二十面体与十二面体对偶性演示

二十面体与十二面体对偶性演示
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2023-03-14 00:38
所属专题 geometriadinamica.es
①本范例演示了二十面体与十二面体的对偶关系,即每个顶点对应一个面,每个面内接一个顶点。②涉及核心数学概念包括多边形、立体几何、几何作图、对称性。③构造过程中使用了GeoGebra命令:OrthogonalLine(正交线)、Circle(圆)、Intersect(交点)、Point(点)、Angle(角度)、If(条件判断)、Ellipse(椭圆)、punto3d(三维点)、Baricentro(重心)、Vector(向量)、Translate(平移)、Line(线)、Segment(线段)、Polygon(多边形)、Midpoint(中点)、Baricentro2(重心2)、Rotate(旋转)、CircleArc(圆弧);对象包括O_0(原点)、Central(中心)、e(单位向量)、d(距离)、H(高)、D1(直径)、ang(角度)、t(参数)、t5、t1、t2、t4、t3、t6、ver1、ver2、ver3、ver4、ver5、carasIco(二十面体面)、verEjes(顶点)、carasDod(十二面体面)、verticesDod(十二面体顶点)、verticesIco(二十面体顶点)、aristasDod(十二面体边)、aristasIco(二十面体边)、fi(黄金比例)、L(线段)、M(点)、O_r(旋转中心)、mira2、B、mira1、A、U、I12、I10、I08、I04、D09。④适合高中及以上学生及数学爱好者学习多面体性质与对偶原理。

GeoGebra 命令及参数

  1. OrthogonalLine(Central, xAxis) → e
  2. Circle(Central, 10.5) → d
  3. Intersect(d, e, 2) → H
  4. Point(d) → D1
  5. Angle(D1, Central, H) → ang
  6. If(t < 1, (abs(sgn(t)) * (sgn(t) - 1) / -2), Min[t - 1, 1]) → t2
  7. If(t < 3, (abs(sgn(t)) * (sgn(t) - 1) / -2), Min[t - 3, 1]) → t4
  8. If(t < 2, 0, Min[t - 2, 1]) → t3
  9. If(t5 < 4, 0, t5 - 4) → t6
  10. If(t1 > 0 ∧ t2 ≟ 0, true, false) → ver1
  11. If(t > 1 ∧ t ≤ 2, true, false) → ver2
  12. If(t3 > 0 ∧ t3 ≤ 1 ∧ t4 ≟ 0, true, false) → ver3
  13. If(t4 > 0 ∧ t6 ≟ 0, true, false) → ver4
  14. If(t6 > 0, true, false) → ver5
  15. Ellipse(O_r - (0, 0.95), O_r + (0, 0.95), 1) → mira2
  16. Point(mira2) → B
  17. Ellipse(O_r - (0.95, 0), O_r + (0.95, 0), 1) → mira1
  18. Point(mira1) → A
  19. punto3d(A, B, M, O_0, O_r, (-fi), 0, -1, U, L) → I12
  20. punto3d(A, B, M, O_0, O_r, fi, 0, -1, U, L) → I10
  21. punto3d(A, B, M, O_0, O_r, -1, (-fi), 0, U, L) → I08
  22. punto3d(A, B, M, O_0, O_r, 0, -1, (-fi), U, L) → I04
  23. Baricentro(I12, I04, I08) → D09
  24. punto3d(A, B, M, O_0, O_r, 0, 1, (-fi), U, L) → I02
  25. Baricentro(I04, I02, I10) → D16
  26. Baricentro(I02, I12, I04) → D17
  27. punto3d(A, B, M, O_0, O_r, -1, fi, 0, U, L) → I07
  28. Baricentro(I02, I07, I12) → D18
  29. punto3d(A, B, M, O_0, O_r, 0, 1, fi, U, L) → I01
  30. punto3d(A, B, M, O_0, O_r, 1, fi, 0, U, L) → I05
  31. Baricentro(I01, I07, I05) → D13
  32. Intersect(mira1, mira2) → Mira1, Mira2, Mira3, Mira4
  33. Angle(M, O_r, B) → θ
  34. Angle(U, O_r, A) → φ
  35. Vector(O_r, O_0) → u
  36. Translate(Xr, u) → X0
  37. Translate(Zr, u) → Z0
  38. Translate(Yr, u) → Y0
  39. Vector(O_0, Z0) → v
  40. Vector(O_0, Y0) → w
  41. Vector(O_0, X0) → z
  42. Circle(O_0, L) → c
  43. Line(O_0, Y0) → a
  44. Line(O_0, yAxis) → b
  45. Line(O_0, X0) → g
  46. Line(Z0, O_0) → j
  47. Translate(P1r, u) → P1
  48. Segment(Mira3, Mira2) → k
  49. Segment((-1, 0), U) → l
  50. Segment((0, -1), M) → m
  51. punto3d(A, B, M, O_0, O_r, 0, -1, fi, U, L) → I03
  52. punto3d(A, B, M, O_0, O_r, 1, (-fi), 0, U, L) → I06
  53. punto3d(A, B, M, O_0, O_r, fi, 0, 1, U, L) → I09
  54. punto3d(A, B, M, O_0, O_r, (-fi), 0, 1, U, L) → I11
  55. Baricentro(I07, I05, I02) → D19
  56. Baricentro(I10, I05, I02) → D20
  57. Baricentro(I01, I11, I07) → D12
  58. Baricentro(I07, I11, I12) → D11
  59. Baricentro(I03, I01, I11) → D04
  60. Baricentro(I11, I12, I08) → D10
  61. Baricentro(I03, I11, I08) → D03
  62. Baricentro(I06, I08, I04) → D08
  63. Baricentro(I06, I08, I03) → D02
  64. Baricentro(I04, I06, I10) → D07
  65. Angle(D19a, M02, D13a) → angM02
  66. Angle(D15b, M01, D14c) → angM01
