PolyhedronData[poly,"property"]
给出名称为 poly 的多面体的指定属性值.
PolyhedronData[poly]
给出名称为 poly 的多面体的图像.
PolyhedronData["class"]
给出指定类的多面体列表.
PolyhedronData
PolyhedronData[poly,"property"]
给出名称为 poly 的多面体的指定属性值.
PolyhedronData[poly]
给出名称为 poly 的多面体的图像.
PolyhedronData["class"]
给出指定类的多面体列表.
更多信息
- 多面体可以通过标准名称来指定,例如 "Dodecahedron" 和 "TruncatedCube".
- 支持的多面体类型包括 "Platonic"、"Archimedean"、"ArchimedeanDual"、"KeplerPoinsot"、 "Johnson" 和 "Uniform".
- PolyhedronData 包括复合多面体.
- PolyhedronData[] 和 PolyhedronData[All] 给出所有可能的多面体列表.
- PolyhedronData[patt] 给出多面体标准名称匹配模式 patt 的列表.
- PolyhedronData[n] 给出 n 个面的多面体列表,面不一定是外侧的.
- PolyhedronData[;;n] 给出有 ≤n 个面的多面体列表.
- PolyhedronData[m;;n] 给出有 m 到 n 个面的标准多面体列表.
- PolyhedronData["class",n] 给出有 n 个面的特殊等级的多面体列表等.
- PolyhedronData["Classes"] 给出所有支持类的列表.
- PolyhedronData["Properties"] 给出多面体可能属性的列表.
- 所有多面体采用单位长度的最小边.
- 整体属性包括:
-
"Classes" 多面体所属类型 "NotationRules" 多面体的索引标注 - 结构属性包括:
-
"VertexCoordinates" 顶点坐标列表 "EdgeIndices" (作为顶点索引对)边列表 "FaceIndices" (作为顶点索引列表)面列表 - 几何原始属性包括:
-
"Polyhedra" 复合多面体组成部分 "Polyhedron" Polyhedron 表达式 "Polygons" 对应于面的多边形列表 "Lines" 对应于边的线列表 "Points" 对应于顶点的点列表 - 图形属性包括:
-
"Graphics3D" 多面体的面的三维图形表示 "GraphicsComplex" 复合图形表达式 "Image" 多面体图像 - 组合属性包括:
-
"EdgeCount" 边的总数 "FaceCount" 面的总数 "VertexCount" 顶点的总数 "NetCount" 可以画出的拓扑学上不同的网格的数目 - 和区域相关的属性包括:
-
"BoundaryMeshRegion" 用边界网格表示 "CoordinateBounds" 坐标范围 "ImplicitRegion" 用不等式和等式表示 "MeshRegion" 用网格表示 "Region" 几何区域 "RegionFunction" 多面体内部结果为 True 的纯函数 - 几何属性包括:
-
"Centroid" 标准嵌入图形的几何中心的坐标 "Circumcenter" 内切球中心 "Circumdiameter" 外接圆半径的两倍 "Circumradius" 外接圆半径,假设单位长度的最小边 "Circumsphere" 内切球的图元 "DehnInvariant" Dehn 不变量 "DihedralAngles" 二面角 "GeneralizedDiameter" 一对顶点的最大长度 "Incenter" 内切球中心 "InertiaTensor" 假定为单位质量的实多面体的惯性张量 "Inradius" 内径,假设单位长度的最小边 "Insphere" 内切球 "Midcenter" 摆动球体的中心 "Midradius" 半径,假设单位长度的最小边 "Midsphere" 摆动球的图元 "StableFaces" 稳定的面 "SurfaceArea" 表面区域总合,假设单位长度的最小边 "UnstableFaces" 不稳定的面 "VertexSubsetHulls" 外壳形成其它立体图形顶点的规则 "Volume" 围绕的体积,假设单位长度的最小边 - 平均长度属性包括:
-
"MeanCylindricalRadius" 多面体区域内
的平均值"MeanInteriorLineSegmentLength" 在多面体区域内随机选取端点的线段的平均长度 "MeanSphericalRadius" 多面体区域内
的平均值"MeanSquareCylindricalRadius" 多面体区域内
的平均值"MeanSquareSphericalRadius" 多面体区域内
的平均值 - 如果多面体属于指定的类别,PolyhedronData[name,"class"] 给出 True.
- 多面体类型包括:
-
"Amphichiral" 双向多面体 "Canonical" 含有棱切球的多面体 "Chiral" 手性多面体 "Compound" 二面或更多面体的组合 "Concave" 凹面体 "Convex" 凸面体 "Deltahedron" 由全等等边三角形组成的实体 "Equilateral" 所有边是单位长度 "Isohedron" 多面体表面上的对称性是可传递的 "Parallelohedron" 平行六面体 "Plesiohedron" plesiohedron 多面体 "Rupert" 满足 Rupert 性质 "SelfDual" 多面体是自身的对偶多面体 "Simple" 简单多面体 "SpaceFilling" 空间填充多面体 "Stellation" 星状多面体 "Stereohedron" stereohedron 立体多面体 "Toroidal" 环状多面体 "Unistable" 单稳态多面体 "Zonohedron" 全对称多面体 - 有限集族的多面体类型包括:
-
"Archimedean" 13 个阿基米得多面体中的一个 "ArchimedeanDual" 13 个阿基米得对称体中的一个 "Johnson" 92 个 Johnson 立体中的一个 "KeplerPoinsot" 4 个 Kepler-Poinsot 固体中的一个 "Platonic" 5 个柏拉图多面体中的一个 "PlatonicDual" 5 个帕拉图对偶中的一个 "Trapezohedron" 正则梯面体 "Uniform" 80 个均匀多面体中的一个 "UniformDual" 80 个均匀对偶中的一个 "Zalgaller" 28 个 Zalgaller 多面体中的一个 - 多面体下标为整数的类型有:
-
"Antiprism" 对角柱 "Dipyramid" 双棱锥体 "Prism" 棱柱 "Pyramid" 棱椎 - 和名称有关的属性包括:
-
"AlternateNames" 用字符串表示的替代英文名称 "AlternateStandardNames" 替代标准 Wolfram 语言名称 "Name" 用字符串表示的英文名称 "Names" 英文名称和替代名称 "Entity" 多面体实体 "StandardName" 标准 Wolfram 语言名称 - PolyhedronData[name,"property","outputtype"] 以 "outputtype" 指定的格式给出多面体的属性,取决于 "property",可能是 "Adjacent"、"Coordinates"、"Count"、"Entity"、"Graph"、"Graphics3D"、"GraphicsComplex"、"Group"、"Image"、"Length"、"Line"、"List"、"Name"、"Notation"、"Point"、"Polygon"、"Polyhedron"、"Rule"、"Tally" 或 "Undirected".
