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球面模型：立方八面体

球面模型：立方八面体
几何画板及绘图内容加载中，请稍等……
2016-05-15 14:32
圆多边形解析几何立体几何几何作图
所属专题 My 3D Collection
该范例演示了如何在球面上构造一个立方八面体（cuboctahedron）的球面投影模型，将多面体的顶点、棱和面映射到球面，形成由圆弧和球面多边形构成的立体几何图形。核心数学概念包括多面体几何、球面几何、正多面体与阿基米德立体，以及平面与球面的交线（大圆或小圆）。作图要点：利用GeoGebra的Plane命令定义切割平面，UnitOrthogonalVector生成法向量，Element提取对象，Surface构造球面，Circle生成球面交线，Segment连接顶点；涉及大量点对象（如I、O、A、S1-S11、R1-R11、Q1-Q11等）和辅助点B、C、P1，通过平面与球面的相交关系构建出立方八面体的球面网格。适合高中或大学阶段的立体几何、多面体与球面几何教学，也可用于数学可视化演示或探究阿基米德立体的性质。

GeoGebra 命令及参数

  1. Plane(A, I, O) → S1
  2. UnitOrthogonalVector(S1) → S2
  3. Plane(E, I, O) → R1
  4. UnitOrthogonalVector(R1) → R2
  5. Plane(A, E, O) → Q1
  6. UnitOrthogonalVector(Q1) → Q2
  7. Plane(B, C, O) → P1
  8. UnitOrthogonalVector(P1) → P2
  9. Plane(A, Midpoint[E, I], O) → B1
  10. UnitOrthogonalVector(B1) → B2
  11. Element(B12, 1, 2) → B13
  12. Element(B12, 1, 3) → B14
  13. Element(B12, 2, 2) → B15
  14. Element(B12, 2, 3) → B16
  15. Element(B12, 3, 2) → B17
  16. Element(B12, 3, 3) → B18
  17. Surface(((B$13 * (4 + t)) * cos(k)) + ((B$14 * (4 + t)) * sin(k)), ((B$15 * (4 + t)) * cos(k)) + ((B$16 * (4 + t)) * sin(k)), ((B$17 * (4 + t)) * cos(k)) + ((B$18 * (4 + t)) * sin(k)), t, 0, 1, k, 0, (2 * π)) → B19
  18. Circle((0, 0, 0), 4, Line[(0, 0, 0), B2]) → B20
  19. Circle((0, 0, 0), 5, Line[(0, 0, 0), B2]) → B21
  20. Plane(E, Midpoint[A, I], O) → C1
  21. UnitOrthogonalVector(C1) → C2
  22. Element(C12, 1, 2) → C13
  23. Element(C12, 1, 3) → C14
  24. Element(C12, 2, 2) → C15
  25. Element(C12, 2, 3) → C16
  26. Element(C12, 3, 2) → C17
  27. Element(C12, 3, 3) → C18
  28. Surface(((C$13 * (4 + t)) * cos(k)) + ((C$14 * (4 + t)) * sin(k)), ((C$15 * (4 + t)) * cos(k)) + ((C$16 * (4 + t)) * sin(k)), ((C$17 * (4 + t)) * cos(k)) + ((C$18 * (4 + t)) * sin(k)), t, 0, 1, k, 0, (2 * π)) → C19
  29. Circle((0, 0, 0), 4, Line[(0, 0, 0), C2]) → C20
  30. Circle((0, 0, 0), 5, Line[(0, 0, 0), C2]) → C21
  31. Plane(I, Midpoint[A, E], O) → D1
  32. UnitOrthogonalVector(D1) → D2
  33. Element(D12, 1, 2) → D13
  34. Element(D12, 1, 3) → D14
  35. Element(D12, 2, 2) → D15
  36. Element(D12, 2, 3) → D16
  37. Element(D12, 3, 2) → D17
  38. Element(D12, 3, 3) → D18
  39. Surface(((D$13 * (4 + t)) * cos(k)) + ((D$14 * (4 + t)) * sin(k)), ((D$15 * (4 + t)) * cos(k)) + ((D$16 * (4 + t)) * sin(k)), ((D$17 * (4 + t)) * cos(k)) + ((D$18 * (4 + t)) * sin(k)), t, 0, 1, k, 0, (2 * π)) → D19
