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RegularPolygon[n]

给出 n 个顶点均匀分布在单位圆上正多边形.

RegularPolygon[r,n]

给出半径为 r 的正多边形.

RegularPolygon[{r,θ},n]

从相对于 轴的角度 θ 开始.

RegularPolygon[{x,y},rspec,n]

将多边形的中心置于 {x,y}.

更多信息和选项
Details and Options Details and Options
范例  
基本范例  
范围  
Graphics  
规范  
样式  
坐标  
区域  
应用  
属性和关系  
巧妙范例  
参见
相关指南
相关链接
历史
按以下格式引用：

RegularPolygon

RegularPolygon[n]

给出 n 个顶点均匀分布在单位圆上正多边形.

RegularPolygon[r,n]

给出半径为 r 的正多边形.

RegularPolygon[{r,θ},n]

从相对于 轴的角度 θ 开始.

RegularPolygon[{x,y},rspec,n]

将多边形的中心置于 {x,y}.

更多信息和选项

范例

打开所有单元 关闭所有单元

基本范例  (3)

五边形：

Wolfram Language code: Graphics[RegularPolygon[5]]

不同样式的 RegularPolygon：

Wolfram Language code: ℛ = RegularPolygon[8]; {Graphics[{Pink, ℛ}], Graphics[{EdgeForm[Thick], Pink, ℛ}], Graphics[{EdgeForm[Dashed], Pink, ℛ}], Graphics[{EdgeForm[Directive[Thick, Dashed, Blue]], Pink, ℛ}]}

面积和几何中心：

Wolfram Language code: Area[RegularPolygon[6]]
Wolfram Language code: RegionCentroid[RegularPolygon[6]]

范围  (17)

Graphics  (7)

规范  (4)

生成等边三角形、正方形、五边形、六边形等正多边形：

Wolfram Language code: Table[Graphics[RegularPolygon[n]], {n, 3, 10}]

生成不同半径的五边形：：

Wolfram Language code: rp = Table[RegularPolygon[r, 5], {r, 1, 4}];
Wolfram Language code: Graphics[{Opacity[0.2], rp}]

生成起始角度不同的三角形：

Wolfram Language code: rp = Table[RegularPolygon[{1, t Pi / 6}, 3], {t, 4}];
Wolfram Language code: Graphics[{Opacity[0.2], rp}]

将六个六边形均匀放置在单位圆上：

Wolfram Language code: cp = CirclePoints[2, 6];
Wolfram Language code: rp = Table[RegularPolygon[p, {1, 0}, 6], {p, cp}];
Wolfram Language code: Graphics[rp]

样式  (2)

用颜色指令指定正多边形面的颜色：

Wolfram Language code: Table[Graphics[{c, RegularPolygon[7]}], {c, {Red, Green, Blue, Yellow}}]

可以用 FaceForm 和 EdgeForm 指定图形内部和边界的样式：

Wolfram Language code: Graphics[{FaceForm[Pink], EdgeForm[Directive[Dashed, Thick, Blue]], RegularPolygon[7]}]

坐标  (1)

使用 Dynamic 坐标：

Wolfram Language code: Slider2D[Dynamic@a, {0, 3}] Graphics[RegularPolygon[Dynamic[a], 5, 5], Frame -> True, PlotRange -> 5]

可变半径：

Wolfram Language code: Slider[Dynamic@b, {1, 3}] Graphics[RegularPolygon[{0, 0}, Dynamic[b], 5], Frame -> True, PlotRange -> 5]

区域  (10)

嵌入维度：

Wolfram Language code: RegionEmbeddingDimension[RegularPolygon[n]]

几何维度：

Wolfram Language code: RegionDimension[RegularPolygon[n]]

判断某点是否为该区域的成员：

Wolfram Language code: {RegionMember[RegularPolygon[7], {0, 0}], RegionMember[RegularPolygon[7], {0, 2}]}

获取成为该区域成员的条件：

Wolfram Language code: RegionMember[RegularPolygon[{0, 0}, {1, 0}, 4], {x, y}]

面积：

Wolfram Language code: ℛ = RegularPolygon[6];
Wolfram Language code: {Area[ℛ], RegionMeasure[ℛ]}

几何中心：

Wolfram Language code: c = RegionCentroid[ℛ]
Wolfram Language code: Graphics[{{Pink, ℛ}, {Black, Point[c]}}]

到一个点的距离：

Wolfram Language code: ℛ = RegularPolygon[6];
Wolfram Language code: {RegionDistance[ℛ, {1, 2}], RegionDistance[ℛ, {0, 0}]}

到单位圆盘上最近的点的距离：

Wolfram Language code: {Plot3D[Evaluate@RegionDistance[ℛ, {x, y}], {x, -2, 2}, {y, -2, 2}, MeshFunctions -> {#3&}, Mesh -> 5, Exclusions -> Norm[{x, y}] == 1], ContourPlot[Evaluate@RegionDistance[ℛ, {x, y}], {x, -3, 3}, {y, -3, 3}, Contours -> {{0.5, Red}, {1, Green}, {1.5, Blue}}]}

到一个点的有向距离：

Wolfram Language code: ℛ = RegularPolygon[6];
Wolfram Language code: {SignedRegionDistance[ℛ, {1, 2}], SignedRegionDistance[ℛ, {0, 0}]}

到单位圆盘的有向距离：

Wolfram Language code: Plot3D[SignedRegionDistance[ℛ, {x, y}], {x, -2, 2}, {y, -2, 2}, MeshFunctions -> {#3&}, Mesh -> {{0}}, MeshShading -> {Red, Green}, Exclusions -> Norm[{x, y}] == 1]

区域中最近的点：

Wolfram Language code: ℛ = RegularPolygon[6];
Wolfram Language code: RegionNearest[ℛ, {5, 6}]

