開ひらけ羅ら五ご邊へん形がた鑲嵌

開ひらけ羅ら五ご邊へん形がた鑲嵌
	歐おう幾里いくさと得とく平面へいめん
類別るいべつ	半はん正せい鑲嵌對偶たいぐう; 平面へいめん鑲嵌
對偶たいぐう多面體ためんたい	扭稜正方形せいほうけい鑲嵌
數學すうがく表示法ひょうじほう
考こう克かつ斯特符號ふごう; （英えい语：Coxeter-Dynkin diagram）	;
施ほどこせ萊夫利り符號ふごう	dsr{6,3}
康かん威たけし表示法ひょうじほう	dsrS
性質せいしつ
二に面めん角かく	平ひら角かく
組成そせい與あずか佈局
面めん的てき種類しゅるい	五ご邊へん形がた
面めん的てき佈局; （英えい语：Face configuration）	V3.3.4.3.4
對稱たいしょう性せい
對稱たいしょう群ぐん	p4g, [4+,4], (4*2); p4, [4,4]+, (442)
旋轉せんてん對稱たいしょう群ぐん; （英語えいご：Rotation_groups）	p4, [4,4]+, (442)
特性とくせい
	面めん可か遞
圖像ずぞう
	; 扭稜正方形せいほうけい鑲嵌; （對偶たいぐう多面體ためんたい）
	; 扭稜正方形せいほうけい鑲嵌; （對偶たいぐう多面體ためんたい）
	查; 论; 编;

在ざい幾何きか學がく中なか，開ひらけ羅ら五ご邊へん形がた鑲嵌是ぜ一いち種しゅ平面へいめん鑲嵌，其為半はん正せい鑲嵌扭稜正方形せいほうけい鑲嵌的てき對偶たいぐう鑲嵌^[1]，密みつ鋪しき於歐氏し平面へいめん，其名為ため「開ひらく羅ら」是ぜ因いん為ため這種幾何きか圖形ずけい經常けいじょう在ざい埃及えじぷと開ひらく羅ら的てき街道かいどう上じょう出現しゅつげん^[2]^[3]，是ぜ15種しゅ已やめ知的ちてき等とう面めん五ご邊へん形がた鑲嵌之の一いち。

康かん威たけし將之まさゆき稱たたえ為ため4-fold pentille^[4]。

它也被ひ稱しょう為ため麥むぎ克かつ馬うま洪ひろし網もう格かく（MacMahon's net）^[5]，出で於珀西にし亞あ歷れき山大やまだい麥むぎ克かつ馬うま洪ひろし1921年ねん出版しゅっぱん的てき《New Mathematical Pastimes》^[6]。

在ざい化學かがく中ちゅう

五ご邊へん石墨せきぼく烯的てき化學かがく結構けっこう與あずか開ひらく羅ら五ご邊へん形がた鑲嵌接近せっきん^[7]這種形態けいたい建たて基はじめ於分析ぶんせき和わ模擬もぎ，在ざい2014年ねん被ひ提出ていしゅつ。^[7]進すすむ一步的計算顯示純粹以此形態存在的碳是不穩定的，^[8]但ただし將はた其氫化か後ご可變かへん得とく穩定。^[9]由よし於其結構けっこう，它罕見地けんち具有ぐゆう負ふ值蒲かば松まつ比ひ，強度きょうど相しょう信しん比ひ石墨せきぼく烯高こう，且據預あずか測はか它能在高ありだか達たち1000K時じ仍為化學かがく穩定。^[7]