  40. Circle((0, 0, 0), 4, Line[(0, 0, 0), D2]) → D20
  41. Circle((0, 0, 0), 5, Line[(0, 0, 0), D2]) → D21
  42. Plane(D, Midpoint[H, I], O) → E1
  43. UnitOrthogonalVector(E1) → E2
  44. Element(E12, 1, 2) → E13
  45. Element(E12, 1, 3) → E14
  46. Element(E12, 2, 2) → E15
  47. Element(E12, 2, 3) → E16
  48. Element(E12, 3, 2) → E17
  49. Element(E12, 3, 3) → E18
  50. Surface(((E$13 * (4 + t)) * cos(k)) + ((E$14 * (4 + t)) * sin(k)), ((E$15 * (4 + t)) * cos(k)) + ((E$16 * (4 + t)) * sin(k)), ((E$17 * (4 + t)) * cos(k)) + ((E$18 * (4 + t)) * sin(k)), t, 0, 1, k, 0, (2 * π)) → E19
  51. Circle((0, 0, 0), 4, Line[(0, 0, 0), E2]) → E20
  52. Circle((0, 0, 0), 5, Line[(0, 0, 0), E2]) → E21
  53. Plane(H, Midpoint[D, I], O) → F1
  54. UnitOrthogonalVector(F1) → F2
  55. Element(F12, 1, 2) → F13
  56. Element(F12, 1, 3) → F14
  57. Element(F12, 2, 2) → F15
  58. Element(F12, 2, 3) → F16
  59. Element(F12, 3, 2) → F17
  60. Element(F12, 3, 3) → F18
  61. Surface(((F$13 * (4 + t)) * cos(k)) + ((F$14 * (4 + t)) * sin(k)), ((F$15 * (4 + t)) * cos(k)) + ((F$16 * (4 + t)) * sin(k)), ((F$17 * (4 + t)) * cos(k)) + ((F$18 * (4 + t)) * sin(k)), t, 0, 1, k, 0, (2 * π)) → F19
  62. Circle((0, 0, 0), 4, Line[(0, 0, 0), F2]) → F20
  63. Circle((0, 0, 0), 5, Line[(0, 0, 0), F2]) → F21
  64. Plane(I, Midpoint[D, H], O) → G1
  65. UnitOrthogonalVector(G1) → G2
  66. Element(G12, 1, 2) → G13
  67. Element(G12, 1, 3) → G14
  68. Element(G12, 2, 2) → G15
  69. Element(G12, 2, 3) → G16
  70. Element(G12, 3, 2) → G17
  71. Element(G12, 3, 3) → G18
  72. Surface(((G$13 * (4 + t)) * cos(k)) + ((G$14 * (4 + t)) * sin(k)), ((G$15 * (4 + t)) * cos(k)) + ((G$16 * (4 + t)) * sin(k)), ((G$17 * (4 + t)) * cos(k)) + ((G$18 * (4 + t)) * sin(k)), t, 0, 1, k, 0, (2 * π)) → G19
  73. Circle((0, 0, 0), 4, Line[(0, 0, 0), G2]) → G20
  74. Circle((0, 0, 0), 5, Line[(0, 0, 0), G2]) → G21
  75. Plane(C, Midpoint[H, L], O) → H1
  76. Plane(H, Midpoint[C, L], O) → I1
  77. Plane(L, Midpoint[C, H], O) → J1
  78. UnitOrthogonalVector(H1) → H2
  79. Element(H12, 1, 2) → H13
  80. Element(H12, 1, 3) → H14
  81. Element(H12, 2, 2) → H15
  82. Element(H12, 2, 3) → H16
  83. Element(H12, 3, 2) → H17
  84. Element(H12, 3, 3) → H18
  85. Surface(((H$13 * (4 + t)) * cos(k)) + ((H$14 * (4 + t)) * sin(k)), ((H$15 * (4 + t)) * cos(k)) + ((H$16 * (4 + t)) * sin(k)), ((H$17 * (4 + t)) * cos(k)) + ((H$18 * (4 + t)) * sin(k)), t, 0, 1, k, 0, (2 * π)) → H19