  67. Angle(D08b, M07, D02b) → angM07
  68. Angle(D20a, M12, D15c) → angM12
  69. Angle(D10c, M06, D03b) → angM06
  70. Angle(D01a, M08, D05b) → angM08
  71. Angle(D16b, M11, D07a) → angM11
  72. Angle(D12b, M04, D04a) → angM04
  73. Angle(D11b, M03, D12a) → angM03
  74. Angle(D06a, M09, D01b) → angM09
  75. Angle(D17a, M10, D18a) → angM10
  76. Angle(D09a, M05, D10a) → angM05
  77. Angle(D14a, D14, D05a) → angD14
  78. Angle(D13c, D13, D12a) → angD13
  79. Angle(D05a, D05, D04a) → angD05
  80. Angle(D01c, D01, D05c) → angD01
  81. Polygon(D06b, D15b, D14c, D05c, D01c) → p01, p01h15, p01h14, p01h05, p01h01, p01h06
  82. Polygon(D14b, D13a, D19a, D20b, D15a) → p02, p02h14, p02h13, p02h19, p02h20, p02h15
  83. Polygon(D11b, D18b, D19c, D13c, D12a) → p03, p03h11, p03h18, p03h19, p03h13, p03h12
  84. Polygon(D04a, D05a, D14a, D13b, D12b) → p04, p04h05, p04h14, p04h13, p04h12, p04h04
  85. Polygon(D18c, D11a, D10a, D09a, D17b) → p05, p05h18, p05h11, p05h10, p05h09, p05h17
  86. Polygon(D04b, D03b, D10c, D11c, D12c) → p06, p06h04, p06h03, p06h10, p06h11, p06h12
  87. Polygon(D08b, D02b, D03c, D10b, D09c) → p07, p07h02, p07h03, p07h10, p07h09, p07h08
  88. Polygon(D02a, D03a, D04c, D05b, D01a) → p08, p08h02, p08h03, p08h04, p08h05, p08h01
  89. Polygon(D08c, D02c, D01b, D06a, D07b) → p09, p09h08, p09h02, p09h01, p09h06, p09h07
  90. Polygon(D17a, D16a, D20c, D19b, D18a) → p10, p10h17, p10h16, p10h20, p10h19, p10h18
  91. Polygon(D07a, D08a, D09b, D17c, D16b) → p11, p11h08, p11h09, p11h17, p11h16, p11h07
  92. Polygon(D07c, D16c, D20a, D15c, D06c) → p12, p12h16, p12h20, p12h15, p12h06, p12h07
  93. Polygon(D14c, D05a, D14a, D13a, D14b, D15b) → h14, h05h14, p04h14', h13h14, p02h14', h14h15, p01h14'
  94. Polygon(D01a, D05b, D04a, D05a, D14c, D05c) → h05, p08h05', h04h05, p04h05', h05h14', p01h05', h01h05
  95. Polygon(D01a, D02a, D01b, D06a, D01c, D05c) → h01, p08h01', h01h02, p09h01', h01h06, p01h01', h01h05'
  96. Polygon(D01c, D06a, D07b, D06c, D15c, D06b) → h06, h01h06', p09h06', h06h07, p12h06', h06h15, p01h06'
  97. Polygon(D06b, D15b, D14b, D15a, D20a, D15c) → h15, p01h15', h14h15', p02h15', h15h20, p12h15', h06h15'
  98. Polygon(D14a, D13b, D12a, D13c, D19a, D13a) → h13, p04h13', h12h13, p03h13', h13h19, p02h13', h13h14'
  99. Polygon(D20b, D19a, D13c, D19c, D18a, D19b) → h19, p02h19', h13h19', p03h19', h18h19, p10h19', h19h20
  100. Polygon(D20a, D16c, D20c, D19b, D20b, D15a) → h20, p12h20', h16h20, p10h20', h19h20', p02h20', h15h20'
  101. Angle(D06c, D06, D15c) → angD06
  102. Angle(D15a, D15, D14b) → angD15
  103. Angle(D20c, D20, D19b) → angD20
  104. Angle(D19c, D19, D13c) → angD19
  105. Angle(D10b, D10, D03c) → angD10
  106. Angle(D03c, D03, D02b) → angD03
  107. Angle(D09b, D09, D08a) → angD09
  108. Angle(D11a, D11, D10a) → angD11
  109. Angle(D12c, D12, D04b) → angD12
  110. Angle(D18c, D18, D11a) → angD18
  111. Angle(D04b, D04, D03b) → angD04
  112. Angle(D07b, D07, D08c) → angD07
  113. Angle(D08b, D08, D09c) → angD08
  114. Angle(D16b, D16, D17c) → angD16
  115. Angle(D17c, D17, D09b) → angD17
  116. Angle(D02c, D02, D01b) → angD02
  117. Polygon(D11c, D10c, D03c, D10b, D09a, D10a) → h10, p06h10', h03h10, p07h10', h09h10, p05h10', h10h11
  118. Polygon(D10c, D03b, D04c, D03a, D02b, D03c) → h03, p06h03', h03h04, p08h03', h02h03, p07h03', h03h10'
  119. Polygon(D17b, D09a, D10b, D09c, D08a, D09b) → h09, p05h09', h09h10', p07h09', h08h09, p11h09', h09h17
