五倍角五角星十二面体及其对偶图的边与面着色
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本范例展示了五倍角五角星十二面体及其对偶图的边与面着色。涉及的核心数学概念包括多面体、对偶图、边与面的着色。使用了Sequence、Sphere、Textfield等GeoGebra命令进行构造。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
Sequence(((zoom * Element[Element[A00d, i], 1]), (zoom * Element[Element[A00d, i], 2]), (zoom * Element[Element[A00d, i], 3])), i, 1, Length[A00d]) → A0dSequence(((zoom * Element[Element[A00, i], 1]), (zoom * Element[Element[A00, i], 2]), (zoom * Element[Element[A00, i], 3])), i, 1, Length[A00]) → A0Sphere(O, r_o) → sp02dTextfield(R1sphere) → InputBox5Sphere(O, R1sphere) → sp01Textfield(r_o) → InputBox6Textfield(jarc) → InputBox8Textfield(jarc_d) → InputBox9Textfield(f_{Poly}) → InputBox11Textfield(k) → InputBox15Textfield(k_d) → InputBox14TableText({Append["i", 1…Length[mm5a]], Append["\fgcolor{orange}{n}", mm5a], Append["\fgcolor{orange}{N}", mm7a], Append["\fgcolor{#007FFF}{n/dual}", mm5ad], Append["\fgcolor{#007FFF}{N}", mm7ad]}, "hr") → text24Textfield(iseg) → InputBox17Textfield(f_{Poly}d) → InputBox18Textfield(isegd) → InputBox19UnicodeToLetter(34) → u34TableText({Append["i", 1…Max[Length[Segn], Length[Segnd]]], Append["\fgcolor{orange}{s_i}", Segn / Segments_o1], Append["\fgcolor{orange}{N}", lLength], Append["\fgcolor{#007FFF}{s_id}", Segnd / Segments_o1d], Append["\fgcolor{#007FFF}{N}", lLengthd]}, "hr") → text23Textfield(n_3) → InputBox20If(n_3 ≟ 0, "", Text["" + n_3]) → txt_3Textfield(nd_3) → InputBox21If(nd_3 ≟ 0, "", Text["" + nd_3]) → txtd_3Circle(A_{farbe}, rfabe) → farbekreisPointIn(farbekreis) → AAngle(A) → αSegment(C, D) → hSort(Sequence[Segment[Element[A0, Element[Element[nom, i], 1]], Element[A0, Element[Element[nom, i], 2]]], i, 1, Length[nom]]) → SegmentsFirst(Segments, i_s) → Segments_oKeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[Segn, 1], Segments) → la1KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[Segn, 2], Segments) → la2KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[Segn, 3], Segments) → la3KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[Segn, 4], Segments) → la4Sequence(Polygon[Element[A0, Element[Element[mm1, f], 1]], Element[A0, Element[Element[mm1, f], 2]], Element[A0, Element[Element[mm1, f], 3]]], f, 1, Length[mm1]) → poly_{3}KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[poly_{3}S, 1], poly_{3}) → poly_{3}1KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[poly_{3}S, 2], poly_{3}) → poly_{3}2KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[poly_{3}S, 3], poly_{3}) → poly_{3}3Sort(Sequence[Segment[Element[A0d, Element[Element[nomd, i], 1]], Element[A0d, Element[Element[nomd, i], 2]]], i, 1, Length[nomd]]) → SegmentsdFirst(Segmentsd, id_s) → Segmentsd_oKeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[Segnd, 1], Segmentsd) → lad1KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[Segnd, 2], Segmentsd) → lad2KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[Segnd, 3], Segmentsd) → lad3KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[Segnd, 4], Segmentsd) → lad4KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[Segnd, 5], Segmentsd) → lad5KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[Segnd, 6], Segmentsd) → lad6KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[Segnd, 7], Segmentsd) → lad7KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[Segnd, 8], Segmentsd) → lad8Sequence(Polygon[Element[A0d, Element[Element[mm1d, f], 1]], Element[A0d, Element[Element[mm1d, f], 2]], Element[A0d, Element[Element[mm1d, f], 3]]], f, 1, Length[mm1d]) → polyd_{3}KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[poly_{3}Sd, 1], polyd_{3}) → polyd_{3}1KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[poly_{3}Sd, 2], polyd_{3}) → polyd_{3}2KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[poly_{3}Sd, 3], polyd_{3}) → polyd_{3}3KeepIf(round((x * 10^(k))) / 10^(k) ≟ Element[poly_{3}Sd, 4], polyd_{3}) → polyd_{3}4Sequence(Polygon[Sequence[A0d(mm6d(1, f, k)), k, 1, Length[mm6d(1, 1)]]], f, 1, Length[mm6d(1)]) → polyd_{5}
AI 绘图提示语参考
绘制一个双截五角星截断十二面体及其对偶多面体,并对其边和面进行着色。图形中包含着色标记和文本标签。构造顺序为先绘制立体图形,再进行着色和标注。
以上提示语为根据原始绘图命令整理而来,仅供参考。