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BeveledPolyhedron[poly]

各辺を斜めに切ることで，poly の斜角多面体を与える．

BeveledPolyhedron[poly,l]

多面体 poly の辺を長さの割合 l で斜めに切る．

詳細とオプション
Details and Options Details and Options
例題  
例  
スコープ  
アプリケーション  
基本的なアプリケーション  
多面体操作  
考えられる問題  
関連項目
関連するガイド
履歴
引用書式

BeveledPolyhedron

BeveledPolyhedron[poly]

各辺を斜めに切ることで，poly の斜角多面体を与える．

BeveledPolyhedron[poly,l]

多面体 poly の辺を長さの割合 l で斜めに切る．

詳細とオプション

例題

すべて開く すべて閉じる

例  (2)

12面体の斜角多面体：

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

スペースシャトルの斜角多面体を求める：

Wolfram Language code: 𝒫 = BeveledPolyhedron[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}}]];

可視化する：

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

スコープ  (4)

BeveledPolyhedronは多面体に使うことができる：

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: BeveledPolyhedron[𝒫]
Wolfram Language code: Graphics3D[%]

プラトンの立体のBeveledPolyhedronにはTetrahedron:が含まれる：

Wolfram Language code: BeveledPolyhedron[Tetrahedron[1]]

Cube：

Wolfram Language code: BeveledPolyhedron[Cube[1]]
Wolfram Language code: Graphics3D[%]

Dodecahedron：

Wolfram Language code: BeveledPolyhedron[Dodecahedron[1]]

Octahedron：

Wolfram Language code: TruncatedPolyhedron[Octahedron[1]]

Icosahedron：

Wolfram Language code: BeveledPolyhedron[Icosahedron[1]]

多面体メッシュをサポートする：

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

多面体の辺をさまざまな長さの割合で斜めに切る：

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[BeveledPolyhedron[𝒫, ratio]], {ratio, {0.1, 0.2, 0.3, 0.4}}]

アプリケーション  (5)

基本的なアプリケーション  (3)

プラトンの立体とその斜角多面体：

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

アルキメデスの立体とその斜角多面体：

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

プラトンの立体の斜角複合多面体：

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

アルキメデスの立体：

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

多面体操作  (2)

BeveledPolyhedronを使って，メタ操作のような多面体操作を計算する：

Wolfram Language code: meta[poly_] := DualPolyhedron[BeveledPolyhedron[poly]]
Wolfram Language code: meta[Tetrahedron[1]]
Wolfram Language code: Graphics3D[%]

BeveledPolyhedronはTruncatedPolyhedronで計算することができる：

Wolfram Language code: bevel[poly_] := TruncatedPolyhedron[TruncatedPolyhedron[poly, 0.5]]
Wolfram Language code: bevel[Tetrahedron[1]]
Wolfram Language code: Graphics3D[%]

考えられる問題  (2)

BeveledPolyhedronがサポートするのは単純多面体だけである：

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: BeveledPolyhedron[𝒫]

BeveledPolyhedronは退化した多面体を返すことがある：

Wolfram Language code: BeveledPolyhedron[Polyhedron[{{-1, 0, 0}, {-1/2, -1/2, -(1/Sqrt[2])}, {-1/2, -1/2, 1/Sqrt[2]}, {-1/2, 1/2, -(1/Sqrt[2])}, {-1/2, 1/2, 1/Sqrt[2]}, {0, -1, 0}, {0, 1, 0}, {1/2, -1/2, -(1/Sqrt[2])}, {1/2, -1/2, 1/Sqrt[2]}, {1/2, 1/2, -(1/Sqrt[2])}, {1/2, 1/2, 1/Sqrt[2]}, {1, 0, 0}}, {{4, 10, 8, 2}, {3, 9, 11, 5}, {9, 6, 8, 12}, {3, 1, 2, 6}, {5, 7, 4, 1}, {11, 12, 10, 7}, {12, 11, 9}, {3, 5, 1}, {6, 9, 3}, {5, 11, 7}, {8, 10, 12}, {1, 4, 2}, {2, 8, 6}, {7, 10, 4}}]]
Wolfram Language code: RegionQ[%]
Wolfram Research (2019), BeveledPolyhedron, Wolfram言語関数， https://reference.wolfram.com/language/ref/BeveledPolyhedron.html.

テキスト

Wolfram Research (2019), BeveledPolyhedron, Wolfram言語関数， https://reference.wolfram.com/language/ref/BeveledPolyhedron.html.

CMS

Wolfram Language. 2019. "BeveledPolyhedron." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/BeveledPolyhedron.html.

APA

Wolfram Language. (2019). BeveledPolyhedron. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BeveledPolyhedron.html

BibTeX

@misc{reference.wolfram_2026_beveledpolyhedron, author="Wolfram Research", title="{BeveledPolyhedron}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/BeveledPolyhedron.html}", note=[Accessed: 08-September-2026]}

BibLaTeX

@online{reference.wolfram_2026_beveledpolyhedron, organization={Wolfram Research}, title={BeveledPolyhedron}, year={2019}, url={https://reference.wolfram.com/language/ref/BeveledPolyhedron.html}, note=[Accessed: 08-September-2026]}