- 与多面体输出和显示相关的输出类型包括:
-
"CompoundInterior" 以图形、复合图形、多面体或比例形式给出的多面体复合体的内部(共同体积) "ConvexHull" 以图形、复合图形、多面体或比例形式给出的凸包 "DihedralAngles" 以角度列表形式给出的二面角或以相邻的面的索引为标记的一组规则 "Dual" 以实体标准名称、实体、图形、复合图形、多面体或比例形式给出的对偶多面体 "Edges" 以索引列表、个数、不同边长的列表、规则列表、线、图形、复合图形或图像形式给出的边 "Faces" 以索引列表、个数、相邻面索引列表、按边数计数的规则列表、多边形、图形、复合图形或图像形式给出的面 "Hull" 以图形、复合图形、多面体或比例形式给出的包(不一定是凸包) "Net" 以图形、复合图形、图像、顶点坐标列表、个数、面的索引列表或图的形式给出的多面体网络 "Skeleton" 以图、顶点坐标列表、图像、图的实体标准名称、图的实体、边的规则列表或无向边列表的形式给出的骨架图 "SymmetryGroup" 以群的标准名称或实体形式给出的对称群 "Vertices" 以索引、个数、点、图形、复合图形或图像形式给出的顶点 - PolyhedronData[name,"property","ann"] 或 PolyhedronData["property","ann"] 给出关于属性的多种注解. 典型注解包括:
-
"Description" 关于属性的简短的文字描述 "Information" 关于更多信息的超级链接 "LongDescription" 关于属性的较长的文字描述 "Value" 属性的值
范例
打开所有单元 关闭所有单元基本范例 (6)
PolyhedronData["Dodecahedron"]PolyhedronData["Dodecahedron", "Net"]PolyhedronData["Dodecahedron", "Net", "Graph"]Graphics3D[{Opacity[.5], Glow[Yellow], EdgeForm[Gray], PolyhedronData["SnubCube", "Polygons"]}, Lighting -> None]Graphics3D[{Opacity[.5], FaceForm[Yellow], PolyhedronData["SnubCube", "Polygons"]}, Lighting -> "Neutral"]PolyhedronData["Icosahedron", "EdgeCount"]PolyhedronData["Icosahedron", "Edges", "Count"]PolyhedronData["Tetrahedron", "VertexCoordinates"]PolyhedronData["Archimedean"]范围 (172)
实体 (4)
PolyhedronData[Entity["Polyhedron", "Cube"]]PolyhedronData[Entity["Polyhedron", "Cube"], "Name"]用 EntityValue 来查询单位立方体的表面积:
EntityValue[Entity["Polyhedron", "Cube"], "SurfaceArea"]EntityValue[Entity["Polyhedron", "Cube"], EntityProperty["Polyhedron", "SurfaceArea"]]与 PolyhedronData 命令比较:
PolyhedronData["Cube", "SurfaceArea"]直接用 PolyhedronData 查询一个类别的成员:
PolyhedronData["KeplerPoinsot"]用 EntityClass 和 EntityList 以一组多面体实体的形式返回成员:
EntityClass["Polyhedron", "KeplerPoinsot"]//EntityListEntityClass["Polyhedron", {"FaceCount" -> 6, "VertexCount" -> 8}]//EntityListEntityClass["Polyhedron", {"FaceCount" -> Between[{6, 8}], "VertexCount" -> 8}]//EntityList名称和类型 (6)
PolyhedronData[All]//ShallowPolyhedronData[]//ShallowPolyhedronData["Cube", "Name"]PolyhedronData["Cube", "AlternateNames"]PolyhedronData["Cube", "AlternateStandardNames"]PolyhedronData[{"Hypercube", 3}, "StandardName"]PolyhedronData["Classes"]PolyhedronData["Platonic"]PolyhedronData["Archimedean"]PolyhedronData["Cube", "Archimedean"]PolyhedronData["Cube", "Platonic"]属性和注解 (2)
属性值 (2)
PolyhedronData["TruncatedDodecahedron", "Volume"]PolyhedronData["Octahedron", "FaceCount"]PolyhedronData["Octahedron", "Centroid"]对于多面体不具备的属性,其值为 Missing["NotAvailable"]:
PolyhedronData["SzilassiPolyhedron", "SymmetryGroup"]对于不能应用于多面体的属性,其值为 Missing["NotApplicable"]:
PolyhedronData["SnubDisphenoid", "Dual"]详细属性 (88)
结构属性 (3)
PolyhedronData["Tetrahedron", "VertexCoordinates"]PolyhedronData["Octahedron", "EdgeIndices"]With[{poly = PolyhedronData["Octahedron", "Polyhedron"]}, Graphics3D[{MapIndexed[Text[#2[[1]], #, Background -> White]&, PolyhedronCoordinates[poly]], poly}]]PolyhedronData["Cube", "FaceIndices"]With[{poly = PolyhedronData["Cube", "Polyhedron"]}, Graphics3D[{MapIndexed[Text[#2[[1]], #, Background -> White]&, PolyhedronCoordinates[poly]], Opacity[.3], poly}, Boxed -> False]]几何基元属性 (4)
以 Polyhedron 对象给出正则八面体:
PolyhedronData["Octahedron", "Polyhedron"]Graphics3D[%]%%//RegionPolyhedronData["Cube", "Polygons"]Graphics3D[%]PolyhedronData["Octahedron", "Lines"]Graphics3D[{AbsoluteThickness[3], %}]PolyhedronData["Cube", "Points"]Graphics3D[{AbsolutePointSize[10], %}]图形属性 (4)
PolyhedronData["Dodecahedron", "Graphics3D"]Head[%]PolyhedronData["Icosahedron", "GraphicsComplex"]Graphics3D[%]PolyhedronData["Cube", "Image"]Head[%]PolyhedronData["Cube", "DualCompound"]组合属性 (4)
PolyhedronData["Icosahedron", "EdgeCount"]PolyhedronData["Cuboctahedron", "FaceCount"]给出二十面体的不同网格 (distinct net) 的个数:
