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AugmentedPolyhedron[poly]

通过用四棱锥替换每个面给出增强多面体 (augmented polyhedron) poly.

AugmentedPolyhedron[poly,h]

给出四棱锥高度为 h 的增强多面体.

更多信息和选项
Details and Options Details and Options
范例  
基本范例  
范围  
应用  
基本应用  
多面体运算  
属性和关系  
可能存在的问题  
参见
相关指南
历史
按以下格式引用：

AugmentedPolyhedron

AugmentedPolyhedron[poly]

通过用四棱锥替换每个面给出增强多面体 (augmented polyhedron) poly.

AugmentedPolyhedron[poly,h]

给出四棱锥高度为 h 的增强多面体.

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  (2)

十二面体的增强多面体：

Wolfram Language code: AugmentedPolyhedron[Dodecahedron[]]
Wolfram Language code: Graphics3D[%]

给出航天飞机的增强多面体：

Wolfram Language code: 𝒫 = AugmentedPolyhedron[Polyhedron[{{-4.999492168426514, -0.6817100048065186, 0.569242000579834}, {-4.999759197235107, -0.4911530017852783, 0.8052060008049011}, {-5.349475860595703, -0.47093498706817627, 0.5660619735717773}, {-4.999759197235107, 0.491153001785278 ... }, {291, 218, 220}, {211, 259, 258}, {280, 206, 218}, {212, 258, 288}, {225, 187, 219}, {245, 197, 196}, {200, 236, 235}, {263, 196, 207}, {274, 205, 193}, {282, 210, 205}, {268, 193, 188}, {226, 219, 210}, {269, 188, 187}, {215, 288, 287}}]];

可视化：

Wolfram Language code: Graphics3D[𝒫, Boxed -> False]

范围  (4)

AugmentedPolyhedron 适用于多面体：

Wolfram Language code: 𝒫 = Polyhedron[{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, {{1, 2, 3}, {1, 2, 4}, {2, 3, 4}, {1, 3, 4}}];
Wolfram Language code: AugmentedPolyhedron[𝒫]
Wolfram Language code: Graphics3D[%]

柏拉图立体的 AugmentedPolyhedron 包括 Tetrahedron：

Wolfram Language code: AugmentedPolyhedron[Tetrahedron[1]]

Cube：

Wolfram Language code: AugmentedPolyhedron[Cube[1]]

Dodecahedron：

Wolfram Language code: AugmentedPolyhedron[Dodecahedron[1]]
Wolfram Language code: Graphics3D[%]

Octahedron：

Wolfram Language code: AugmentedPolyhedron[Octahedron[1]]

Icosahedron：

Wolfram Language code: AugmentedPolyhedron[Icosahedron[1]]

支持多面体网格：

Wolfram Language code: 𝒫 = ExampleData[{"Geometry3D", "SpaceShuttle"}, "BoundaryMeshRegion"]
Wolfram Language code: AugmentedPolyhedron[𝒫]
Wolfram Language code: Graphics3D[%]

用不同高度的四棱锥构建增强多面体：

Wolfram Language code: 𝒫 = Polyhedron[{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, {{1, 2, 3}, {1, 2, 4}, {2, 3, 4}, {1, 3, 4}}];
Wolfram Language code: Table[Graphics3D[AugmentedPolyhedron[𝒫, h]], {h, {0.1, 0.2, 0.3, 0.4}}]

应用  (4)

基本应用  (3)

柏拉图立体及其增强多面体图集：

Wolfram Language code: Grid[Table[{Graphics3D[f[1], Boxed -> False], [image], Graphics3D[AugmentedPolyhedron[f[1]], Boxed -> False]}, {f, {Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron}}]]

阿基米德立体及其增强多面体图集：

Wolfram Language code: Multicolumn[Table[Row[{Graphics3D[f, Boxed -> False, ImageSize -> 50], [image], Graphics3D[AugmentedPolyhedron[f], Boxed -> False, ImageSize -> 50]}], {f, PolyhedronData["Archimedean", "Polyhedron"]}], 2, Spacings -> 3]

柏拉图立体的增强多面体组合：

Wolfram Language code: Table[Graphics3D[{Opacity[0.5], AugmentedPolyhedron[f[1]], f[1]}, Boxed -> False], {f, {Tetrahedron, Cube, Dodecahedron}}]

阿基米德立体：

Wolfram Language code: Table[Graphics3D[{Opacity[0.5], f, AugmentedPolyhedron[f]}, Boxed -> False], {f, PolyhedronData["Archimedean", "Polyhedron"]}]

多面体运算  (1)

用 AugmentedPolyhedron 进行多面体运算，如 zip 运算：

Wolfram Language code: zip[poly_] := DualPolyhedron[AugmentedPolyhedron[poly]]
Wolfram Language code: zip[Tetrahedron[1]]
Wolfram Language code: Graphics3D[%]

属性和关系  (1)

增强简单多面体还是简单多面体：

Wolfram Language code: 𝒫 = Polyhedron[{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, {{1, 2, 3}, {1, 2, 4}, {2, 3, 4}, {1, 3, 4}}];
Wolfram Language code: SimplePolyhedronQ[#]& /@ {𝒫, AugmentedPolyhedron[𝒫]}

可能存在的问题  (2)

AugmentedPolyhedron 只支持简单多面体：

Wolfram Language code: 𝒫 = Polyhedron[{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}, {1, 0, 0}, {2, 0, 0}, {1, 1, 0}, {1, 0, 1}}, {{1, 2, 3}, {1, 2, 4}, {2, 3, 4}, {1, 3, 4}, {5, 6, 7}, {5, 6, 8}, {6, 7, 8}, {5, 7, 8}}];
Wolfram Language code: SimplePolyhedronQ[𝒫]
Wolfram Language code: AugmentedPolyhedron[𝒫]

AugmentedPolyhedron 可以返回退化多面体：

Wolfram Language code: AugmentedPolyhedron[Polyhedron[{{-4.999492168426514, -0.6817100048065186, 0.569242000579834}, {-4.999759197235107, -0.4911530017852783, 0.8052060008049011}, {-5.349475860595703, -0.47093498706817627, 0.5660619735717773}, {-4.999759197235107, 0.491153001785278 ... }, {291, 218, 220}, {211, 259, 258}, {280, 206, 218}, {212, 258, 288}, {225, 187, 219}, {245, 197, 196}, {200, 236, 235}, {263, 196, 207}, {274, 205, 193}, {282, 210, 205}, {268, 193, 188}, {226, 219, 210}, {269, 188, 187}, {215, 288, 287}}]]
Wolfram Language code: RegionQ[%]
Wolfram Research (2019)，AugmentedPolyhedron，Wolfram 语言函数，https://reference.wolfram.com/language/ref/AugmentedPolyhedron.html.

文本

Wolfram Research (2019)，AugmentedPolyhedron，Wolfram 语言函数，https://reference.wolfram.com/language/ref/AugmentedPolyhedron.html.

CMS

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

APA

Wolfram 语言. (2019). AugmentedPolyhedron. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/AugmentedPolyhedron.html 年

BibTeX

@misc{reference.wolfram_2026_augmentedpolyhedron, author="Wolfram Research", title="{AugmentedPolyhedron}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/AugmentedPolyhedron.html}", note=[Accessed: 19-August-2026]}

BibLaTeX

@online{reference.wolfram_2026_augmentedpolyhedron, organization={Wolfram Research}, title={AugmentedPolyhedron}, year={2019}, url={https://reference.wolfram.com/language/ref/AugmentedPolyhedron.html}, note=[Accessed: 19-August-2026]}