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CanonicalizePolyhedron[poly]

共有座標および外側と内側の境界で表す多面体 poly の正準表現を与える．

詳細
Details and Options Details and Options
例題  
例  
スコープ  
アプリケーション  
特性と関係  
考えられる問題  
関連項目
関連するガイド
履歴
引用書式

CanonicalizePolyhedron

CanonicalizePolyhedron[poly]

共有座標および外側と内側の境界で表す多面体 poly の正準表現を与える．

詳細

  • CanonicalizePolyhedronは，多面体の単純な標準的表現をさまざまな表現とさまざまな説明から得るために使われる．
  • CanonicalizePolyhedronは，多面体を最適化された標準形式のPolyhedron[{p1,p2,…},{outer1,outer2inner2,…}]に変換する．
  • 点 piは交差しない多面体面の頂点の点で，Sort順にソートされる．
  • 外側境界 outeriは，辺のところで接触している可能性がある多面体面{fi1,fi2,…}の閉じた曲面である．
  • 内側境界 inneriは，辺のところで接触している可能性がある多面体面{fj1,fj2,…}の閉じた曲面である．

例題

すべて開く すべて閉じる

例  (1)

Polyhedronの正準形を求める：

Wolfram Language code: 𝒫 = Polyhedron[{{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, {{0, 1, 0}, {1, 0, 0}, {0, 0, 0}}, {{0, 0, 1}, {0, 0, 0}, {1, 0, 0}}, {{0, 0, 0}, {0, 0, 1}, {0, 1, 0}}}];
Wolfram Language code: CanonicalizePolyhedron[𝒫]
Wolfram Language code: Graphics3D[%]

スコープ  (3)

CanonicalizePolyhedronは多面体に使うことができる：

Wolfram Language code: Polyhedron[{{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, {{0, 1, 0}, {1, 0, 0}, {0, 0, 0}}, {{0, 0, 1}, {0, 0, 0}, {1, 0, 0}}, {{0, 0, 0}, {0, 0, 1}, {0, 1, 0}}}];
Wolfram Language code: CanonicalizePolyhedron[%]

Tetrahedron：

Wolfram Language code: CanonicalizePolyhedron[Tetrahedron[]]

Octahedron：

Wolfram Language code: CanonicalizePolyhedron[Octahedron[]]

空隙のある多面体：

Wolfram Language code: Polyhedron[{{0, 0, 0}, {0, 3, 0}, {3, 3, 0}, {3, 0, 0}, {0, 0, 3}, {0, 3, 3}, {3, 3, 3}, {3, 0, 3}, {1, 1, 1}, {1, 2, 1}, {2, 2, 1}, {2, 1, 1}, {1, 1, 2}, {1, 2, 2}, {2, 2, 2}, {2, 1, 2}}, {{2, 3, 4, 1}, {1, 4, 8, 5}, {4, 3, 7, 8}, {3, 2, 6, 7}, {2, 1, 5, 6}, {5, 8, 7, 6}} -> {{{10, 11, 12, 9}, {9, 12, 16, 13}, {12, 11, 15, 16}, {11, 10, 14, 15}, {10, 9, 13, 14}, {13, 16, 15, 14}}}];
Wolfram Language code: CanonicalizePolyhedron[%]
Wolfram Language code: Graphics3D[{Opacity[0.5], %}]

不連続成分がある多面体：

Wolfram Language code: Polyhedron[{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}, {1, 1, 1}, {2, 1, 1}, {1, 2, 1}, {1, 1, 2}}, {{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: CanonicalizePolyhedron[%]

アプリケーション  (1)

共通座標を有する複合グラフィックスを設定する：

Wolfram Language code: 𝒞𝒫 = CanonicalizePolyhedron[Polyhedron[{{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, {{0, 1, 0}, {1, 0, 0}, {0, 0, 0}}, {{0, 0, 1}, {0, 0, 0}, {1, 0, 0}}, {{0, 0, 0}, {0, 0, 1}, {0, 1, 0}}}]]
Wolfram Language code: Graphics3D[{GraphicsComplex[𝒞𝒫[[1]], Polyhedron[𝒞𝒫[[2]]]]}]

