八边形反棱柱
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该范例展示了八边形反棱柱的几何构造,涉及多面体中顶点分布的极端情况。使用了If, Length, Sequence, Sum等GeoGebra命令进行构造。适合高中及以上学生学习立体几何和最值优化。
GeoGebra 命令及参数
If(bu0, A00, A00d) → A00_0Length(A00_0) → nLength(l2) → läl2Sequence(sgn(Determinant[{Element[A00_0, i1] - Element[A00_0, j], Element[A00_0, i2] - Element[A00_0, j], Element[A00_0, i3] - Element[A00_0, j]}]), j, 1, n) → l01Length(A00d) → zzzSum(Zip[(T * F), T, SysTimeAkt1, F, {1, 1000, 60000, 3600000, 86400000}]) → TimeAbs1Sum(Zip[(T * F), T, SysTimeAkt2, F, {1, 1000, 60000, 3600000, 86400000}]) → TimeAbs2Div(TimeRelab, 3600) → HDiv(TimeRelab - (H * 3600), 60) → MElement(ZwZeit, step) → text10TableText({Append["a duration", Last[ZwZeit, Min[10, Length[ZwZeit]]]]}, "v") → text2cLength(A00) → lm1If(Length[Unique[l01 \ {0}]] ≟ 1, 7, -7) → a7Sum(Zip[(T * F), T, SysTimeAkt0, F, {1, 1000, 60000, 3600000, 86400000}]) → TimeAbs0Div(TimeRelab0, 3600) → H0Div(TimeRelab0 - (H0 * 3600), 60) → M0Text("" + (TimeRelab0 - (H0 * 3600) - (M0 * 60))) → S0aText("" + (TimeRelab - (H * 3600) - (M * 60))) → SIndexOf(".", S) → indexIndexOf(".", S0a) → indexaFirst(S, index + 1) → txtSFirst(S0a, indexa + 1) → txtS0aIf(bu0, " ", "d") → txtbuoMax(Length[A00], Length[A00d]) → maxläElement(A00, 24) → m11TableText({{"\underline{Polyhedron}"}, Append["Vertices: n=", {Length[A00]}], Append["r=", {r}], Append["\bar{r}=", {r_m}], Append["k-gon : k=", mm5a], Append["their\; numbers: n_k=", mm7a], Append["Volume: V=", {Vol_r}]}, "hr ") → text7TableText({{"\underline{dual\;Polyhedron}"}, Append["Vertices: n=", {Length[A00d]}], Append["r=", {r_d}], Append[" \bar{r_d}= ", {r_md}], Append["k-gon : k=", mm5ad], Append["their\; numbers: n_k=", mm7ad], Append["Volume: V=", {Vold_r}]}, "hr ") → text20
AI 绘图提示语参考
绘制一个正八边形反棱柱及其对偶多面体。先构造一个八边形反棱柱,上下底面为平行的正八边形,上下底面相对旋转45度,侧面由16个等腰三角形连接。展示其顶点分布,并同时显示其对偶多面体,对偶多面体的顶点对应原多面体的面。标注顶点数、棱长、体积等数据,并用表格列出多面体与对偶多面体的顶点数、面数、体积等属性。整体呈现三维立体几何结构,突出顶点分布的极值特性。
以上提示语为根据原始绘图命令整理而来,仅供参考。