PolyhedronData["Icosahedron", "NetCount"]PolyhedronData["Cuboctahedron", "VertexCount"]PolyhedronData["Cuboctahedron", "VertexCoordinates"]//Length与区域相关的属性 (7)
PolyhedronData["SmallTriambicIcosahedron", "BoundaryMeshRegion"]Head[%]bounds = PolyhedronData["Icosahedron", "CoordinateBounds"]Graphics3D[{PolyhedronData["Icosahedron", "GraphicsComplex"], Opacity[.5], Cuboid@@Transpose[bounds]}]RegionPlot3D[Evaluate[PolyhedronData["Icosahedron", "RegionFunction"][x, y, z]], Evaluate[Sequence@@Flatten /@ Transpose[{{x, y, z}, bounds}]]]PolyhedronData["Dodecahedron", "ImplicitRegion"]RegionPlot3D[%, PlotPoints -> 40]PolyhedronData["SmallTriambicIcosahedron", "MeshRegion"]Head[%]PolyhedronData["SmallTriambicIcosahedron", "Region"]Head[%]PolyhedronData["Tetrahedron", "RegionFunction"]通过把区域转换成 ImplicitRegion 可视化该区域:
RegionPlot3D[ImplicitRegion[%[x, y, z], {x, y, z}], PlotPoints -> 25]PolyhedronData["Cuboctahedron", "RegionFunction"]PolyhedronData["Cuboctahedron", "RegionFunction"][x, y, z]//TraditionalFormWith[{r = 1}, RegionPlot3D[PolyhedronData["Cuboctahedron", "RegionFunction"][x, y, z], {x, -r, r}, {y, -r, r}, {z, -r, r}, ...]]几何属性 (20)
PolyhedronData["DuererSolid", "Centroid"]PolyhedronData["Tetrahedron", "Circumcenter"]PolyhedronData["Tetrahedron", "Circumdiameter"]PolyhedronData["Tetrahedron", "Circumradius"]PolyhedronData["Tetrahedron", "Circumsphere"]Graphics3D[{PolyhedronData["Tetrahedron", "GraphicsComplex"], Opacity[.4], PolyhedronData["Tetrahedron", "Circumsphere"]}, ...]PolyhedronData["Cube", "Circumsphere"]Graphics3D[{PolyhedronData["Cube", "GraphicsComplex"], Opacity[.4], PolyhedronData["Cube", "Circumsphere"]}, ...]PolyhedronData["Cube", "DehnInvariant"]Union[PolyhedronData[#, "DehnInvariant"]& /@ PolyhedronData["SpaceFilling"]]PolyhedronData["Cube", "DihedralAngleRules"]Union[Last /@ %]PolyhedronData["Cube", "GeneralizedDiameter"]Norm /@ Subtract@@@Subsets[PolyhedronData["Cube", "VertexCoordinates"], {2}]Max[%]PolyhedronData["Cube", "Incenter"]PolyhedronData["MathematicaPolyhedron", "InertiaTensor"]//Style[#, Small]&//TraditionalFormPolyhedronData["Cube", "Inradius"]PolyhedronData["Cube", "Insphere"]Graphics3D[{PolyhedronData["Cube", "Insphere"], Opacity[.4], PolyhedronData["Cube", "GraphicsComplex"]}, ...]PolyhedronData["Cube", "Midcenter"]PolyhedronData["Cube", "Midradius"]PolyhedronData["Cube", "Midsphere"]Graphics3D[{PolyhedronData["Cube", "Midsphere"], Opacity[.4], PolyhedronData["Cube", "DualCompound", "GraphicsComplex"]}, ...]Graphics3D[{
{Green, PolyhedronData["ConwayGuyPolyhedron", "StableFaces"]},
Opacity[.2], PolyhedronData["ConwayGuyPolyhedron", "UnstableFaces"]}, Boxed -> False, BoxRatios -> 1]PolyhedronData["Cube", "SurfaceArea"]Graphics3D[{
Opacity[.2],
{Green, PolyhedronData["ConwayGuyPolyhedron", "UnstableFaces"]},
Red, PolyhedronData["ConwayGuyPolyhedron", "StableFaces"]}, Boxed -> False, BoxRatios -> 1]PolyhedronData["Dodecahedron", "VertexSubsetHulls"]Function[hulls, Graphics3D[Table[{Hue[(i - 1) / Length[hulls]], ConvexHullRegion[PolyhedronData["Dodecahedron", "VertexCoordinates"][[hulls[[i]]]]]}, {i, Length[hulls]}]]] /@ PolyhedronData["Dodecahedron", "VertexSubsetHulls"][[All, 2]]PolyhedronData["Cube", "Volume"]平均长度属性 (5)
PolyhedronData["Cube", "MeanCylindricalRadius"]PolyhedronData["Cube", "MeanSphericalRadius"]PolyhedronData["Cube", "MeanInteriorLineSegmentLength"]PolyhedronData["Cube", "MeanSquareCylindricalRadius"]PolyhedronData["Cube", "MeanSquareSphericalRadius"]全局属性 (2)
多面体类型 (18)