參まいり見み

參考さんこう文獻ぶんけん

^ Weisstein, Eric W. (编). Dual tessellation. at MathWorld--A Wolfram Web Resource. Wolfram Research, Inc. （英えい语）.
^ Alsina, Claudi; Nelsen, Roger B., Charming proofs: a journey into elegant mathematics, Dolciani mathematical expositions 42, Mathematical Association of America: 164, 2010 [2014-06-11], ISBN 978-0-88385-348-1, （原始げんし内容ないよう存そん档于2014-07-05） .
^ Martin, George Edward, Transformation Geometry: An Introduction to Symmetry, Undergraduate Texts in Mathematics, Springer: 119, 1982 [2014-06-11], ISBN 978-0-387-90636-2, （原始げんし内容ないよう存そん档于2014-07-05） .
^ Conway, John H.; Burgiel, Heidi; Goodman-Strass, Chaim, The Symmetries of Things, AK Peters: 288, 2008, ISBN 978-1-56881-220-5
^ Plane nets in crystal chemistry. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences. 1980-02-29, 295 (1417): 553–618 [2020-05-04]. ISSN 0080-4614. doi:10.1098/rsta.1980.0150. （原始げんし内容ないよう存そん档于2019-10-24）（英えい语）.
^ Macmahon, Major P. A., New Mathematical Pastimes, University Press, 1921 .
^ ^7.0 ^7.1 ^7.2 Shunhong Zhang, Jian Zhou, Qian Wang, Xiaoshuang Chen, Yoshiyuki Kawazoe, Puru Jena. Penta-graphene: A new carbon allotrope. Proceedings of the National Academy of Sciences. 2015-02-24, 112 (8): 2372–2377 [2020-05-04]. ISSN 0027-8424. PMC 4345574 . PMID 25646451. doi:10.1073/pnas.1416591112 （英えい语）.
^ Christopher P. Ewels, Xavier Rocquefelte, Harold W. Kroto, Mark J. Rayson, Patrick R. Briddon, Malcolm I. Heggie. Predicting experimentally stable allotropes: Instability of penta-graphene. Proceedings of the National Academy of Sciences. 2015-12-22, 112 (51): 15609–15612 [2020-05-04]. ISSN 0027-8424. PMC 4697406 . PMID 26644554. doi:10.1073/pnas.1520402112 （英えい语）.
^ Hamideh Einollahzadeh, Seyed Mahdi Fazeli, Reza Sabet Dariani. Studying the electronic and phononic structure of penta-graphane. Science and Technology of Advanced Materials. 2016-12, 17 (1): 610–617 [2020-05-04]. ISSN 1468-6996. PMC 5102001 . PMID 27877907. doi:10.1080/14686996.2016.1219970. （原始げんし内容ないよう存そん档于2020-08-15）（英えい语）.

延伸えんしん阅读

Grünbaum, Branko ; and Shephard, G. C. Tilings and Patterns. New York: W. H. Freeman. 1987. ISBN 0-7167-1193-1. (Chapter 2.1: Regular and uniform tilings, p.58-65) (Page 480, Tilings by polygons, #24 of 24 polygonal isohedral types by pentagons)
Williams, Robert. The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. 1979: 38. ISBN 0-486-23729-X.
Wells, David, The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, p. 23, 1991.

外部がいぶ連結れんけつ

[3] Weisstein, Eric W. (编). Dual tessellation. at MathWorld--A Wolfram Web Resource. Wolfram Research, Inc. （英えい语）.

[4] Alsina, Claudi; Nelsen, Roger B., Charming proofs: a journey into elegant mathematics, Dolciani mathematical expositions 42, Mathematical Association of America: 164, 2010 [2014-06-11], ISBN 978-0-88385-348-1, （原始げんし内容ないよう存そん档于2014-07-05） .

[5] Martin, George Edward, Transformation Geometry: An Introduction to Symmetry, Undergraduate Texts in Mathematics, Springer: 119, 1982 [2014-06-11], ISBN 978-0-387-90636-2, （原始げんし内容ないよう存そん档于2014-07-05） .

[conway-6] Conway, John H.; Burgiel, Heidi; Goodman-Strass, Chaim, The Symmetries of Things, AK Peters: 288, 2008, ISBN 978-1-56881-220-5

[7] Plane nets in crystal chemistry. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences. 1980-02-29, 295 (1417): 553–618 [2020-05-04]. ISSN 0080-4614. doi:10.1098/rsta.1980.0150. （原始げんし内容ないよう存そん档于2019-10-24）（英えい语）.

[8] Macmahon, Major P. A., New Mathematical Pastimes, University Press, 1921 .

[pnas-9] 7.0 ^7.1 ^7.2 Shunhong Zhang, Jian Zhou, Qian Wang, Xiaoshuang Chen, Yoshiyuki Kawazoe, Puru Jena. Penta-graphene: A new carbon allotrope. Proceedings of the National Academy of Sciences. 2015-02-24, 112 (8): 2372–2377 [2020-05-04]. ISSN 0027-8424. PMC 4345574 . PMID 25646451. doi:10.1073/pnas.1416591112 （英えい语）.

[pnas2-10] Christopher P. Ewels, Xavier Rocquefelte, Harold W. Kroto, Mark J. Rayson, Patrick R. Briddon, Malcolm I. Heggie. Predicting experimentally stable allotropes: Instability of penta-graphene. Proceedings of the National Academy of Sciences. 2015-12-22, 112 (51): 15609–15612 [2020-05-04]. ISSN 0027-8424. PMC 4697406 . PMID 26644554. doi:10.1073/pnas.1520402112 （英えい语）.

[stam-11] Hamideh Einollahzadeh, Seyed Mahdi Fazeli, Reza Sabet Dariani. Studying the electronic and phononic structure of penta-graphane. Science and Technology of Advanced Materials. 2016-12, 17 (1): 610–617 [2020-05-04]. ISSN 1468-6996. PMC 5102001 . PMID 27877907. doi:10.1080/14686996.2016.1219970. （原始げんし内容ないよう存そん档于2020-08-15）（英えい语）.

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