  86. Circle((0, 0, 0), 4, Line[(0, 0, 0), H2]) → H20
  87. Circle((0, 0, 0), 5, Line[(0, 0, 0), H2]) → H21
  88. UnitOrthogonalVector(I1) → I2
  89. Element(I12, 1, 2) → I13
  90. Element(I12, 1, 3) → I14
  91. Element(I12, 2, 2) → I15
  92. Element(I12, 2, 3) → I16
  93. Element(I12, 3, 2) → I17
  94. Element(I12, 3, 3) → I18
  95. Surface(((I$13 * (4 + t)) * cos(k)) + ((I$14 * (4 + t)) * sin(k)), ((I$15 * (4 + t)) * cos(k)) + ((I$16 * (4 + t)) * sin(k)), ((I$17 * (4 + t)) * cos(k)) + ((I$18 * (4 + t)) * sin(k)), t, 0, 1, k, 0, (2 * π)) → I19
  96. Circle((0, 0, 0), 4, Line[(0, 0, 0), I2]) → I20
  97. Circle((0, 0, 0), 5, Line[(0, 0, 0), I2]) → I21
  98. UnitOrthogonalVector(J1) → J2
  99. Element(J12, 1, 2) → J13
  100. Element(J12, 1, 3) → J14
  101. Element(J12, 2, 2) → J15
  102. Element(J12, 2, 3) → J16
  103. Element(J12, 3, 2) → J17
  104. Element(J12, 3, 3) → J18
  105. Surface(((J$13 * (4 + t)) * cos(k)) + ((J$14 * (4 + t)) * sin(k)), ((J$15 * (4 + t)) * cos(k)) + ((J$16 * (4 + t)) * sin(k)), ((J$17 * (4 + t)) * cos(k)) + ((J$18 * (4 + t)) * sin(k)), t, 0, 1, k, 0, (2 * π)) → J19
  106. Circle((0, 0, 0), 4, Line[(0, 0, 0), J2]) → J20
  107. Circle((0, 0, 0), 5, Line[(0, 0, 0), J2]) → J21
  108. Plane(B, Midpoint[L, E], O) → K1
  109. Plane(L, Midpoint[B, E], O) → L1
  110. Plane(E, Midpoint[B, L], O) → M1
  111. UnitOrthogonalVector(K1) → K2
  112. Element(K12, 1, 2) → K13
  113. Element(K12, 1, 3) → K14
  114. Element(K12, 2, 2) → K15
  115. Element(K12, 2, 3) → K16
  116. Element(K12, 3, 2) → K17
  117. Element(K12, 3, 3) → K18
  118. Surface(((K$13 * (4 + t)) * cos(k)) + ((K$14 * (4 + t)) * sin(k)), ((K$15 * (4 + t)) * cos(k)) + ((K$16 * (4 + t)) * sin(k)), ((K$17 * (4 + t)) * cos(k)) + ((K$18 * (4 + t)) * sin(k)), t, 0, 1, k, 0, (2 * π)) → K19
  119. Circle((0, 0, 0), 4, Line[(0, 0, 0), K2]) → K20
  120. Circle((0, 0, 0), 5, Line[(0, 0, 0), K2]) → K21
  121. UnitOrthogonalVector(L1) → L2
  122. Element(L12, 1, 2) → L13
  123. Element(L12, 1, 3) → L14
  124. Element(L12, 2, 2) → L15
  125. Element(L12, 2, 3) → L16
  126. Element(L12, 3, 2) → L17
  127. Element(L12, 3, 3) → L18
  128. Surface(((L$13 * (4 + t)) * cos(k)) + ((L$14 * (4 + t)) * sin(k)), ((L$15 * (4 + t)) * cos(k)) + ((L$16 * (4 + t)) * sin(k)), ((L$17 * (4 + t)) * cos(k)) + ((L$18 * (4 + t)) * sin(k)), t, 0, 1, k, 0, (2 * π)) → L19
  129. Circle((0, 0, 0), 4, Line[(0, 0, 0), L2]) → L20