(amphichiral = PolyhedronData["Amphichiral"])//Short[#, 2]&Union[PolyhedronData[#, "Amphichiral"]& /@ amphichiral]PolyhedronData["Canonical"]//Short[#, 5]&PolyhedronData["Chiral"]Union[PolyhedronData[#, "Chiral"]& /@ %]PolyhedronData["Compound"]//Short[#, 10]&GraphicsGrid[Partition[Tooltip[Show[PolyhedronData[#, "Graphics3D"], ...], #]& /@ PolyhedronData["Compound"], UpTo[7]], ImageSize -> Large]PolyhedronData["Concave"]//Short[#, 5]&PolyhedronData["Convex"]//Short[#, 5]&PolyhedronData["Convex"]//Short[#, 5]&GraphicsGrid[Partition[Tooltip[Show[#3, Boxed -> False, Method -> {"ShrinkWrap" -> True}], Column[{#1, #2}]]&@@@Sort[PolyhedronData["Deltahedron", {"FaceCount", "StandardName", "Graphics3D"}]], UpTo[4]]]PolyhedronData["Equilateral"]//Short[#, 5]&PolyhedronData["Isohedron"]GraphicsGrid[Partition[Tooltip[Show[#3, Boxed -> False, Method -> {"ShrinkWrap" -> True}], Column[{#1, #2}]]&@@@Sort[PolyhedronData["Isohedron", {"FaceCount", "StandardName", "Graphics3D"}]], UpTo[10]]]PolyhedronData["Parallelohedron"]PolyhedronData["Plesiohedron"]PolyhedronData["Rupert"]//Short[#, 10]&PolyhedronData["SelfDual"]PolyhedronData["SpaceFilling"]GraphicsGrid[Partition[Tooltip[Show[#2, Boxed -> False, Method -> {"ShrinkWrap" -> True}], #1]&@@@Sort[PolyhedronData["SpaceFilling", {"StandardName", "Graphics3D"}]], UpTo[6]]]PolyhedronData["Stereohedron"]PolyhedronData["Stellation"]GraphicsGrid[Partition[Tooltip[Show[#2, Boxed -> False, Method -> {"ShrinkWrap" -> True}], #1]&@@@Sort[PolyhedronData["Stellation", {"StandardName", "Graphics3D"}]], UpTo[5]]]PolyhedronData["Unistable"]PolyhedronData["Zonohedron"]GraphicsGrid[Partition[Tooltip[Show[#2, Boxed -> False, Method -> {"ShrinkWrap" -> True}], #1]&@@@Sort[PolyhedronData["Zonohedron", {"StandardName", "Graphics3D"}]], UpTo[5]]]有限族 (9)
PolyhedronData["Archimedean"]GraphicsGrid[Partition[Tooltip[Show[PolyhedronData[#, "Graphics3D"], Boxed -> False, Method -> {"ShrinkWrap" -> True}], #]& /@ PolyhedronData["Archimedean"], UpTo[5]]]PolyhedronData["ArchimedeanDual"]GraphicsGrid[Partition[Tooltip[Show[PolyhedronData[#, "Graphics3D"], Boxed -> False, Method -> {"ShrinkWrap" -> True}], #]& /@ PolyhedronData["ArchimedeanDual"], UpTo[5]]]PolyhedronData["Johnson"]//Short[#, 5]&GraphicsGrid[Partition[Tooltip[Show[PolyhedronData[#, "Graphics3D"], Boxed -> False, Method -> {"ShrinkWrap" -> True}], #]& /@ PolyhedronData["Johnson"], UpTo[12]]]PolyhedronData["KeplerPoinsot"]GraphicsRow[Tooltip[Show[PolyhedronData[#, "Graphics3D"], Boxed -> False, Method -> {"ShrinkWrap" -> True}], #]& /@ PolyhedronData["KeplerPoinsot"]]PolyhedronData["Platonic"]GraphicsRow[Tooltip[Show[PolyhedronData[#, "Graphics3D"], Boxed -> False, Method -> {"ShrinkWrap" -> True}], #]& /@ PolyhedronData["Platonic"]]PolyhedronData["PlatonicDual"]SameQ@@Sort /@ {PolyhedronData["PlatonicDual"], PolyhedronData["Platonic"]}PolyhedronData["Trapezohedron"]GraphicsRow[Tooltip[Show[#2, Boxed -> False, Method -> {"ShrinkWrap" -> True}], #1]&@@@Sort[PolyhedronData["Trapezohedron", {"StandardName", "Graphics3D"}]]]PolyhedronData["Uniform"]GraphicsGrid[Partition[Tooltip[Show[PolyhedronData[#, "Graphics3D"], Boxed -> False, Method -> {"ShrinkWrap" -> True}], #]& /@ PolyhedronData["Uniform"], UpTo[10]]]PolyhedronData["UniformDual"]GraphicsGrid[Partition[Tooltip[Show[PolyhedronData[#, "Graphics3D"], Boxed -> False, Method -> {"ShrinkWrap" -> True}], #]& /@ PolyhedronData["UniformDual"], UpTo[5]]]下标为整数的多面体类型 (5)
PolyhedronData["Antiprism"]GraphicsGrid[Partition[Tooltip[Show[PolyhedronData[#, "Graphics3D"], Boxed -> False, Method -> {"ShrinkWrap" -> True}], #]& /@ SortBy[PolyhedronData["Antiprism"], PolyhedronData[#, "FaceCount"]&], UpTo[4]]]PolyhedronData["Dipyramid"]GraphicsRow[Tooltip[Show[PolyhedronData[#, "Graphics3D"], Boxed -> False, Method -> {"ShrinkWrap" -> True}], #]& /@ SortBy[PolyhedronData["Dipyramid"], PolyhedronData[#, "FaceCount"]&]]PolyhedronData["Prism"]GraphicsGrid[Partition[Tooltip[Show[PolyhedronData[#, "Graphics3D"], Boxed -> False, Method -> {"ShrinkWrap" -> True}], #]& /@ SortBy[PolyhedronData["Prism"], PolyhedronData[#, "FaceCount"]&], UpTo[4]]]PolyhedronData["Pyramid"]GraphicsRow[Tooltip[Show[PolyhedronData[#, "Graphics3D"], Boxed -> False, Method -> {"ShrinkWrap" -> True}], #]& /@ SortBy[PolyhedronData["Pyramid"], PolyhedronData[#, "FaceCount"]&]]PolyhedronData["Zalgaller"]GraphicsGrid[Partition[Tooltip[Show[PolyhedronData[#, "Graphics3D"], Boxed -> False, Method -> {"ShrinkWrap" -> True}], #]& /@ SortBy[PolyhedronData["Zalgaller"], PolyhedronData[#, "FaceCount"]&], UpTo[8]], ImageSize -> Medium]与名称相关的属性 (7)
PolyhedronData["Cube", "AlternateNames"]PolyhedronData["Octahedron", "AlternateStandardNames"]PolyhedronData["Cube", "Entity"]PolyhedronData["Cube", "Name"]PolyhedronData["Cube", "Names"]PolyhedronData["Cube", "NotationRules"]PolyhedronData[{"Hypercube", 3}, "StandardName"]PolyhedronData["Cube", "AlternateStandardNames"]Union[PolyhedronData[#, "StandardName"]& /@ %]注释属性 (70)
"CompoundInterior" (1)
PolyhedronData[{"CubeFiveCompound", 1}, "CompoundInterior"]PolyhedronData[{"CubeFiveCompound", 1}, "CompoundInterior", "Polyhedron"]PolyhedronData[{"CubeFiveCompound", 1}, "CompoundInterior", "Name"]PolyhedronData[{"CubeFiveCompound", 1}, "CompoundInterior", "Scale"]With[{pname = {"CubeFiveCompound", 1}},
Graphics3D[{PolyhedronData[pname, "Lines"], Opacity[.8], PolyhedronData[pname, "CompoundInterior", "Polyhedron"]}]]"ConvexHull" (1)
PolyhedronData["GreatIcosahedron", "ConvexHull"]PolyhedronData["GreatIcosahedron", "ConvexHull", "Polyhedron"]PolyhedronData["GreatIcosahedron", "ConvexHull", "Name"]PolyhedronData["GreatIcosahedron", "ConvexHull", "Scale"]With[{pname = "GreatIcosahedron"},
Graphics3D[{
{EdgeForm[None], PolyhedronData[pname, "Polyhedron"]},
{Opacity[.7], EdgeForm[Thick], PolyhedronData[pname, "ConvexHull", "Polyhedron"]}}]]"DihedralAngles" (2)
PolyhedronData["Cuboctahedron", "DihedralAngles"]PolyhedronData["Cuboctahedron", "DihedralAngles", "Rule"]Rule@@@Transpose[{PolyhedronData["Cuboctahedron", "Faces", "Adjacent"], PolyhedronData["Cuboctahedron", "DihedralAngles"]}]"Dual" (7)
PolyhedronData["Dodecahedron", "Dual"]PolyhedronData["Dodecahedron", "Dual", "Name"]PolyhedronData["Dodecahedron", "Dual", "Entity"]PolyhedronData["Cube", "Dual", "Graphics3D"]PolyhedronData["Cube", "Dual", "GraphicsComplex"]Graphics3D[%]PolyhedronData["Cube", "Dual", "Image"]返回对偶多面体相对于单位实体 (unit primary solid) 的比例:
PolyhedronData["Dodecahedron", "Dual", "Scale"]"DualCompound" (6)
PolyhedronData["Dodecahedron", "DualCompound"]PolyhedronData["Dodecahedron", "DualCompound", "Name"]PolyhedronData["Dodecahedron", "DualCompound", "Entity"]PolyhedronData["Cube", "DualCompound", "Graphics3D"]PolyhedronData["Cube", "DualCompound", "GraphicsComplex"]Graphics3D[%]PolyhedronData["Cube", "DualCompound", "Image"]"Edges" (11)
PolyhedronData[{"Prism", 5}, "Edges"]Graph3D[UndirectedEdge@@@%]Graphics3D[{Blue, Thick, GraphicsComplex[PolyhedronData[{"Prism", 5}, "VertexCoordinates"], Line[PolyhedronData[{"Prism", 5}, "Edges"]]]}, Boxed -> False]PolyhedronData[{"Prism", 5}, "Edges", "Count"]% == PolyhedronData[{"Prism", 5}, "EdgeCount"]Show[PolyhedronData[{"Prism", 5}, "Edges", "Graphics3D"], Boxed -> False]Head[%]PolyhedronData[{"Prism", 5}, "Edges", "GraphicsComplex"]Graphics3D[%, Boxed -> False]PolyhedronData[{"Prism", 5}, "Edges", "Image"]Head[%]PolyhedronData["DeltoidalHexecontahedron", "Edges", "Length"]PolyhedronData["DeltoidalHexecontahedron", "Edges", "Length"]Union[FullSimplify[Flatten[PolyhedronData["DeltoidalHexecontahedron", "Edges", "Line"]] /. Line[l_] :> EuclideanDistance@@l]]PolyhedronData["Cube", "Edges", "Line"]PolyhedronData[{"Prism", 5}, "Edges", "List"]% === PolyhedronData[{"Prism", 5}, "Edges"]PolyhedronData[{"Prism", 5}, "Edges", "Rule"]用 GraphPlot 绘图:
