六棱柱的展开图
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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,可以构造出六棱柱的各个面和棱。适合初中及以上学生学习立体几何。
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
绘制一个正六棱柱的展开图。先画一个正六边形作为底面,并向上拉伸形成六棱柱。然后,将六棱柱的各个侧面和顶面分别绕其相邻棱边旋转展开,使它们平铺在底面所在的平面上。展开过程中,各面保持形状不变,并围绕公共棱边旋转,最终形成一个由六个矩形侧面和一个正六边形顶面组成的平面展开图,所有面共边连接。
以上提示语为根据原始绘图命令整理而来,仅供参考。