  120. Polygon(D12b, D13b, D12a, D11b, D12c, D04b) → h12, p04h12', h12h13', p03h12', h11h12, p06h12', h04h12
  121. Polygon(D11c, D12c, D11b, D18b, D11a, D10a) → h11, p06h11', h11h12', p03h11', h11h18, p05h11', h10h11'
  122. Polygon(D18b, D19c, D18a, D17a, D18c, D11a) → h18, p03h18', h18h19', p10h18', h17h18, p05h18', h11h18'
  123. Polygon(D05b, D04c, D03b, D04b, D12b, D04a) → h04, p08h04', h03h04', p06h04', h04h12', p04h04', h04h05'
  124. Polygon(D07c, D06c, D07b, D08c, D07a, D16b) → h07, p12h07', h06h07', p09h07', h07h08, p11h07', h07h16
  125. Polygon(D07a, D08a, D09c, D08b, D02c, D08c) → h08, p11h08', h08h09', p07h08', h02h08, p09h08', h07h08'
  126. Polygon(D16a, D20c, D16c, D07c, D16b, D17c) → h16, p10h16', h16h20', p12h16', h07h16', p11h16', h16h17
  127. Polygon(D16a, D17a, D18c, D17b, D09b, D17c) → h17, p10h17', h17h18', p05h17', h09h17', p11h17', h16h17'
  128. Polygon(D03a, D02a, D01b, D02c, D08b, D02b) → h02, p08h02', h01h02', p09h02', h02h08', p07h02', h02h03'
  129. Polygon(E05b, E05a, E05c) → t05, e05c, e05b, e05a
  130. Polygon(E03a, E03c, E03b) → t03, e03b, e03a, e03c
  131. Polygon(E13a, E13c, E13b) → t13, e13b, e13a, e13c
  132. Polygon(E19a, E19b, E19c) → t19, e19c, e19a, e19b
  133. Polygon(E01c, E01b, E01a) → t01, e01a, e01c, e01b
  134. Polygon(E15c, E15a, E15b) → t15, e15b, e15c, e15a
  135. Polygon(E07c, E07a, E07b) → t07, e07b, e07c, e07a
  136. Polygon(E14c, E14b, E14a) → t14, e14a, e14c, e14b
  137. Polygon(E02b, E02c, E02a) → t02, e02a, e02b, e02c
  138. Polygon(E11b, E11c, E11a) → t11, e11a, e11b, e11c
  139. Polygon(E10c, E10a, E10b) → t10, e10b, e10c, e10a
  140. Polygon(E12a, E12b, E12c) → t12, e12c, e12a, e12b
  141. Polygon(E16a, E16c, E16b) → t16, e16b, e16a, e16c
  142. Polygon(E20b, E20c, E20a) → t20, e20a, e20b, e20c
  143. Polygon(E06a, E06b, E06c) → t06, e06c, e06a, e06b
  144. Polygon(E18b, E18a, E18c) → t18, e18c, e18b, e18a
  145. Polygon(E08b, E08a, E08c) → t08, e08c, e08b, e08a
  146. Polygon(E17c, E17b, E17a) → t17, e17a, e17c, e17b
  147. Polygon(E09b, E09a, E09c) → t09, e09c, e09b, e09a
  148. Polygon(E04a, E04b, E04c) → t04, e04c, e04a, e04b
  149. Polygon(E15a, E14c, E14a, E13a, E13c, E19b, E19a, E20b, E20a, E15b) → d01, d0103, d01t15, d01t14, d0106, d01t13, d0102, d01t19, d0107, d01t20, d0111
  150. Polygon(E13c, E13b, E12a, E12c, E11c, E11b, E18c, E18b, E19c, E19b) → d02, d02t13, d0102', d0206, d02t12, d0209, d02t11, d0208, d02t18, d0207, d02t19
  151. Polygon(E14c, E15a, E15c, E06a, E06c, E01a, E01b, E05b, E05a, E14b) → d03, d0103', d03t14, d03t15, d0311, d03t06, d0304, d03t01, d0310, d03t05, d0306
  152. Polygon(E06c, E01a, E01c, E02c, E02a, E08c, E08b, E07c, E07a, E06b) → d04, d0304', d04t06, d04t01, d0410, d04t02, d0405, d04t08, d0412, d04t07, d0411
  153. Polygon(E08c, E02a, E02b, E03a, E03b, E10a, E10b, E09c, E09b, E08a) → d05, d0405', d05t08, d05t02, d0510, d05t03, d0509, d05t10, d0508, d05t09, d0512
  154. Polygon(E05c, E04b, E04c, E12b, E12a, E13b, E13a, E14a, E14b, E05a) → d06, d0610, d06t05, d06t04, d0609, d06t12, d0206', d06t13, d0106', d06t14, d0306'
  155. Polygon(E20b, E19a, E19c, E18b, E18a, E17b, E17a, E16c, E16a, E20c) → d07, d0107', d07t20, d07t19, d0207', d07t18, d0708, d07t17, d0712, d07t16, d0711
  156. Polygon(E11a, E10c, E10b, E09c, E09a, E17c, E17b, E18a, E18c, E11b) → d08, d0809, d08t11, d08t10, d0508', d08t09, d0812, d08t17, d0708', d08t18, d0208'