GraphPlot[%]PolyhedronData[{"Prism", 5}, "Edges", "Undirected"]转换成 Graph 表达式:
Graph[%]"Faces" (11)
PolyhedronData[{"Pyramid", 4}, "Faces", "List"]Graphics3D[GraphicsComplex[PolyhedronData[{"Pyramid", 4}, "VertexCoordinates"], Polygon[PolyhedronData[{"Pyramid", 4}, "Faces", "List"]]]]adj = PolyhedronData[{"Pyramid", 4}, "Faces", "Adjacent"]polys = PolyhedronData[{"Pyramid", 4}, "Faces", "Polygon"];Graphics3D[polys[[#]]]& /@ adjPolyhedronData[{"Prism", 5}, "Faces", "Count"]% == PolyhedronData[{"Prism", 5}, "FaceCount"]Show[PolyhedronData[{"Prism", 5}, "Faces", "Graphics3D"], Boxed -> False]Head[%]PolyhedronData[{"Prism", 5}, "Faces", "GraphicsComplex"]Graphics3D[%, Boxed -> False]PolyhedronData[{"Prism", 5}, "Faces", "Image"]Head[%]PolyhedronData[{"Prism", 5}, "Faces", "List"]% === PolyhedronData[{"Prism", 5}, "FaceIndices"]PolyhedronData["Cube", "Faces", "Polygon"]PolyhedronData["Cube", "Polygons"] === %PolyhedronData[{"Johnson", 80}, "Faces", "Tally"]Rule@@@Tally[Sort[Length /@ PolyhedronData[{"Johnson", 80}, "FaceIndices"]]]PolyhedronData[{"Johnson", 80}, "Graphics3D", "Colored"]inds = PolyhedronData["TetrahedronFiveCompound", "Polyhedron", "List"]poly = PolyhedronData["TetrahedronFiveCompound", "Faces", "Polygon"];Graphics3D[poly[[#]]]& /@ indsShow[%]Graphics3D[{#1, poly[[#2]]}&@@@Transpose[{{Red, Yellow, Orange, Green, Blue}, inds}]]"Net" (11)
PolyhedronData["Icosahedron", "Net"]Head[%]用显式的 "Graphics" 注释来做同样的事情:
PolyhedronData["Icosahedron", "Net", "Graphics"]PolyhedronData["JabulaniPolyhedron", "Net", "Colored"]PolyhedronData["Icosahedron", "Net", "Coordinates"]PolyhedronData["Cube", "Net", "Count"]% == PolyhedronData["Cube", "NetCount"]用 Graph 对象的形式给出十二面体的网格:
PolyhedronData["Dodecahedron", "Net", "Graph"]PolyhedronData["Cuboctahedron", "Net", "Graphics"]用 GraphicsComplex 给出八面体的网格的各个面:
PolyhedronData["Octahedron", "Net", "GraphicsComplex"]Graphics[{EdgeForm[Black], LightYellow, %}]以 GraphicsComplex 给出二十面体网的边:
PolyhedronData["Icosahedron", "Net", "GraphicsComplex"]Graphics[{EdgeForm[Black], LightYellow, %}]PolyhedronData["Icosahedron", "Net", "List"]Graphics[{EdgeForm[Black], LightYellow, GraphicsComplex[PolyhedronData["Icosahedron", "Net", "Coordinates"], Polygon[%]]}]PolyhedronData["Dodecahedron", "Net", "Image"]Head[%]PolyhedronData["Cube", "Net", "Polygon"]Graphics[{EdgeForm[Black], LightYellow, %}]"Polyhedron" (1)
用 Polyhedron 显示星形八面体:
PolyhedronData["StellaOctangula", "Polyhedron"]Region[%]"Skeleton" (8)
PolyhedronData["Dodecahedron", "Skeleton"]Head[%]PolyhedronData["Dodecahedron", "Skeleton", "Coordinates"]用 Entity 给出骨架图:
PolyhedronData["Cube", "Skeleton", "Entity"]用 Graph 对象给出十二面体的骨架图:
PolyhedronData["Dodecahedron", "Skeleton", "Graph"]PolyhedronData["Dodecahedron", "Skeleton"]PolyhedronData["Cube", "Skeleton", "Name"]GraphData[%]PolyhedronData["Cube", "Skeleton", "Image"]Head[%]PolyhedronData["Dodecahedron", "Skeleton", "Rule"]用 GraphPlot 可视化:
GraphPlot[%]用 GraphPlot3D 可视化:
GraphPlot3D[%%]用 UndirectedEdge 列表给出骨架图的边:
PolyhedronData["Dodecahedron", "Skeleton", "Undirected"]Graph[%]"SymmetryGroup" (4)
用 FiniteGroupData 标准名称显示立方体的对称群:
PolyhedronData["Cube", "SymmetryGroup"]PolyhedronData["Cube", "SymmetryGroup", "Name"]PolyhedronData["Cube", "SymmetryGroup", "Entity"]PolyhedronData["Cube", "SymmetryGroup", "Group"]PolyhedronData["Cube", "SymmetryGroup", "Notation"]"Vertices" (7)
PolyhedronData["Tetrahedron", "Vertices"]PolyhedronData["Tetrahedron", "VertexCoordinates"] == %PolyhedronData["Tetrahedron", "VertexCoordinates"] == %%Graphics3D[{PointSize[.1], Red, Point[PolyhedronData["Tetrahedron", "Vertices", "Coordinates"]]}]Graphics3D[{PointSize[.1], Red, PolyhedronData["Tetrahedron", "Points"]}]PolyhedronData[{"Prism", 5}, "Vertices", "Count"]% == PolyhedronData[{"Prism", 5}, "VertexCount"]PolyhedronData[{"Prism", 5}, "Vertices", "Graphics3D"]Head[%]PolyhedronData[{"Prism", 5}, "Vertices", "GraphicsComplex"]Graphics3D[%]PolyhedronData["TruncatedIcosahedron", "Vertices", "Image"]Head[%]PolyhedronData[{"Prism", 5}, "Vertices", "List"]PolyhedronData["Cube", "Vertices", "Point"]推广和延伸 (1)
