六棱柱的展开图 by powere
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①本范例演示了六棱柱的展开图,直观展示其表面由六个矩形和两个正六边形组成;②涉及的核心数学概念包括立体几何、多边形性质、相似变换;③作图要点提炼自GeoGebra命令:使用Polygon绘制多边形,Prism生成棱柱,Segment和Point创建顶点,Rotate和Mirror实现旋转与镜像变换;④适合高中阶段学习立体几何、几何作图的学生使用,也可用于教学演示。
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,包含六个矩形和两个六边形,展示其表面结构。首先绘制一个六边形,然后向上延伸形成柱体,接着将六边形和矩形展开,通过旋转和镜像操作得到完整的展开图,最后将所有部分组合在一起,呈现六棱柱的展开形态。
以上提示语为根据原始绘图命令整理而来,仅供参考。