  157. Polygon(E03c, E04a, E04c, E12b, E12c, E11c, E11a, E10c, E10a, E03b) → d09, d0910, d09t03, d09t04, d0609', d09t12, d0209', d09t11, d0809', d09t10, d0509'
  158. Polygon(E01c, E01b, E05b, E05c, E04b, E04a, E03c, E03a, E02b, E02c) → d10, d10t01, d0410', d0310', d10t05, d0610', d10t04, d0910', d10t03, d0510', d10t02
  159. Polygon(E20a, E15b, E15c, E06a, E06b, E07a, E07b, E16b, E16a, E20c) → d11, d0111', d11t20, d11t15, d0311', d11t06, d0411', d11t07, d1112, d11t16, d0711'
  160. Polygon(E07c, E08b, E08a, E09b, E09a, E17c, E17a, E16c, E16b, E07b) → d12, d0412', d12t07, d12t08, d0512', d12t09, d0812', d12t17, d0712', d12t16, d1112'
  161. Angle(E19b, F01, E13c) → angF01
  162. Angle(E18b, F07, E19c) → angF07
  163. Angle(E18c, F02, E11b) → angF02
  164. Angle(E04c, F09, E12b) → angF09
  165. Angle(E12b, F06, E04c) → angF06
  166. Angle(E15a, F03, E14c) → angF03
  167. Angle(E20a, F11, E15b) → angF11
  168. Angle(E02c, F10, E01c) → angF10
  169. Angle(E08c, F05, E02a) → angF05
  170. Angle(E09c, F08, E10b) → angF08
  171. Angle(E07a, F04, E06b) → angF04
  172. Angle(E16b, F12, E07b) → angF12
  173. Angle(E14c, D14, E14a) → angT14
  174. Angle(E13c, D13, E13b) → angT13
  175. Angle(E15b, D15, E15a) → angT15
  176. Angle(E19c, D19, E19b) → angT19
  177. Angle(E20c, D20, E20b) → angT20
  178. Angle(E01c, D01, E01a) → angT01
  179. Angle(E02a, D02, E02c) → angT02
  180. Angle(E08b, D08, E08c) → angT08
  181. Angle(E07b, D07, E07a) → angT07
  182. Angle(E06b, D06, E06a) → angT06
  183. Angle(E04a, D04, E04b) → angT04
  184. Angle(E12c, D12, E12b) → angT12
  185. Angle(E16b, D16, E16c) → angT16
  186. Angle(E17a, D17, E17c) → angT17
  187. Angle(E09c, D09, E09a) → angT09
  188. Angle(E18a, D18, E18c) → angT18
  189. Angle(E11b, D11, E11a) → angT11
  190. Angle(E10c, D10, E10b) → angT10
  191. Angle(E03b, D03, E03a) → angT03
  192. Angle(E05c, D05, E05b) → angT05
  193. Baricentro(G16a, G16c, G16b) → TR16
  194. Angle(G16a, TR16, G16b) → angTR16
  195. Polygon(G16a, G16c, G16b) → tr16, g16b, g16a, g16c
  196. Polygon(G17b, G17c, G17a) → tr17, g17b, g17c, g17a
  197. Polygon(G09a, G09c, G09b) → tr09, g09b, g09a, g09c
  198. Baricentro(G09a, G09c, G09b) → TR09
  199. Angle(G09a, TR09, G09b) → angTR09
  200. Baricentro(G17a, G17b, G17c) → TR17
  201. Angle(G17a, TR17, G17c) → angTR17
  202. Baricentro(G15a, G15b, G15c) → TR15
  203. Angle(G15a, TR15, G15c) → angTR15
  204. Baricentro(G14c, G14a, G14b) → TR14
  205. Angle(G14c, TR14, G14b) → angTR14
  206. Baricentro(G13b, G13a, G13c) → C
  207. Baricentro(G13b, G13a, G13c) → D
  208. Angle(G13b, D, G13c) → angTR13
  209. Polygon(G15a, G15b, G15c) → tr15, g15c, g15a, g15b
  210. Polygon(G14c, G14a, G14b) → tr14, g14b, g14c, g14a
  211. Polygon(G13c, G13b, G13a) → tr13, g13a, g13c, g13b
  212. Polygon(G01a, G01b, G01c) → tr01, g01c, g01a, g01b
  213. Polygon(G02a, G02b, G02c) → tr02, g02c, g02a, g02b
  214. Polygon(G03a, G03b, G03c) → tr03, g03c, g03a, g03b
  215. Polygon(G04a, G04b, G04c) → tr04, g04c, g04a, g04b
  216. Polygon(G05a, G05b, G05c) → tr05, g05c, g05a, g05b
  217. Polygon(G06a, G06b, G06c) → tr06, g06c, g06a, g06b
  218. Polygon(G07a, G07b, G07c) → tr07, g07c, g07a, g07b
  219. Polygon(G08a, G08b, G08c) → tr08, g08c, g08a, g08b
  220. Polygon(G10a, G10b, G10c) → tr10, g10c, g10a, g10b
  221. Polygon(G11a, G11b, G11c) → tr11, g11c, g11a, g11b
  222. Polygon(G12a, G12b, G12c) → tr12, g12c, g12a, g12b
  223. Polygon(G18a, G18b, G18c) → tr18, g18c, g18a, g18b