  130. Circle((0, 0, 0), 5, Line[(0, 0, 0), L2]) → L21
  131. UnitOrthogonalVector(M1) → M2
  132. Element(M12, 1, 2) → M13
  133. Element(M12, 1, 3) → M14
  134. Element(M12, 2, 2) → M15
  135. Element(M12, 2, 3) → M16
  136. Element(M12, 3, 2) → M17
  137. Element(M12, 3, 3) → M18
  138. Surface(((M$13 * (4 + t)) * cos(k)) + ((M$14 * (4 + t)) * sin(k)), ((M$15 * (4 + t)) * cos(k)) + ((M$16 * (4 + t)) * sin(k)), ((M$17 * (4 + t)) * cos(k)) + ((M$18 * (4 + t)) * sin(k)), t, 0, 1, k, 0, (2 * π)) → M19
  139. Circle((0, 0, 0), 4, Line[(0, 0, 0), M2]) → M20
  140. Circle((0, 0, 0), 5, Line[(0, 0, 0), M2]) → M21
  141. Plane(H, E, O) → N1
  142. UnitOrthogonalVector(N1) → N2
  143. Element(N12, 1, 2) → N13
  144. Element(N12, 1, 3) → N14
  145. Element(N12, 2, 2) → N15
  146. Element(N12, 2, 3) → N16
  147. Element(N12, 3, 2) → N17
  148. Element(N12, 3, 3) → N18
  149. Surface(((N$13 * (4 + t)) * cos(k)) + ((N$14 * (4 + t)) * sin(k)), ((N$15 * (4 + t)) * cos(k)) + ((N$16 * (4 + t)) * sin(k)), ((N$17 * (4 + t)) * cos(k)) + ((N$18 * (4 + t)) * sin(k)), t, 0, 1, k, 0, (2 * π)) → N19
  150. Circle((0, 0, 0), 4, Line[(0, 0, 0), N2]) → N20
  151. Circle((0, 0, 0), 5, Line[(0, 0, 0), N2]) → N21
  152. Plane(I, L, O) → O1
  153. UnitOrthogonalVector(O1) → O2
  154. Element(O12, 1, 2) → O13
  155. Element(O12, 1, 3) → O14
  156. Element(O12, 2, 2) → O15
  157. Element(O12, 2, 3) → O16
  158. Element(O12, 3, 2) → O17
  159. Element(O12, 3, 3) → O18
  160. Surface(((O$13 * (4 + t)) * cos(k)) + ((O$14 * (4 + t)) * sin(k)), ((O$15 * (4 + t)) * cos(k)) + ((O$16 * (4 + t)) * sin(k)), ((O$17 * (4 + t)) * cos(k)) + ((O$18 * (4 + t)) * sin(k)), t, 0, 1, k, 0, (2 * π)) → O19
  161. Circle((0, 0, 0), 4, Line[(0, 0, 0), O2]) → O20
  162. Circle((0, 0, 0), 5, Line[(0, 0, 0), O2]) → O21
  163. Element(P8, 1, 2) → P13
  164. Element(P8, 1, 3) → P14
  165. Element(P8, 2, 2) → P15
  166. Element(P8, 2, 3) → P16
  167. Element(P8, 3, 2) → P17
  168. Element(P8, 3, 3) → P18
  169. Surface(((P$13 * (4 + t)) * cos(k)) + ((P$14 * (4 + t)) * sin(k)), ((P$15 * (4 + t)) * cos(k)) + ((P$16 * (4 + t)) * sin(k)), ((P$17 * (4 + t)) * cos(k)) + ((P$18 * (4 + t)) * sin(k)), t, 0, 1, k, 0, (2 * π)) → P19
  170. Circle((0, 0, 0), 4, Line[(0, 0, 0), P2]) → P20
  171. Circle((0, 0, 0), 5, Line[(0, 0, 0), P2]) → P21
  172. Element(Q12, 1, 2) → Q13
  173. Element(Q12, 1, 3) → Q14
  174. Element(Q12, 2, 2) → Q15
