六棱柱的展开图 by Eduardo Neto
几何画板及绘图内容加载中,请稍等……
该范例演示了六棱柱的展开图。涉及的核心数学概念包括多边形和立体几何。通过使用GeoGebra命令如Polygon、Prism、Segment、Rotate、Mirror等,可以构造六棱柱的各个面和棱。适合初中和高中学生学习立体几何。
GeoGebra 命令及参数
Polygon(A, B, 6, xOyPlane) → poly1, a, F, b, c, d, e, f, C, D, EPrism(poly1, A + (0, 0, 4)) → g, G, faceEFKJ, face2, face3, edge1, edgeBG, edgeCH, edgeDI, edgeEJ, edgeFK, edge2, H, edgeGH, edgeHI, edgeIJ, edgeJK, edge3, I, J, K, face1, faceBCHG, faceCDIH, faceDEJISegment(M, M + (0, 0, 2)) → hPoint(h) → NRotate(Polygon[E, D, I, J], (90° * t), Segment[D, E]) → poly2Rotate(Polygon[G, H, I, J, K, L], (90° * t), Segment[I, J]) → poly3Rotate(poly3, (90° * t), Segment[D, E]) → poly3'Rotate(Polygon[C, D, I, H], (60° * t), Segment[D, I]) → poly4Rotate(poly4, (90° * t), Segment[D, E]) → poly4'Mirror(poly4, OrthogonalPlane[Midpoint[D, E], Segment[D, E]]) → poly4'_1Rotate(poly4'_1, (90° * t), Segment[D, E]) → poly5Rotate(C, (60° * t), Segment[D, I]) → C'Mirror(Polygon[D, E, J, I], OrthogonalPlane[Midpoint[D, C'], Segment[D, C']]) → poly6Mirror(poly6, OrthogonalPlane[Midpoint[D, E], Segment[D, E]]) → poly6'Rotate(poly6, (90° * t), Segment[D, E]) → poly6'_1Rotate(poly6', (90° * t), Segment[D, E]) → poly6''Mirror(E, OrthogonalPlane[Midpoint[D, C'], Segment[D, C']]) → E'Mirror(poly4, OrthogonalPlane[Midpoint[E', C'], Segment[E', C']]) → poly4'_2Rotate(poly4'_2, (90° * t), Segment[D, E]) → poly7Rotate(poly3, (90° * t), Segment[D, E]) → poly3'_1Polygon(A, B, 6, xOyPlane) → poly8, i, R, j, k, l, m, n, O, P, QRotate(poly6', (90° * t), Segment[D, E]) → poly6''_1Rotate(poly4'_1, (90° * t), Segment[D, E]) → poly9Rotate(Polygon[E, D, I, J], (90° * t), Segment[D, E]) → poly10Rotate(poly4, (90° * t), Segment[D, E]) → poly4'_3Rotate(poly6, (90° * t), Segment[D, E]) → poly6'_2Rotate(poly4'_2, (90° * t), Segment[D, E]) → poly11
AI 绘图提示语参考
画一个六棱柱的展开图,包含六个相同的六边形和一个矩形,六边形排列成两排,中间用矩形连接,展示棱柱的侧面和底面。先画出底部的六边形,然后向上延伸出六个矩形侧面,最后在顶部画出另一个六边形,完成展开图。
以上提示语为根据原始绘图命令整理而来,仅供参考。