特性と関係  (5)

CanonicalizePolyhedronを使ってPolyhedronCoordinatesを得る：

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

プラトンの立体のCanonicalizePolyhedronは多面体である：

Wolfram Language code: CanonicalizePolyhedron[Icosahedron[]]

単純多面体のCanonicalizePolyhedronは多面体座標の数を保持する：

Wolfram Language code: 𝒫 = Polyhedron[{{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, {{0, 1, 0}, {1, 0, 0}, {0, 0, 0}}, {{0, 0, 1}, {0, 0, 0}, {1, 0, 0}}, {{0, 0, 0}, {0, 0, 1}, {0, 1, 0}}}];
Wolfram Language code: SimplePolyhedronQ[𝒫]
Wolfram Language code: Length[PolyhedronCoordinates[#]]& /@ {𝒫, CanonicalizePolyhedron[𝒫]}

OuterPolyhedronは外側多面体の正準表現を与える：

Wolfram Language code: OuterPolyhedron[Polyhedron[{{-Sqrt[1 + 2/Sqrt[5]], 0, Root[1 - 20*#1^2 + 80*#1^4 & , 3, 0]}, {Sqrt[1 + 2/Sqrt[5]], 0, Root[1 - 20*#1^2 + 80*#1^4 & , 2, 0]}, {Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0], (-3 - Sqrt[5])/4, Root[1 - 20*#1^2 + 80*#1^4 & , 3, 0]}, {R ... }, {11, 12, 8, 16, 7}, {12, 6, 20, 4, 8}, {6, 2, 13, 18, 20}, {2, 5, 19, 17, 13}, {4, 20, 18, 10, 15}, {18, 13, 17, 9, 10}, {17, 19, 3, 14, 9}, {3, 7, 16, 1, 14}, {16, 8, 4, 15, 1}, {22, 23, 24}, {23, 22, 21}, {24, 21, 22}, {21, 24, 23}}]]

InnerPolyhedronは内側多面体の正準表現を与える：

Wolfram Language code: InnerPolyhedron[Polyhedron[{{-Sqrt[1 + 2/Sqrt[5]], 0, Root[1 - 20*#1^2 + 80*#1^4 & , 3, 0]}, {Sqrt[1 + 2/Sqrt[5]], 0, Root[1 - 20*#1^2 + 80*#1^4 & , 2, 0]}, {Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0], (-3 - Sqrt[5])/4, Root[1 - 20*#1^2 + 80*#1^4 & , 3, 0]}, {R ... }, {11, 12, 8, 16, 7}, {12, 6, 20, 4, 8}, {6, 2, 13, 18, 20}, {2, 5, 19, 17, 13}, {4, 20, 18, 10, 15}, {18, 13, 17, 9, 10}, {17, 19, 3, 14, 9}, {3, 7, 16, 1, 14}, {16, 8, 4, 15, 1}, {22, 23, 24}, {23, 22, 21}, {24, 21, 22}, {21, 24, 23}}]]

考えられる問題  (1)

CanonicalizePoyhedronは幾何領域でのみ使うことができる：

Wolfram Language code: 𝒫 = Polyhedron[{{0, 0, 0}, {1, 1, 0}, {0, 1, 0}, {0, 0, 1}}, {{2, 3, 4}, {3, 2, 1}}];
Wolfram Language code: {CanonicalizePolyhedron[𝒫], RegionQ[𝒫]}
Wolfram Research (2019), CanonicalizePolyhedron, Wolfram言語関数， https://reference.wolfram.com/language/ref/CanonicalizePolyhedron.html.

テキスト

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_canonicalizepolyhedron, author="Wolfram Research", title="{CanonicalizePolyhedron}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/CanonicalizePolyhedron.html}", note=[Accessed: 08-August-2026]}

BibLaTeX

@online{reference.wolfram_2026_canonicalizepolyhedron, organization={Wolfram Research}, title={CanonicalizePolyhedron}, year={2019}, url={https://reference.wolfram.com/language/ref/CanonicalizePolyhedron.html}, note=[Accessed: 08-August-2026]}