截十四面体的星形构造

截十四面体的星形构造
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2016-05-02 12:52
①本范例演示了截十四面体的星形构造过程;②涉及的核心数学概念包括多面体、星形多面体、立体几何;③作图要点——使用了 GeoGebra 命令 stel14sz, stel14kw 以及对象 A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, Z, A1, B1, C1, D1, E1, F1, A2, B2, C2, D2, E2, F2, A3, B3, C3, D3;④适合高中立体几何学习或数学建模参考。

GeoGebra 命令及参数

  1. stel14sz(A1, B1, C1, D1, E1, F1) → G1, H1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, I1, AA1, AB1, AC1, AD1, AE1, AF1, AG1, AH1, AI1, AJ1, J1, K1, L1, M1, N1, O1, P1
  2. stel14sz(A2, B2, C2, D2, E2, F2) → G2, H2, Q2, R2, S2, T2, U2, V2, W2, X2, Y2, Z2, I2, AA2, AB2, AC2, AD2, AE2, AF2, AG2, AH2, AI2, AJ2, J2, K2, L2, M2, N2, O2, P2
  3. stel14sz(A3, B3, C3, D3, E3, F3) → G3, H3, Q3, R3, S3, T3, U3, V3, W3, X3, Y3, Z3, I3, AA3, AB3, AC3, AD3, AE3, AF3, AG3, AH3, AI3, AJ3, J3, K3, L3, M3, N3, O3, P3
  4. stel14sz(A4, B4, C4, D4, E4, F4) → G4, H4, Q4, R4, S4, T4, U4, V4, W4, X4, Y4, Z4, I4, AA4, AB4, AC4, AD4, AE4, AF4, AG4, AH4, AI4, AJ4, J4, K4, L4, M4, N4, O4, P4
  5. stel14sz(A5, B5, C5, D5, E5, F5) → G5, H5, Q5, R5, S5, T5, U5, V5, W5, X5, Y5, Z5, I5, AA5, AB5, AC5, AD5, AE5, AF5, AG5, AH5, AI5, AJ5, J5, K5, L5, M5, N5, O5, P5
  6. stel14sz(A6, B6, C6, D6, E6, F6) → G6, H6, Q6, R6, S6, T6, U6, V6, W6, X6, Y6, Z6, I6, AA6, AB6, AC6, AD6, AE6, AF6, AG6, AH6, AI6, AJ6, J6, K6, L6, M6, N6, O6, P6
  7. stel14sz(A7, B7, C7, D7, E7, F7) → G7, H7, Q7, R7, S7, T7, U7, V7, W7, X7, Y7, Z7, I7, AA7, AB7, AC7, AD7, AE7, AF7, AG7, AH7, AI7, AJ7, J7, K7, L7, M7, N7, O7, P7
  8. stel14sz(A8, B8, C8, D8, E8, F8) → G8, H8, Q8, R8, S8, T8, U8, V8, W8, X8, Y8, Z8, I8, AA8, AB8, AC8, AD8, AE8, AF8, AG8, AH8, AI8, AJ8, J8, K8, L8, M8, N8, O8, P8
  9. stel14kw(A9, B9, C9, D9) → E9, F9, O9, P9, Q9, R9, S9, T9, U9, V9, W9, X9, G9, Y9, Z9, AA9, AB9, AC9, AD9, AE9, AF9, AG9, AH9, H9, AI9, AJ9, I9, J9, K9, L9, M9, N9
  10. stel14kw(A10, B10, C10, D10) → E10, F10, O10, P10, Q10, R10, S10, T10, U10, V10, W10, X10, G10, Y10, Z10, AA10, AB10, AC10, AD10, AE10, AF10, AG10, AH10, H10, AI10, AJ10, I10, J10, K10, L10, M10, N10
  11. stel14kw(A11, B11, C11, D11) → E11, F11, O11, P11, Q11, R11, S11, T11, U11, V11, W11, X11, G11, Y11, Z11, AA11, AB11, AC11, AD11, AE11, AF11, AG11, AH11, H11, AI11, AJ11, I11, J11, K11, L11, M11, N11
  12. stel14kw(A12, B12, C12, D12) → E12, F12, O12, P12, Q12, R12, S12, T12, U12, V12, W12, X12, G12, Y12, Z12, AA12, AB12, AC12, AD12, AE12, AF12, AG12, AH12, H12, AI12, AJ12, I12, J12, K12, L12, M12, N12
  13. stel14kw(A13, B13, C13, D13) → E13, F13, O13, P13, Q13, R13, S13, T13, U13, V13, W13, X13, G13, Y13, Z13, AA13, AB13, AC13, AD13, AE13, AF13, AG13, AH13, H13, AI13, AJ13, I13, J13, K13, L13, M13, N13
  14. stel14kw(A14, B14, C14, D14) → E14, F14, O14, P14, Q14, R14, S14, T14, U14, V14, W14, X14, G14, Y14, Z14, AA14, AB14, AC14, AD14, AE14, AF14, AG14, AH14, H14, AI14, AJ14, I14, J14, K14, L14, M14, N14

AI 绘图提示语参考

绘制一个星形截锥体,展示其星状多面体和固体几何的构造过程。首先构建多个六边形和五边形组合,形成截锥体的基本框架,然后通过延伸和连接这些多边形的顶点,形成复杂的星状结构。最终呈现出一个由多个面和棱构成的立体图形,体现截锥体的星状 stellated 过程和几何美感。
以上提示语为根据原始绘图命令整理而来,仅供参考。