  224. Polygon(G19a, G19b, G19c) → tr19, g19c, g19a, g19b
  225. Polygon(G20a, G20b, G20c) → tr20, g20c, g20a, g20b
  226. Baricentro(G01a, G01b, G01c) → TR01
  227. Baricentro(G02a, G02b, G02c) → TR02
  228. Baricentro(G03a, G03b, G03c) → TR03
  229. Baricentro(G04a, G04b, G04c) → TR04
  230. Baricentro(G05a, G05b, G05c) → TR05
  231. Baricentro(G06a, G06b, G06c) → TR06
  232. Baricentro(G07a, G07b, G07c) → TR07
  233. Baricentro(G08a, G08b, G08c) → TR08
  234. Baricentro(G10a, G10b, G10c) → TR10
  235. Baricentro(G11a, G11b, G11c) → TR11
  236. Baricentro(G12a, G12b, G12c) → TR12
  237. Baricentro(G13a, G13b, G13c) → TR13
  238. Baricentro(G18a, G18b, G18c) → TR18
  239. Baricentro(G19a, G19b, G19c) → TR19
  240. Baricentro(G20a, G20b, G20c) → TR20
  241. Angle(G06b, TR06, G06c) → angTR06
  242. Angle(G01a, TR01, G01c) → angTR01
  243. Angle(G05a, TR05, G05c) → angTR05
  244. Angle(G11a, TR11, G11b) → angTR11
  245. Angle(G18a, TR18, G18c) → angTR18
  246. Angle(G12a, TR12, G12c) → angTR12
  247. Angle(G07a, TR07, G07b) → angTR07
  248. Angle(G08b, TR08, G08a) → angTR08
  249. Angle(G02a, TR02, G02c) → angTR02
  250. Angle(G10a, TR10, G10c) → angTR10
  251. Angle(G03a, TR03, G03c) → angTR03
  252. Angle(G19b, TR19, G19a) → angTR19
  253. Angle(G20c, TR20, G20b) → angTR20
  254. Angle(G04c, TR04, G04a) → angTR04
  255. Angle(G19c, MD01, G19a) → angMD01
  256. Angle(G13b, MD06, G13a) → angMD06
  257. Angle(G11c, MD02, G11b) → angMD02
  258. Angle(G17b, MD07, G17c) → angMD07
  259. Angle(G07a, MD11, G07c) → angMD11
  260. Angle(G01b, MD03, G01c) → angMD03
  261. Angle(G09a, MD12, G09c) → angMD12
  262. Angle(G09c, MD08, G09b) → angMD08
  263. Angle(G12a, MD09, G12b) → angMD09
  264. Angle(G05a, MD10, G05b) → angMD10
  265. Angle(G06b, MD04, G06a) → angMD04
  266. Angle(G10a, MD05, G10b) → angMD05
  267. Polygon(G16b, G17b, G17a, G09c, G09a, G08c, G08b, G07b, G07c, G16a) → dec12, md0712, g16a_1, g17b_1, md0812, g09c_1, md0512, g08c_1, md0412, g07b_1, md1112
  268. Polygon(G17c, G18b, G18a, G11c, G11a, G10c, G10b, G09b, G09c, G17a) → dec08, md0708, g17a_2, g18b_1, md0208, g11c_1, md0809, g10c_1, md0508, g09b_1, g09c_2
  269. Polygon(G08c, G09a, G09b, G10b, G10a, G03b, G03a, G02c, G02b, G08a) → dec05, g08c_2, g08a_1, g09a_2, g09b_2, g10b_2, md0509, g03b_1, md0510, g02c_1, md0405
  270. Polygon(G06b, G07a, G07b, G08b, G08a, G02b, G02a, G01a, G01c, G06a) → dec04, md0411, g06a_1, g07a_1, g07b_2, g08b_2, g08a_2, g02b_2, md0410, g01a_1, md0304
  271. Polygon(G05a, G01b, G01a, G02a, G02c, G03a, G03c, G04a, G04b, G05b) → dec10, md0310, g05b_1, g01b_1, g01a_2, g02a_2, g02c_2, g03a_2, md0910, g04a_1, md0610
  272. Polygon(G12b, G11b, G11a, G10c, G10a, G03b, G03c, G04a, G04c, G12a) → dec09, md0209, g12a_1, g11b_1, g11a_2, g10c_2, g10a_2, g03b_2, g03c_2, g04a_2, md0609
  273. Polygon(G05b, G04b, G04c, G12a, G12c, G13a, G13b, G14b, G14a, G05c) → dec06, g05b_2, g05c_1, g04b_2, g04c_2, g12a_2, md0206, g13a_1, md0106, g14b_1, md0306
  274. Polygon(G19a, G13c, G13b, G14b, G14c, G15b, G15c, G20b, G20c, G19c) → dec01, md0102, g19c_1, g13c_1, g13b_2, g14b_2, md0103, g15b_2, md0111, g20b_1, md0107
  275. Polygon(G16a, G07c, G07a, G06b, G06c, G15a, G15c, G20b, G20a, G16c) → dec11, g16a_2, g16c_1, g07c_2, g07a_2, g06b_2, md0311, g15a_2, g15c_2, g20b_2, md0711
  276. Polygon(G05a, G05c, G14a, G14c, G15b, G15a, G06c, G06a, G01c, G01b) → dec03, g05a_2, g01b_2, g05c_2, g14a_2, g14c_1, g15b_1, g15a_1, g06c_1, g06a_2, g01c_2