  175. Element(Q12, 2, 3) → Q16
  176. Element(Q12, 3, 2) → Q17
  177. Element(Q12, 3, 3) → Q18
  178. Surface(((Q$13 * (4 + t)) * cos(k)) + ((Q$14 * (4 + t)) * sin(k)), ((Q$15 * (4 + t)) * cos(k)) + ((Q$16 * (4 + t)) * sin(k)), ((Q$17 * (4 + t)) * cos(k)) + ((Q$18 * (4 + t)) * sin(k)), t, 0, 1, k, 0, (2 * π)) → Q19
  179. Circle((0, 0, 0), 4, Line[(0, 0, 0), Q2]) → Q20
  180. Circle((0, 0, 0), 5, Line[(0, 0, 0), Q2]) → Q21
  181. Element(R12, 1, 2) → R13
  182. Element(R12, 1, 3) → R14
  183. Element(R12, 2, 2) → R15
  184. Element(R12, 2, 3) → R16
  185. Element(R12, 3, 2) → R17
  186. Element(R12, 3, 3) → R18
  187. Surface(((R$13 * (4 + t)) * cos(k)) + ((R$14 * (4 + t)) * sin(k)), ((R$15 * (4 + t)) * cos(k)) + ((R$16 * (4 + t)) * sin(k)), ((R$17 * (4 + t)) * cos(k)) + ((R$18 * (4 + t)) * sin(k)), t, 0, 1, k, 0, (2 * π)) → R19
  188. Circle((0, 0, 0), 4, Line[(0, 0, 0), R2]) → R20
  189. Circle((0, 0, 0), 5, Line[(0, 0, 0), R2]) → R21
  190. Element(S12, 1, 2) → S13
  191. Element(S12, 1, 3) → S14
  192. Element(S12, 2, 2) → S15
  193. Element(S12, 2, 3) → S16
  194. Element(S12, 3, 2) → S17
  195. Element(S12, 3, 3) → S18
  196. Surface(((S$13 * (4 + t)) * cos(k)) + ((S$14 * (4 + t)) * sin(k)), ((S$15 * (4 + t)) * cos(k)) + ((S$16 * (4 + t)) * sin(k)), ((S$17 * (4 + t)) * cos(k)) + ((S$18 * (4 + t)) * sin(k)), t, 0, 1, k, 0, (2 * π)) → S19
  197. Circle((0, 0, 0), 4, Line[(0, 0, 0), S2]) → S20
  198. Circle((0, 0, 0), 5, Line[(0, 0, 0), S2]) → S21
  199. Plane(D, H, O) → T1
  200. Plane(D, I, O) → U1
  201. Plane(H, I, O) → V1
  202. UnitOrthogonalVector(T1) → T2
  203. Element(T12, 1, 2) → T13
  204. Element(T12, 1, 3) → T14
  205. Element(T12, 2, 2) → T15
  206. Element(T12, 2, 3) → T16
  207. Element(T12, 3, 2) → T17
  208. Element(T12, 3, 3) → T18
  209. Surface(((T$13 * (4 + t)) * cos(k)) + ((T$14 * (4 + t)) * sin(k)), ((T$15 * (4 + t)) * cos(k)) + ((T$16 * (4 + t)) * sin(k)), ((T$17 * (4 + t)) * cos(k)) + ((T$18 * (4 + t)) * sin(k)), t, 0, 1, k, 0, (2 * π)) → T19
  210. Circle((0, 0, 0), 4, Line[(0, 0, 0), T2]) → T20
  211. Circle((0, 0, 0), 5, Line[(0, 0, 0), T2]) → T21
  212. UnitOrthogonalVector(U1) → U2
  213. Element(U12, 1, 2) → U13
  214. Element(U12, 1, 3) → U14
  215. Element(U12, 2, 2) → U15
  216. Element(U12, 2, 3) → U16
  217. Element(U12, 3, 2) → U17
  218. Element(U12, 3, 3) → U18
