截角十二面体, n=60
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该范例展示了具有极端等价顶点分布的截角十二面体。涉及的核心数学概念包括立体几何和几何作图。通过使用GeoGebra命令如Sum, If, Length, Sequence等,可以构造出具有特定顶点分布的多面体。适合高中及以上学生或数学爱好者学习和探索。
GeoGebra 命令及参数
Text("" + p) → txt_pSum(Flatten[Sequence[Append[Sequence[Element[txt_p, i], i, m01(k), m02(k)], " "], k, 1, 5]]) → txtUm1If(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}], Append["Average\; distance: p=", {txtUm1}]}, "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
绘制一个截角十二面体,具有60个等价顶点,并展示其极端的顶点分布。图形需包含该多面体及其对偶多面体,标注顶点数、外接球半径、平均距离、各面边数及数量、体积等数据。构造时先确定顶点集,再通过行列式符号判断顶点共面性,进而生成面。同时显示时间相关的动态文本和统计表格,突出几何构造与数学分析。
以上提示语为根据原始绘图命令整理而来,仅供参考。