  277. Polygon(G19b, G19a, G13c, G13a, G12c, G12b, G11b, G11c, G18a, G18c) → dec02, g19b_1, md0207, g19a_2, g13c_2, g13a_2, g12c_2, g12b_2, g11b_2, g11c_2, g18a_2
  278. Polygon(G17b, G16b, G16c, G20a, G20c, G19c, G19b, G18c, G18b, G17c) → dec07, g17b_2, g17c_2, g16b_2, g16c_2, g20a_2, g20c_2, g19c_2, g19b_2, g18c_2, g18b_2
  279. Midpoint(D14, D05) → H01
  280. Midpoint(D14, D13) → H02
  281. Midpoint(D14, D15) → H03
  282. Midpoint(D12, D13) → H04
  283. Midpoint(D19, D13) → H05
  284. Midpoint(D19, D18) → H06
  285. Midpoint(D19, D20) → H07
  286. Midpoint(D15, D20) → H08
  287. Midpoint(D16, D20) → H09
  288. Midpoint(D06, D15) → H10
  289. Midpoint(D11, D18) → H11
  290. Midpoint(D17, D18) → H12
  291. Midpoint(D11, D12) → H13
  292. Midpoint(D04, D12) → H14
  293. Midpoint(D06, D07) → H15
  294. Midpoint(D06, D01) → H16
  295. Midpoint(D05, D01) → H17
  296. Midpoint(D05, D04) → H18
  297. Midpoint(D03, D04) → H19
  298. Midpoint(D01, D02) → H20
  299. Midpoint(D07, D16) → H21
  300. Midpoint(D17, D16) → H22
  301. Midpoint(D17, D09) → H23
  302. Midpoint(D11, D10) → H24
  303. Midpoint(D07, D08) → H25
  304. Midpoint(D02, D03) → H26
  305. Midpoint(D02, D08) → H27
  306. Midpoint(D03, D10) → H28
  307. Midpoint(D09, D10) → H29
  308. Midpoint(D09, D08) → H30
  309. Angle(J12d, F12, J12e) → angP12
  310. Angle(J08b, F08, J08c) → angP08
  311. Angle(J05c, F05, J05d) → angP05
  312. Angle(J09a, F09, J09b) → angP09
  313. Angle(J10a, F10, J10b) → angP10
  314. Angle(J04c, F04, J04d) → angP04
  315. Angle(J07c, F07, J07d) → angP07
  316. Polygon(J12b, J12a, J12e, J12d, J12c) → pen12, j12b, j12a, j12e, j12d, j12c
  317. Polygon(J08b, J08a, J08e, J08d, J08c) → pen08, j08b, j08a, j08e, j08d, j08c
  318. Polygon(J05b, J05a, J05e, J05d, J05c) → pen05, j05b, j05a, j05e, j05d, j05c
  319. Polygon(J09b, J09a, J09e, J09d, J09c) → pen09, j09b, j09a, j09e, j09d, j09c
  320. Polygon(J10a, J10e, J10d, J10c, J10b) → pen10, j10a, j10e, j10d, j10c, j10b
  321. Polygon(J04b, J04a, J04e, J04d, J04c) → pen04, j04b, j04a, j04e, j04d, j04c
  322. Polygon(J12e, J08a, J08b, J05e, J05a, J12d) → poly1, j12e_1, j08a_1, j08b_1, j05e_1, j05a_1, j12d_1
  323. Polygon(J12c, J12d, J05a, J05b, J04e, J04a) → poly2, j12c_1, j12d_2, j05a_2, j05b_1, j04e_1, j04a_1
  324. Polygon(J04e, J05b, J05c, J10d, J10e, J04d) → poly3, j04e_2, j05b_2, j05c_1, j10d_1, j10e_1, j04d_1
  325. Polygon(J09a, J10c, J10d, J05c, J05d, J09e) → poly4, j09a_1, j10c_1, j10d_2, j05c_2, j05d_1, j09e_1
  326. Polygon(J09d, J08c, J08b, J05e, J05d, J09e) → poly5, j09d_1, j08c_1, j08b_2, j05e_2, j05d_2, j09e_2
  327. Polygon(J07c, J07b, J07a, J07e, J07d) → pen07, j07c, j07b, j07a, j07e, j07d
  328. Polygon(J12a, J12e, J08a, J08e, J07d, J07c) → poly6, j12a_1, j12e_2, j08a_2, j08e_1, j07d_1, j07c_1
  329. Polygon(J11b, J11a, J11e, J11d, J11c) → pen11, j11b, j11a, j11e, j11d, j11c
  330. Angle(J11c, F11, J11d) → angP11
  331. Angle(J01c, F01, J01d) → angP01
  332. Angle(J02e, F02, J02a) → angP02
  333. Angle(J03a, F03, J03b) → angP03
  334. Angle(J06b, F06, J06c) → angP06
  335. Polygon(J07b, J07c, J12a, J12b, J11d, J11e) → poly7, j07b_1, j07c_2, j12a_2, j12b_1, j11d_1, j11e_1
  336. Polygon(J01c, J01b, J01a, J01e, J01d) → pen01, j01c, j01b, j01a, j01e, j01d
  337. Polygon(J07a, J07b, J11e, J11a, J01c, J01d) → poly8, j07a_1, j07b_2, j11e_2, j11a_1, j01c_1, j01d_1
  338. Polygon(J02d, J02c, J02b, J02a, J02e) → pen02, j02d, j02c, j02b, j02a, j02e
