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六边形金字塔设计

六边形金字塔设计
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2019-05-01 23:41
多边形立体几何几何作图
①本范例演示了如何通过 GeoGebra 构建六边形金字塔的立体图形；②涉及的核心数学概念包括多边形构造、立体几何、函数与变换；③作图要点——从下方『构造摘要』提炼用到了 Polygon（多边形）、Point（点）、Tetrahedron（四面体）、Pyramid（金字塔）等 GeoGebra 命令与对象；④适合高中及以上学生学习和教师教学演示，可用于立体几何与几何作图的实践。

GeoGebra 命令及参数

  1. Polygon(A, B, 6, xOyPlane) → poly1, f, F, g, h, i, j, k, C, D, E
  2. Point(Circle[Midpoint[A, B], (Distance[A, B] * sqrt(3) / 2), Segment[A, B]]) → G
  3. Tetrahedron(A, B, G) → a, H, edgeGH, edgeBH, faceABG, faceAGH, faceABH, faceBGH, edgeAG, edgeAB, edgeBG, edgeAH
  4. Point(Circle[Midpoint[B, C], (Distance[B, C] * sqrt(3) / 2), Segment[B, C]]) → I
  5. Tetrahedron(B, C, I) → b, J, edgeIJ, edgeCJ, faceBCI, faceBIJ, faceBCJ, faceCIJ, edgeBI, edgeBC, edgeCI, edgeBJ
  6. Point(Circle[Midpoint[C, D], (Distance[C, D] * sqrt(3) / 2), Segment[C, D]]) → K
  7. Tetrahedron(C, D, K) → c, L, edgeKL, edgeDL, faceCDK, faceCKL, faceCDL, faceDKL, edgeCK, edgeCD, edgeDK, edgeCL
  8. Point(Circle[Midpoint[D, E], (Distance[D, E] * sqrt(3) / 2), Segment[D, E]]) → M
  9. Tetrahedron(D, E, M) → d, N, edgeMN, edgeEN, faceDEM, faceDMN, faceDEN, faceEMN, edgeDM, edgeDE, edgeEM, edgeDN
  10. Point(Circle[Midpoint[E, F], (Distance[E, F] * sqrt(3) / 2), Segment[E, F]]) → O
  11. Tetrahedron(E, F, O) → e, P, edgeOP, edgeFP, faceEFO, faceEOP, faceEFP, faceFOP, edgeEO, edgeEF, edgeFO, edgeEP
  12. Point(Circle[Midpoint[F, A], (Distance[F, A] * sqrt(3) / 2), Segment[F, A]]) → Q
  13. Tetrahedron(F, A, Q) → l, R, edgeQR, edgeAR, faceAFQ, faceFQR, faceAFR, faceAQR, edgeFQ, edgeAF, edgeAQ, edgeFR
  14. Point(Circle[Midpoint[P, R], (Distance[P, R] * sqrt(3) / 2), Segment[P, R]]) → S
  15. Tetrahedron(P, R, S) → m, T, edgeST, edgeRT, facePRS, facePST, facePRT, faceRST, edgePS, edgePR, edgeRS, edgePT
  16. Point(Circle[Midpoint[R, H], (Distance[R, H] * sqrt(3) / 2), Segment[R, H]]) → U
  17. Tetrahedron(R, H, U) → n, V, edgeUV, edgeHV, faceHRU, faceRUV, faceHRV, faceHUV, edgeRU, edgeHR, edgeHU, edgeRV
  18. Point(Circle[Midpoint[H, J], (Distance[H, J] * sqrt(3) / 2), Segment[H, J]]) → W
  19. Tetrahedron(H, J, W) → o, Z, edgeWZ, edgeJZ, faceHJW, faceHWZ, faceHJZ, faceJWZ, edgeHW, edgeHJ, edgeJW, edgeHZ
  20. Point(Circle[Midpoint[J, L], (Distance[J, L] * sqrt(3) / 2), Segment[J, L]]) → A_1
  21. Tetrahedron(J, L, A_1) → p, B_1, edge5, edge4, face1, face3, face2, face4, edge1, edgeJL, edge3, edge2
  22. Point(Circle[Midpoint[L, N], (Distance[L, N] * sqrt(3) / 2), Segment[L, N]]) → C_1
  23. Tetrahedron(L, N, C_1) → q, D_1, edge10, edge9, face5, face7, face6, face8, edge6, edgeLN, edge8, edge7
  24. Point(Circle[Midpoint[N, P], (Distance[N, P] * sqrt(3) / 2), Segment[N, P]]) → E_1
  25. Tetrahedron(N, P, E_1) → r, F_1, edge15, edge14, face9, face11, face10, face12, edge11, edgeNP, edge13, edge12
  26. Polygon(B_1, D_1, F_1, T, V, Z) → poly2, b_1, d_1, f_1, t, v, z_1
  27. Pyramid(poly2, Q) → s, face15, edgeQT, edgeQV, edgeQZ, face16, face13, faceQTV, faceQVZ, face14, edge16, edge17, edge18