最近的点：

Wolfram Language code: pts = Table[2{Cos[k ], Sin[k]}, {k, 0., 15}]; nst = RegionNearest[ℛ, #]& /@ pts;
Wolfram Language code: Legended[Graphics[{{Gray, ℛ}, {Thin, Gray, Line[Transpose[{pts, nst}]]}, {Red, Point[pts]}, {Blue, Point[nst]}}], PointLegend[{Red, Blue}, {"start", "nearest"}]]

正多边形是有界的：

Wolfram Language code: ℛ = RegularPolygon[6];
Wolfram Language code: BoundedRegionQ[ℛ]

算出它的范围：

Wolfram Language code: rr = RegionBounds[ℛ]
Wolfram Language code: Graphics[{StandardGreen, ℛ, {EdgeForm[{Dashed, Red}], Opacity[0.1, Yellow], Cuboid@@Transpose[rr]}}]

在六边形上积分：

Wolfram Language code: ℛ = RegularPolygon[{Subscript[x, 0], Subscript[y, 0]}, {r, 0}, 6];
Wolfram Language code: Integrate[x y, {x, y}∈ℛ]//Simplify

在六边形上最优化：

Wolfram Language code: ℛ = RegularPolygon[6];
Wolfram Language code: {MinValue[{x y - x, {x, y}∈ℛ}, {x, y}], ArgMin[{x y - x, {x, y}∈ℛ}, {x, y}]}

在六边形上解方程：

Wolfram Language code: ℛ = RegularPolygon[{1, 2}, {3, 0}, 6];
Wolfram Language code: Solve[x^2 + y^2 == 7 && x y == 1 && {x, y}∈ℛ, {x, y}]
Wolfram Language code: Show[{Graphics[{{StandardGreen, ℛ}, {Blue, Circle[{0, 0}, Sqrt[7]]}}], Plot[1 / x, {x, -3, 5}, PlotRange -> {{-3, 5}, {-3, 6}}], Graphics[{PointSize[Large], Red, Point[{x, y}] /. %}]}, Axes -> True]

应用  (4)

通过对共同原点的旋转三角形取 RegionUnion，生成一个星形区域：

Wolfram Language code: ℛ = RegionUnion@@Table[RegularPolygon[{1, t Pi / 6}, 3], {t, 4}];
Wolfram Language code: Region[ℛ]

用 RegionProduct 生成一个三维挤压件：

Wolfram Language code: ℛ = RegionProduct[RegularPolygon[5], Line[{{0}, {1}}]];
Wolfram Language code: Region[ℛ]

在六边形上绘制函数：

Wolfram Language code: Plot3D[Sin[x + Cos[y]], {x, y}∈RegularPolygon[6]]

有些晶格的晶胞为正多边形. 如果晶格基元为：

Wolfram Language code: b = {{-Sqrt[3], -1}, {-Sqrt[3], 1}};

生成晶格点和片：

Wolfram Language code: pts = Tuples[Range[0, 4], 2].b;
Wolfram Language code: tiles = Table[RegularPolygon[p, {1, 0}, 6], {p, pts}];

可视化晶格点和镶嵌：

Wolfram Language code: Graphics[{Gray, tiles, Red, Point[pts]}]

属性和关系  (3)

RegularPolygon 是 个顶点在单位圆上均匀分布的 Polygon：

Wolfram Language code: n = 7;
Wolfram Language code: p = Polygon[CirclePoints[n]];
Wolfram Language code: rp = RegularPolygon[n];
Wolfram Language code: Graphics /@ {p, rp}

用 CirclePoints 来生成在单位圆上均匀分布的点：

Wolfram Language code: n = 7; {rp, cp} = {RegularPolygon[n], CirclePoints[n]};
Wolfram Language code: Graphics[{rp, PointSize[Large], Red, Point[cp]}]

当 时，单位圆上的正多边形的面积为单位 Disk 的面积：

Wolfram Language code: Limit[Area[RegularPolygon[n]], n -> Infinity]
Wolfram Language code: Area[Disk[]]

巧妙范例  (2)

一组随意排列的正多边形：

Wolfram Language code: Graphics[{EdgeForm[Black], Table[{Opacity[0.2], Hue[RandomReal[]], RegularPolygon[RandomReal[9, 2], {RandomReal[], 0}, RandomInteger[{3, 7}]]}, {200}]}]

将半径和顶点数不断增加正多边形叠放在一起：

Wolfram Language code: rp = Table[RegularPolygon[r, r + 2], {r, 9}];
Wolfram Language code: Graphics[{Opacity[0.15], rp}]
Wolfram Research (2015)，RegularPolygon，Wolfram 语言函数，https://reference.wolfram.com/language/ref/RegularPolygon.html （更新于 2019 年）.

文本

Wolfram Research (2015)，RegularPolygon，Wolfram 语言函数，https://reference.wolfram.com/language/ref/RegularPolygon.html （更新于 2019 年）.

CMS

Wolfram 语言. 2015. "RegularPolygon." Wolfram 语言与系统参考资料中心. Wolfram Research. 最新版本 2019. https://reference.wolfram.com/language/ref/RegularPolygon.html.

APA

Wolfram 语言. (2015). RegularPolygon. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/RegularPolygon.html 年

BibTeX

@misc{reference.wolfram_2026_regularpolygon, author="Wolfram Research", title="{RegularPolygon}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/RegularPolygon.html}", note=[Accessed: 02-September-2026]}

BibLaTeX

@online{reference.wolfram_2026_regularpolygon, organization={Wolfram Research}, title={RegularPolygon}, year={2019}, url={https://reference.wolfram.com/language/ref/RegularPolygon.html}, note=[Accessed: 02-September-2026]}