应用 (8)
PolyhedronData[8]EntityClass["Polyhedron", "FaceCount" -> 8]//EntityListPolyhedronData["SpaceFilling", 8]Length[%]Union[PolyhedronData[#, {"VertexCount", "SpaceFilling"}]& /@ %%]PolyhedronData[{"Archimedean", "Chiral"}]PolyhedronData[-5]Union[PolyhedronData[#, "VertexCount"]& /@ %]Max[%] ≤ 5绘图显示一个半径为 5/4 的球被一个边为单位长度的十二面体剪切的情形:
Show[SphericalPlot3D[1.25, {θ, 0, Pi}, {ϕ, 0, 2Pi}, RegionFunction -> PolyhedronData["Dodecahedron", "RegionFunction"], ...], Graphics3D[{Opacity[0.5], PolyhedronData["Dodecahedron", "GraphicsComplex"]}]]绘制带有不同节点数的多面体数目,节点由 PolyhedronData 提供:
ListLinePlot[Table[Length[PolyhedronData["Simple", n]], {n, 50}]]ListPlot[Tooltip[Most[#], Last[#]]& /@ PolyhedronData["Simple", {"EdgeCount", "VertexCount", "StandardName"}]]ListPlot[l = PolyhedronData["Prism", {"EdgeCount", "VertexCount"}]]Rationalize[FindFit[l, m x + b, {b, m}, x], 10 ^ -4]GraphicsGrid[Partition[Tooltip[Show[PolyhedronData[#, "Graphics3D"], ...], #]& /@ SortBy[PolyhedronData[{"Chiral", "Simple"}], PolyhedronData[#, "FaceCount"]&], UpTo[6]], ImageSize -> Medium]属性和关系 (8)
platonics = PolyhedronData["Platonic"]builtin = Symbol[#][]& /@ platonics;GraphicsGrid[{PolyhedronData /@ platonics, Graphics3D /@ builtin}]PolyhedronData[{"Antiprism", 5}]PolyhedronData[{"Antiprism", 5}, "Skeleton"]ToEntity[%]Graph[PolyhedronData[{"Antiprism", 5}, "Vertices", "List"], UndirectedEdge@@@PolyhedronData[{"Antiprism", 5}, "Edges"]]ToEntity[%]CanonicalName[%]GraphData[{"Antiprism", 5}, "PolyhedralEmbeddings"]GraphData[{"Antiprism", 5}, "Graph", "3D"]s1 = PolyhedronData["Octahedron", "SurfaceArea"]TriangleArea3D[{{x1_, y1_, z1_}, {x2_, y2_, z2_}, {x3_, y3_, z3_}}] := Sqrt[(-x2 y1 + x3 y1 + x1 y2 - x3 y2 - x1 y3 + x2 y3) ^ 2 + (x2 z1 - x3 z1 - x1 z2 + x3 z2 + x1 z3 - x2 z3) ^ 2 + (-y2 z1 + y3 z1 + y1 z2 - y3 z2 - y1 z3 + y2 z3) ^ 2] / 2PolygonArea3D[l_List] := Module[{triangulate = Join[{1}, #]& /@ Partition[Range[2, Length[l]], 2, 1]},
Total[TriangleArea3D[l[[#]]]& /@ triangulate]]s2 = Total[Flatten[PolyhedronData["Octahedron", "Faces", "Polygon"]] /. Polygon :> PolygonArea3D]PolygonArea[l_List] := Total[Det /@ Partition[l, 2, 1, 1]] / 2s3 = Total[Flatten[PolyhedronData["Octahedron", "Net", "Polygon"]] /. Polygon :> PolygonArea]使用 Area 通过对面部区域求和计算曲面:
s4 = Total[Area /@ Flatten[PolyhedronData["Octahedron", "Polygons"]]]s5 = SurfaceArea[PolyhedronData["Octahedron", "Polyhedron"]]s1 == s2 == s3 == s4 == s5比较通过将 Area 应用到对应的区域边界获得的值:
Area[RegionBoundary[PolyhedronData["Octahedron", "Region"]]]% == 2Sqrt[3]PolyhedronData["Cube"](ineq = PolyhedronData["Cube", "RegionFunction"][x, y, z])//TraditionalFormWith[{r = .7}, RegionPlot3D[ineq, {x, -r, r}, {y, -r, r}, {z, -r, r}, Mesh -> False, PlotPoints -> 35]]v1 = PolyhedronData["Octahedron", "Volume"]v2 = Integrate[Boole[PolyhedronData["Octahedron", "RegionFunction"][x, y, z]], {x, -Infinity, Infinity}, {y, -Infinity, Infinity}, {z, -Infinity, Infinity}]polys = Flatten[PolyhedronData["Octahedron", "Polygons"]]v3 = Total[(1/3)Area[#]RegionDistance[#, {0, 0, 0}]& /@ polys]v1 == v2 == v3验证结果是否与通过将 Volume 应用于区域计算的体积一致:
PolyhedronData["Octahedron", "Region"]Volume[%]% == Sqrt[2] / 3PolyhedronData["Cube", "Centroid"]{v, cx, cy, cz} = Integrate[{1, x, y, z}Boole[PolyhedronData["Cube", "RegionFunction"][x, y, z]], {x, -Infinity, Infinity}, {y, -Infinity, Infinity}, {z, -Infinity, Infinity}]{cx, cy, cz} / v验证结果是否与通过将 RegionCentroid 应用到区域计算的质心一致:
PolyhedronData["Cube", "Region"]RegionCentroid[%]Graphics3D[{PointSize[.02], PolyhedronData["TruncatedIcosahedron", "Points"]}]Graphics3D[ConvexHullRegion[PolyhedronData["TruncatedIcosahedron", "VertexCoordinates"]]]Show[{%, %%}]内置多边形运算适用于 PolyhedronData 对象:
Graphics3D[PolyhedronData["Cube", "Polyhedron"]]Graphics3D[TruncatedPolyhedron[PolyhedronData["Cube", "Polyhedron"]]]PolyhedronData["Platonic"]GraphicsRow[Graphics3D /@ TruncatedPolyhedron /@ PolyhedronData["Platonic", "Polyhedron"]]GraphicsRow[Graphics3D /@ AugmentedPolyhedron /@ PolyhedronData["Platonic", "Polyhedron"]]可能存在的问题 (6)
PolyhedronData["snub dodecahedron", "VertexCount"]直接使用 PolyhedronData 中的字符模式:
PolyhedronData["Sn*"]Select[Cases[PolyhedronData[All], _String], StringMatchQ[#, "snub" ~~ ___, IgnoreCase -> True]&]PolyhedronData["SnubDodecahedron", "VertexCount"]PolyhedronData["SnubDodecahedron", "vertex count"]Select[PolyhedronData["SnubDodecahedron", "Properties"], StringMatchQ[#, "vertex" ~~ ___, IgnoreCase -> True]&]PolyhedronData["SnubDodecahedron", "VertexCount"]算术运算符不能在 Missing 项上执行:
PolyhedronData["Cube", "NetCount"] < PolyhedronData["TruncatedCube", "NetCount"]在执行操作前移除 Missing 项:
Short[First /@ Select[DeleteCases[{#, PolyhedronData[#, "Centroid"]}& /@ PolyhedronData[All], {_, _Missing}], Last[#] == {0, 0, 0}&], 5]PolyhedronData["Cube", "Circumradius"]PolyhedronData["SnubCube", "Circumradius"]PolyhedronData["SnubDisphenoid", "Circumradius"]可能无法获得带有相交多边形的实心形体的 "Region" 及相关属性:
PolyhedronData["CubeOctahedronCompound", "BoundaryMeshRegion"]PolyhedronData["CubeOctahedronCompound", "MeshRegion"]互动范例 (1)
巧妙范例 (4)
With[{p = "DuererSolid"}, Graphics3D[{{Opacity[.5], PolyhedronData[p, "Circumsphere"]}, PolyhedronData[p, "GraphicsComplex"], Red, PointSize[.03], PolyhedronData[p, "Points"]}, ...]]Graphics3D[PolyhedronData[{"PentagonalHexecontahedron", #}, "Polyhedron"]& /@ {"Laevo", "Dextro"}]colorize[GraphicsComplex[v_, Polygon[poly_]]] := Module[{color = Association[{3 -> Red, 4 -> Orange, 5 -> Yellow, 6 -> Green, 8 -> Blue, 10 -> Purple}]}, GraphicsComplex[N[v], ({Glow[color[Length[First[#]]]], Polygon[#]}&) /@ SplitBy[Sort[poly], Length]]]GraphicsGrid[Partition[Graphics3D[Tooltip[colorize[PolyhedronData[#, "GraphicsComplex"]], #], IconizedObject[«opts»]]& /@ PolyhedronData["Archimedean"], UpTo[5]], ImageSize -> Medium]Length[lines = Partition[RandomPoint[reg = PolyhedronData["Dodecahedron", "Region"], 10 ^ 7], 2]]//TimingGraphics3D[{{Opacity[.2], EdgeForm[], BoundaryDiscretizeRegion[reg]}, Red, Line /@ Take[lines, UpTo@1000]}]lengths = Norm /@ Subtract@@@lines;//TimingHistogram[lengths, {.01}]Mean[lengths]PolyhedronData["Dodecahedron", "MeanInteriorLineSegmentLength"]N[%]历史
2007年引入 (6.0) | 在以下年份被更新:2008 (7.0) ▪ 2010 (8.0) ▪ 2014 (10.0) ▪ 2015 (10.2) ▪ 2016 (10.4) ▪ 2017 (11.1) ▪ 2019 (12.0) ▪ 2020 (12.1) ▪ 2020 (12.2) ▪ 2021 (13.0) ▪ 2022 (13.1) ▪ 2024 (14.0) ▪ 2024 (14.1)
文本
Wolfram Research (2007),PolyhedronData,Wolfram 语言函数,https://reference.wolfram.com/language/ref/PolyhedronData.html (更新于 2024 年).
CMS
Wolfram 语言. 2007. "PolyhedronData." Wolfram 语言与系统参考资料中心. Wolfram Research. 最新版本 2024. https://reference.wolfram.com/language/ref/PolyhedronData.html.
APA
Wolfram 语言. (2007). PolyhedronData. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/PolyhedronData.html 年
BibTeX
@misc{reference.wolfram_2026_polyhedrondata, author="Wolfram Research", title="{PolyhedronData}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/PolyhedronData.html}", note=[Accessed: 17-June-2026]}
BibLaTeX
@online{reference.wolfram_2026_polyhedrondata, organization={Wolfram Research}, title={PolyhedronData}, year={2024}, url={https://reference.wolfram.com/language/ref/PolyhedronData.html}, note=[Accessed: 17-June-2026]}