  339. Polygon(J03b, J03c, J03d, J03e, J03a) → pen03, j03b, j03c, j03d, j03e, j03a
  340. Polygon(J06a, J06e, J06d, J06c, J06b) → pen06, j06a, j06e, j06d, j06c, j06b
  341. Polygon(J01a, J06b, J06a, J03c, J03b, J01b) → poly9, j01a_1, j06b_1, j06a_1, j03c_1, j03b_1, j01b_1
  342. Polygon(J09b, J06d, J06c, J02b, J02a, J09c) → poly10, j09b_1, j06d_1, j06c_1, j02b_1, j02a_1, j09c_1
  343. Polygon(J02e, J02a, J09c, J09d, J08c, J08d) → poly11, j02e_1, j02a_2, j09c_2, j09d_2, j08c_2, j08d_1
  344. Polygon(J11b, J11a, J01c, J01b, J03b, J03a) → poly12, j11b_1, j11a_2, j01c_2, j01b_2, j03b_2, j03a_1
  345. Polygon(J11c, J04b, J04c, J03e, J03a, J11b) → poly13, j11c_1, j04b_1, j04c_1, j03e_1, j03a_2, j11b_2
  346. Polygon(J02c, J02b, J06c, J06b, J01a, J01e) → poly14, j02c_1, j02b_2, j06c_2, j06b_2, j01a_2, j01e_1
  347. Polygon(J07e, J02d, J02c, J01e, J01d, J07a) → poly15, j07e_1, j02d_1, j02c_2, j01e_2, j01d_2, j07a_2
  348. Polygon(J10a, J10e, J04d, J04c, J03e, J03d) → poly16, j10a_1, j10e_2, j04d_2, j04c_2, j03e_2, j03d_1
  349. Polygon(J10b, J06e, J06a, J03c, J03d, J10a) → poly17, j10b_1, j06e_1, j06a_2, j03c_2, j03d_2, j10a_2
  350. Polygon(J04a, J04b, J11c, J11d, J12b, J12c) → poly18, j04a_2, j04b_2, j11c_2, j11d_2, j12b_2, j12c_2
  351. Polygon(J10c, J09a, J09b, J06d, J06e, J10b) → poly19, j10c_2, j09a_2, j09b_2, j06d_2, j06e_2, j10b_2
  352. Polygon(J02d, J07e, J07d, J08e, J08d, J02e) → poly20, j02d_2, j07e_2, j07d_2, j08e_2, j08d_2, j02e_2
  353. Baricentro2(J10b, J06e, J10a, J03d, J03c, J06a) → BA17
  354. Baricentro2(J10a, J03d, J03e, J04c, J04d, J10e) → BA16
  355. Angle(J03c, BA17, J06a) → angBA17
  356. Angle(J04c, BA16, J03e) → angBA16
  357. Baricentro2(J06a, J03c, J03b, J01b, J01a, J06b) → BA09
  358. Angle(J03b, BA09, J01b) → angBA09
  359. Baricentro2(J03b, J01b, J03a, J11b, J11a, J01c) → BA12
  360. Angle(J11a, BA12, J01c) → angBA12
  361. Baricentro2(J11b, J03a, J03e, J04c, J04b, J11c) → BA13
  362. Angle(J04b, BA13, J11c) → angBA13
  363. Baricentro2(J09d, J08c, J09c, J02a, J02e, J08d) → BA11
  364. Angle(J02e, BA11, J08d) → angBA11
  365. Baricentro2(J08d, J02e, J08e, J07d, J07e, J02d) → BA20
  366. Angle(J02d, BA20, J07e) → angBA20
  367. Baricentro2(J02a, J09c, J02b, J06c, J06d, J09b) → BA10
  368. Angle(J02a, BA10, J09c) → angBA10
  369. Baricentro2(J01a, J06b, J06c, J02b, J02c, J01e) → BA14
  370. Angle(J01e, BA14, J02c) → angBA14
  371. Baricentro2(J01e, J02c, J01d, J07a, J02d, J07e) → BA15
  372. Angle(J01d, BA15, J07a) → angBA15
  373. Baricentro2(J11a, J01c, J01d, J07a, J07b, J11e) → BA08
  374. Angle(J11e, BA08, J07b) → angBA08
  375. Baricentro2(J04b, J11c, J04a, J12c, J12b, J11d) → BA18
  376. Angle(J11c, BA18, J04b) → angBA18
  377. Baricentro2(J11e, J07b, J07c, J12a, J12b, J11d) → BA07
  378. Angle(J12a, BA07, J07c) → angBA07
  379. Baricentro2(J06e, J10b, J10c, J09a, J09b, J06d) → BA19
  380. Angle(J10b, BA19, J06e) → angBA19
  381. Baricentro2(J09a, J10c, J10d, J05c, J05d, J09e) → BA04
  382. Angle(J09e, BA04, J05d) → angBA04
  383. Baricentro2(J12a, J07c, J07d, J08e, J08a, J12e) → BA06
  384. Angle(J12e, BA06, J08a) → angBA06
  385. Baricentro2(J10e, J04d, J10d, J05c, J04e, J05b) → BA03
  386. Angle(J04d, BA03, J10e) → angBA03
  387. Baricentro2(J12e, J08a, J08b, J05e, J05a, J12d) → BA01
  388. Angle(J05e, BA01, J08b) → angBA01
  389. Baricentro2(J05a, J12d, J12c, J04a, J04e, J05b) → BA02
