate(Translate[B4, Vector[(k * E4)]], (k * α), Line[W, C4]) → F4
  38. Rotate(Translate[B5, Vector[(k * E5)]], (k * α), Line[W, C5]) → F5
  39. Rotate(Translate[B6, Vector[(k * E6)]], (k * α), Line[W, C6]) → F6
  40. Rotate(Translate[B7, Vector[(k * E7)]], (k * α), Line[W, C7]) → F7
  41. Rotate(Translate[B8, Vector[(k * E8)]], (k * α), Line[W, C8]) → F8
  42. Rotate(Translate[B9, Vector[(k * E9)]], (k * α), Line[W, C9]) → F9
  43. Rotate(Translate[B10, Vector[(k * E10)]], (k * α), Line[W, C10]) → F10
  44. Rotate(Translate[B11, Vector[(k * E11)]], (k * α), Line[W, C11]) → F11
  45. Rotate(Translate[B12, Vector[(k * E12)]], (k * α), Line[W, C12]) → F12
  46. Vertex(F1) → G1, H1, I1, J1, K1
  47. Vertex(F2) → G2, H2, I2, J2, K2
  48. Vertex(F3) → G3, H3, I3, J3, K3
  49. Vertex(F4) → G4, H4, I4, J4, K4
  50. Vertex(F5) → G5, H5, I5, J5, K5
  51. Vertex(F6) → G6, H6, I6, J6, K6
  52. Vertex(F7) → G7, H7, I7, J7, K7
  53. Vertex(F8) → G8, H8, I8, J8, K8
  54. Vertex(F9) → G9, H9, I9, J9, K9
  55. Vertex(F10) → G10, H10, I10, J10, K10
  56. Vertex(F11) → G11, H11, I11, J11, K11
  57. Vertex(F12) → G12, H12, I12, J12, K12
  58. Polygon(G12, J11, K12) → 다각형1, k12, g12, j11
  59. Polygon(K12, J11, I7) → 다각형2, i7, k12_1, j11_1
  60. Polygon(K12, I7, J7) → 다각형3, j7, k12_2, i7_1
  61. Polygon(K12, J7, J12) → 다각형4, j12, k12_3, j7_1
  62. Polygon(J12, J7, I8) → 다각형5, i8, j12_1, j7_2
  63. Polygon(J12, I8, J8) → 다각형6, j8, j12_2, i8_1
  64. Polygon(J12, J8, I12) → 다각형7, i12, j12_3, j8_1
  65. Polygon(I12, J8, I9) → 다각형8, i9, i12_1, j8_2
  66. Polygon(I12, I9, J9) → 다각형9, j9, i12_2, i9_1
  67. Polygon(I12, J9, H12) → 다각형10, h12, i12_3, j9_1
  68. Polygon(H12, J9, J10) → 다각형11, j10, h12_1, j9_2
  69. Polygon(H12, J10, K10) → 다각형12, k10, h12_2, j10_1
  70. Polygon(H12, K10, G12) → 다각형13, g12_1, h12_3, k10_1
  71. Polygon(G12, K10, I11) → 다각형14, i11, g12_2, k10_2
  72. Polygon(G12, I11, J11) → 다각형15, j11_2, g12_3, i11_1
  73. Polygon(J9, K9, J10) → 다각형16, j10_2, j9_3, k9
  74. Polygon(J10, K9, I10) → 다각형17, i10, j10_3, k9_1
  75. Polygon(K10, G10, I11) → 다각형18, i11_2, k10_3, g10
  76. Polygon(I11, G10, H11) → 다각형19, h11, i11_3, g10_1
  77. Polygon(J11, K11, I7) → 다각형20, i7_2, j11_3, k11
  78. Polygon(I7, K11, H7) → 다각형21, h7, i7_3, k11_1
  79. Polygon(J7, K7, I8) → 다각형22, i8_2, j7_3, k7
  80. Polygon(I8, K7, H8) → 다각형23, h8, i8_3, k7_1
  81. Polygon(J8, K8, I9) → 다각형24, i9_2, j8_3, k8
  82. Polygon(I9, K8, H9) → 다각형25, h9, i9_3, k8_1
  83. Polygon(K8, G8, J5) → 다각형26, j5, k8_2, g8
  84. Polygon(K8, J5, H9) → 다각형27, h9_1, k8_3, j5_1
  85. Polygon(H9, J5, K5) → 다각형28, k5, h9_2, j5_2
  86. Polygon(H9, K5, G9) → 다각형29, g9, h9_3, k5_1