  219. Surface(((U$13 * (4 + t)) * cos(k)) + ((U$14 * (4 + t)) * sin(k)), ((U$15 * (4 + t)) * cos(k)) + ((U$16 * (4 + t)) * sin(k)), ((U$17 * (4 + t)) * cos(k)) + ((U$18 * (4 + t)) * sin(k)), t, 0, 1, k, 0, (2 * π)) → U19
  220. Circle((0, 0, 0), 4, Line[(0, 0, 0), U2]) → U20
  221. Circle((0, 0, 0), 5, Line[(0, 0, 0), U2]) → U21
  222. UnitOrthogonalVector(V1) → V2
  223. Element(V12, 1, 2) → V13
  224. Element(V12, 1, 3) → V14
  225. Element(V12, 2, 2) → V15
  226. Element(V12, 2, 3) → V16
  227. Element(V12, 3, 2) → V17
  228. Element(V12, 3, 3) → V18
  229. Surface(((V$13 * (4 + t)) * cos(k)) + ((V$14 * (4 + t)) * sin(k)), ((V$15 * (4 + t)) * cos(k)) + ((V$16 * (4 + t)) * sin(k)), ((V$17 * (4 + t)) * cos(k)) + ((V$18 * (4 + t)) * sin(k)), t, 0, 1, k, 0, (2 * π)) → V19
  230. Circle((0, 0, 0), 4, Line[(0, 0, 0), V2]) → V20
  231. Circle((0, 0, 0), 5, Line[(0, 0, 0), V2]) → V21
  232. Plane(C, H, O) → W1
  233. Plane(C, L, O) → X1
  234. Plane(H, L, O) → Y1
  235. UnitOrthogonalVector(W1) → W2
  236. Element(W12, 1, 2) → W13
  237. Element(W12, 1, 3) → W14
  238. Element(W12, 2, 2) → W15
  239. Element(W12, 2, 3) → W16
  240. Element(W12, 3, 2) → W17
  241. Element(W12, 3, 3) → W18
  242. Surface(((W$13 * (4 + t)) * cos(k)) + ((W$14 * (4 + t)) * sin(k)), ((W$15 * (4 + t)) * cos(k)) + ((W$16 * (4 + t)) * sin(k)), ((W$17 * (4 + t)) * cos(k)) + ((W$18 * (4 + t)) * sin(k)), t, 0, 1, k, 0, (2 * π)) → W19
  243. Circle((0, 0, 0), 4, Line[(0, 0, 0), W2]) → W20
  244. Circle((0, 0, 0), 5, Line[(0, 0, 0), W2]) → W21
  245. UnitOrthogonalVector(X1) → X2
  246. Element(X12, 1, 2) → X13
  247. Element(X12, 1, 3) → X14
  248. Element(X12, 2, 2) → X15
  249. Element(X12, 2, 3) → X16
  250. Element(X12, 3, 2) → X17
  251. Element(X12, 3, 3) → X18
  252. Surface(((X$13 * (4 + t)) * cos(k)) + ((X$14 * (4 + t)) * sin(k)), ((X$15 * (4 + t)) * cos(k)) + ((X$16 * (4 + t)) * sin(k)), ((X$17 * (4 + t)) * cos(k)) + ((X$18 * (4 + t)) * sin(k)), t, 0, 1, k, 0, (2 * π)) → X19
  253. Circle((0, 0, 0), 4, Line[(0, 0, 0), X2]) → X20
  254. Circle((0, 0, 0), 5, Line[(0, 0, 0), X2]) → X21
  255. UnitOrthogonalVector(Y1) → Y2
  256. Element(Y12, 1, 2) → Y13
  257. Element(Y12, 1, 3) → Y14
  258. Element(Y12, 2, 2) → Y15
  259. Element(Y12, 2, 3) → Y16
  260. Element(Y12, 3, 2) → Y17
  261. Element(Y12, 3, 3) → Y18
  262. Surface(((Y$13 * (4 + t)) * cos(k)) + ((Y$14 * (4 + t)) * sin(k)), ((Y$15 * (4 + t)) * cos(k)) + ((Y$16 * (4 + t)) * sin(k)), ((Y$17 * (4 + t)) * cos(k)) + ((Y$18 * (4 + t)) * sin(k)), t, 0, 1, k, 0, (2 * π)) → Y19