  390. Angle(J05a, BA02, J12d) → angBA02
  391. Baricentro2(J05e, J08b, J08c, J09d, J09e, J05d) → BA05
  392. Angle(J05d, BA05, J09e) → angBA05
  393. Polygon(K09, K03, K01) → poly21, k01, k09, k03
  394. Polygon(K09, K05, K01) → poly22, k01_1, k09_1, k05
  395. Polygon(K01, K07, K05) → poly23, k05_1, k01_2, k07
  396. Polygon(K09, K10, K05) → poly24, k05_2, k09_2, k10
  397. Polygon(K10, K02, K05) → poly25, k05_3, k10_1, k02
  398. Polygon(K02, K05, K07) → poly26, k07_1, k02_1, k05_4
  399. Polygon(K09, K06, K10) → poly27, k10_2, k09_3, k06
  400. Polygon(K06, K09, K03) → poly28, k03_1, k06_1, k09_4
  401. Polygon(K03, K01, K11) → poly29, k11, k03_2, k01_3
  402. Polygon(K01, K11, K07) → poly30, k07_2, k01_4, k11_1
  403. Polygon(K06, K08, K03) → poly31, k03_3, k06_2, k08
  404. Polygon(K03, K08, K11) → poly32, k11_2, k03_4, k08_1
  405. Polygon(K06, K08, K04) → poly33, k04, k06_3, k08_2
  406. Polygon(K06, K10, K04) → poly34, k04_1, k06_4, k10_3
  407. Polygon(K10, K04, K02) → poly35, k02_2, k10_4, k04_2
  408. Polygon(K02, K12, K04) → poly36, k04_3, k02_3, k12
  409. Polygon(K12, K07, K02) → poly37, k02_4, k12_1, k07_3
  410. Polygon(K11, K07, K12) → poly38, k12_2, k11_3, k07_4
  411. Polygon(K08, K12, K04) → poly39, k04_4, k08_3, k12_3
  412. Polygon(K08, K11, K12) → poly40, k12_4, k08_4, k11_4
  413. Baricentro(K01, K05, K07) → E
  414. Angle(K07, E, K05) → ang33
  415. Baricentro(K04, K08, K12) → F
  416. Angle(K12, F, K04) → ang39
  417. Baricentro(K06, K03, K08) → G
  418. Angle(K08, G, K06) → ang31
  419. Baricentro(K08, K03, K11) → H_1
  420. Angle(K11, H_1, K08) → ang32
  421. Baricentro(K12, K08, K11) → I
  422. Angle(K08, I, K11) → ang40
  423. Baricentro(K06, K09, K03) → J
  424. Angle(K06, J, K09) → ang28
  425. Baricentro(K06, K09, K10) → K
  426. Angle(K09, K, K06) → ang27
  427. Baricentro(K04, K02, K12) → N
  428. Angle(K02, N, K04) → ang36
  429. Baricentro(K10, K06, K04) → O
  430. Angle(K04, O, K10) → ang34
  431. Baricentro(K10, K02, K04) → P
  432. Angle(K04, P, K02) → ang35
  433. Baricentro(K03, K01, K11) → Q
  434. Baricentro(K01, K11, K07) → R
  435. Baricentro(K01, K09, K05) → S
  436. Baricentro(K09, K10, K05) → T
  437. Baricentro(K01, K03, K09) → V
  438. Baricentro(K01, K05, K07) → W
  439. Baricentro(K07, K12, K02) → Z
  440. Baricentro(K05, K07, K02) → A1
  441. Baricentro(K05, K02, K10) → B1
  442. Angle(K01, V, K03) → ang21
  443. Angle(K01, Q, K11) → ang29
  444. Angle(K11, R, K01) → ang30
  445. Baricentro(K11, K07, K12) → C1
  446. Angle(K07, C1, K12) → ang38
  447. Angle(K12, Z, K07) → ang37
  448. Angle(K05, W, K07) → ang23
  449. Angle(K09, S, K05) → ang22
  450. Angle(K10, T, K05) → ang24
  451. Angle(K10, B1, K02) → ang25
  452. Angle(K02, A1, K07) → ang26
  453. Rotate(H, 324°, O_0) → E1
  454. Rotate(H, 275.99999999999994°, O_0) → F1
  455. Rotate(H, 252°, O_0) → G1
  456. Rotate(H, 218.00000000000003°, O_0) → H1
  457. Rotate(H, 180°, O_0) → I1
  458. Rotate(H, 140°, O_0) → J1
  459. Rotate(H, 108°, O_0) → K1
  460. Rotate(H, 78°, O_0) → L1
  461. Rotate(H, 36°, O_0) → M1
  462. CircleArc(O_0, M1, E1) → f
  463. CircleArc(O_0, E1, M1) → h

AI 绘图提示语参考

绘制一个以原点为中心的双曲面多面体对偶演示图:先取中央点并作水平与垂直方向的参考轴,给出一个以中央为圆心、固定半径的圆及其与正交参考线的交点形成高度点,并标注相关夹角;再以两个在不同方向上的椭圆为“视线轨迹”,取它们的交点得到两组关键空间点的基准;由这两组基准点结合黄金比例相关的参数,在三维空间构造多组对称位置的点,并用三点质心确定若干对偶面中心。最后连出由一对视线交点形成的线段,并在平面中再给出以原点为中心的圆与三条坐标方向的直线轮廓,体现向量与旋转对称关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。