  87. Polygon(K9, G9, J6) → 다각형30, j6, k9_2, g9_1
  88. Polygon(K9, J6, I10) → 다각형31, i10_1, k9_3, j6_1
  89. Polygon(I10, J6, K6) → 다각형32, k6, i10_2, j6_2
  90. Polygon(I10, K6, H10) → 다각형33, h10, i10_3, k6_1
  91. Polygon(H10, K6, J3) → 다각형34, j3, h10_1, k6_2
  92. Polygon(H10, J3, K3) → 다각형35, k3, h10_2, j3_1
  93. Polygon(G10, H10, K3) → 다각형36, k3_1, g10_2, h10_3
  94. Polygon(G10, K3, H11) → 다각형37, h11_1, g10_3, k3_2
  95. Polygon(H11, K3, G3) → 다각형38, g3, h11_2, k3_3
  96. Polygon(H11, G3, G11) → 다각형39, g11, h11_3, g3_1
  97. Polygon(K11, G11, J2) → 다각형40, j2, k11_2, g11_1
  98. Polygon(K11, J2, H7) → 다각형41, h7_1, k11_3, j2_1
  99. Polygon(H7, J2, K2) → 다각형42, k2, h7_2, j2_2
  100. Polygon(H7, K2, G7) → 다각형43, g7, h7_3, k2_1
  101. Polygon(G7, K2, I4) → 다각형44, i4, g7_1, k2_2
  102. Polygon(K7, G7, J4) → 다각형45, j4, k7_2, g7_2
  103. Polygon(G7, I4, J4) → 다각형46, j4_1, g7_3, i4_1
  104. Polygon(K7, J4, H8) → 다각형47, h8_1, k7_3, j4_2
  105. Polygon(H8, J4, K4) → 다각형48, k4, h8_2, j4_3
  106. Polygon(H8, K4, G8) → 다각형49, g8_1, h8_3, k4_1
  107. Polygon(G8, K4, I5) → 다각형50, i5, g8_2, k4_2
  108. Polygon(G8, I5, J5) → 다각형51, j5_3, g8_3, i5_1
  109. Polygon(K4, G4, I5) → 다각형52, i5_2, k4_3, g4
  110. Polygon(I5, G4, H5) → 다각형53, h5, i5_3, g4_1
  111. Polygon(K2, G2, I4) → 다각형54, i4_2, k2_3, g2
  112. Polygon(I4, G2, H4) → 다각형55, h4, i4_3, g2_1
  113. Polygon(G11, G3, I2) → 다각형56, i2, g11_2, g3_2
  114. Polygon(G11, I2, J2) → 다각형57, j2_3, g11_3, i2_1
  115. Polygon(G3, H3, I2) → 다각형58, i2_2, g3_3, h3
  116. Polygon(I2, H3, H2) → 다각형59, h2, i2_3, h3_1
  117. Polygon(K6, G6, J3) → 다각형60, j3_2, k6_3, g6
  118. Polygon(J3, G6, I3) → 다각형61, i3, j3_3, g6_1
  119. Polygon(G9, K5, I6) → 다각형62, i6, g9_2, k5_2
  120. Polygon(G9, I6, J6) → 다각형63, j6_3, g9_3, i6_1
  121. Polygon(K5, G5, I6) → 다각형64, i6_2, k5_3, g5
  122. Polygon(I6, G5, H6) → 다각형65, h6, i6_3, g5_1
  123. Polygon(H5, K1, G5) → 다각형66, g5_2, h5_1, k1
  124. Polygon(G5, K1, H6) → 다각형67, h6_1, g5_3, k1_1
  125. Polygon(H6, K1, G1) → 다각형68, g1, h6_2, k1_2
  126. Polygon(H6, G1, G6) → 다각형69, g6_2, h6_3, g1_1
  127. Polygon(G6, G1, I3) → 다각형70, i3_1, g6_3, g1_2
  128. Polygon(G1, H1, I3) → 다각형71, i3_2, g1_3, h1
  129. Polygon(I3, H1, H3) → 다각형72, h3_2, i3_3, h1_1
  130. Polygon(H1, H2, H3) → 다각형73, h3_3, h1_2, h2_1
  131. Polygon(H5, J1, K1) → 다각형74, k1_3, h5_2, j1
  132. Polygon(H5, G4, J1) → 다각형75, j1_1, h5_3, g4_2
  133. Polygon(G4, H4, J1) → 다각형76, j1_2, g4_3, h4_1
  134. Polygon(J1, H4, I1) → 다각형77, i1, j1_3, h4_2
  135. Polygon(H4, G2, I1) → 다각형78, i1_1, h4_3, g2_2
  136. Polygon(G2, I1, H2) → 다각형79, h2_2, g2_3, i1_2
  137. Polygon(I1, H2, H1) → 다각형80, h1_3, i1_3, h2_3