  263. Circle((0, 0, 0), 4, Line[(0, 0, 0), Y2]) → Y20
  264. Circle((0, 0, 0), 5, Line[(0, 0, 0), Y2]) → Y21
  265. Plane(B, L, O) → Z1
  266. Plane(B, E, O) → AA1
  267. Plane(L, E, O) → AB1
  268. UnitOrthogonalVector(Z1) → Z2
  269. Element(Z12, 1, 2) → Z13
  270. Element(Z12, 1, 3) → Z14
  271. Element(Z12, 2, 2) → Z15
  272. Element(Z12, 2, 3) → Z16
  273. Element(Z12, 3, 2) → Z17
  274. Element(Z12, 3, 3) → Z18
  275. Surface(((Z$13 * (4 + t)) * cos(k)) + ((Z$14 * (4 + t)) * sin(k)), ((Z$15 * (4 + t)) * cos(k)) + ((Z$16 * (4 + t)) * sin(k)), ((Z$17 * (4 + t)) * cos(k)) + ((Z$18 * (4 + t)) * sin(k)), t, 0, 1, k, 0, (2 * π)) → Z19
  276. Circle((0, 0, 0), 4, Line[(0, 0, 0), Z2]) → Z20
  277. Circle((0, 0, 0), 5, Line[(0, 0, 0), Z2]) → Z21
  278. UnitOrthogonalVector(AA1) → AA2
  279. Element(AA12, 1, 2) → AA13
  280. Element(AA12, 1, 3) → AA14
  281. Element(AA12, 2, 2) → AA15
  282. Element(AA12, 2, 3) → AA16
  283. Element(AA12, 3, 2) → AA17
  284. Element(AA12, 3, 3) → AA18
  285. Surface(((AA$13 * (4 + t)) * cos(k)) + ((AA$14 * (4 + t)) * sin(k)), ((AA$15 * (4 + t)) * cos(k)) + ((AA$16 * (4 + t)) * sin(k)), ((AA$17 * (4 + t)) * cos(k)) + ((AA$18 * (4 + t)) * sin(k)), t, 0, 1, k, 0, (2 * π)) → AA19
  286. Circle((0, 0, 0), 4, Line[(0, 0, 0), AA2]) → AA20
  287. Circle((0, 0, 0), 5, Line[(0, 0, 0), AA2]) → AA21
  288. UnitOrthogonalVector(AB1) → AB2
  289. Element(AB12, 1, 2) → AB13
  290. Element(AB12, 1, 3) → AB14
  291. Element(AB12, 2, 2) → AB15
  292. Element(AB12, 2, 3) → AB16
  293. Element(AB12, 3, 2) → AB17
  294. Element(AB12, 3, 3) → AB18
  295. Surface(((AB$13 * (4 + t)) * cos(k)) + ((AB$14 * (4 + t)) * sin(k)), ((AB$15 * (4 + t)) * cos(k)) + ((AB$16 * (4 + t)) * sin(k)), ((AB$17 * (4 + t)) * cos(k)) + ((AB$18 * (4 + t)) * sin(k)), t, 0, 1, k, 0, (2 * π)) → AB19
  296. Circle((0, 0, 0), 4, Line[(0, 0, 0), AB2]) → AB20
  297. Circle((0, 0, 0), 5, Line[(0, 0, 0), AB2]) → AB21
  298. Segment(O + (4 * AD1), O + (5 * AD1)) → AE1
  299. Segment(O + (4 * AD2), O + (5 * AD2)) → AE2
  300. Segment(O + (4 * AD3), O + (5 * AD3)) → AE3
  301. Segment(O + (4 * AD4), O + (5 * AD4)) → AE4
  302. Segment(O + (4 * AD5), O + (5 * AD5)) → AE5
  303. Segment(O + (4 * AD6), O + (5 * AD6)) → AE6
  304. Segment(O + (4 * AD7), O + (5 * AD7)) → AE7
  305. Segment(O + (4 * AD8), O + (5 * AD8)) → AE8
  306. Segment(O + (4 * AD9), O + (5 * AD9)) → AE9
  307. Segment(O + (4 * AD10), O + (5 * AD10)) → AE10
  308. Segment(O + (4 * AD11), O + (5 * AD11)) → AE11
  309. Segment(O + (4 * AD12), O + (5 * AD12)) → AE12
  310. Segment(O + (4 * AD13), O + (5 * AD13)) → AE13
  311. Segment(O + (4 * AD14), O + (5 * AD14)) → AE14
  312. Segment(O + (4 * AD15), O + (5 * AD15)) → AE15
  313. Segment(O + (4 * AD16), O + (5 * AD16)) → AE16
  314. Segment(O + (4 * AD17), O + (5 * AD17)) → AE17
  315. Segment(O + (4 * AD18), O + (5 * AD18)) → AE18
  316. Segment(O + (4 * AD19), O + (5 * AD19)) → AE19
  317. Segment(O + (4 * AD20), O + (5 * AD20)) → AE20
  318. Segment(O + (4 * AD21), O + (5 * AD21)) → AE21
  319. Segment(O + (4 * AD22), O + (5 * AD22)) → AE22
  320. Segment(O + (4 * AD23), O + (5 * AD23)) → AE23
  321. Segment(O + (4 * AD24), O + (5 * AD24)) → AE24
  322. Segment(O + (4 * AD25), O + (5 * AD25)) → AE25
  323. Segment(O + (4 * AD26), O + (5 * AD26)) → AE26
  324. Segment(O + (4 * AD27), O + (5 * AD27)) → AE27
  325. Segment(O + (4 * AD28), O + (5 * AD28)) → AE28
  326. Segment(O + (4 * AD30), O + (5 * AD30)) → AE30
  327. Segment(O + (4 * AD31), O + (5 * AD31)) → AE31
  328. Segment(O + (4 * AD32), O + (5 * AD32)) → AE32
  329. Segment(O + (4 * AD33), O + (5 * AD33)) → AE33
  330. Segment(O + (4 * AD34), O + (5 * AD34)) → AE34
  331. Segment(O + (4 * AD35), O + (5 * AD35)) → AE35
  332. Segment(O + (4 * AD36), O + (5 * AD36)) → AE36
  333. Segment(O + (4 * AD37), O + (5 * AD37)) → AE37
  334. Segment(O + (4 * AD38), O + (5 * AD38)) → AE38
  335. Segment(O + (4 * AD39), O + (5 * AD39)) → AE39
  336. Segment(O + (4 * AD40), O + (5 * AD40)) → AE40
  337. Segment(O + (4 * AD41), O + (5 * AD41)) → AE41
  338. Segment(O + (4 * AD42), O + (5 * AD42)) → AE42
  339. Segment(O + (4 * AD43), O + (5 * AD43)) → AE43
  340. Segment(O + (4 * AD44), O + (5 * AD44)) → AE44
  341. Segment(O + (4 * AD45), O + (5 * AD45)) → AE45
  342. Segment(O + (4 * AD46), O + (5 * AD46)) → AE46
  343. Segment(O + (4 * AD47), O + (5 * AD47)) → AE47
  344. Segment(O + (4 * AD48), O + (5 * AD48)) → AE48
  345. Segment(O + (4 * AD49), O + (5 * AD49)) → AE49
  346. Segment(O + (4 * AD50), O + (5 * AD50)) → AE50

AI 绘图提示语参考

绘制一个球面立方八面体模型，将立方八面体的顶点、边和面映射到球面上，形成由圆弧和球面多边形组成的实体几何图形。首先定义多个切割平面，生成正交单位向量，然后通过平面与球面的交线（大圆或小圆）创建球面多边形，最后连接顶点形成曲面和圆。展示多面体几何、球面几何、阿基米德立体和球面平面交点的核心概念，适合用于立体几何、多面体和球面几何的教学与可视化。
以上提示语为根据原始绘图命令整理而来，仅供参考。