Cairo pentagonal tiling (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Cairo pentagonal tiling" in English language version.

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12doi.org

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mathscinet.ams.org

Schattschneider, Doris (1978), "Tiling the plane with congruent pentagons", Mathematics Magazine, 51 (1): 29–44, doi:10.1080/0025570X.1978.11976672, JSTOR 2689644, MR 0493766
Goodman-Strauss, C.; Sloane, N. J. A. (2019), "A coloring-book approach to finding coordination sequences" (PDF), Acta Crystallographica Section A, 75 (1): 121–134, arXiv:1803.08530, doi:10.1107/s2053273318014481, MR 3896412, PMID 30575590, S2CID 4553572, archived from the original (PDF) on 2022-02-17, retrieved 2021-06-18
Chung, Ping Ngai; Fernandez, Miguel A.; Li, Yifei; Mara, Michael; Morgan, Frank; Plata, Isamar Rosa; Shah, Niralee; Vieira, Luis Sordo; Wikner, Elena (2012), "Isoperimetric pentagonal tilings", Notices of the American Mathematical Society, 59 (5): 632–640, doi:10.1090/noti838, MR 2954290
Morgan, Frank (2019), "My undercover mission to find Cairo tilings", The Mathematical Intelligencer, 41 (3): 19–22, doi:10.1007/s00283-019-09906-7, MR 3995312, S2CID 198468426

archive.org

Macmahon, Major P. A. (1921), New Mathematical Pastimes, University Press, p. 101
Nisbet, Harry (1906), Grammar of Textile Design, London: Scott, Greenwood & Son, p. 101

arxiv.org

Rao, Michaël (2017), Exhaustive search of convex pentagons which tile the plane (PDF), arXiv:1708.00274
Goodman-Strauss, C.; Sloane, N. J. A. (2019), "A coloring-book approach to finding coordination sequences" (PDF), Acta Crystallographica Section A, 75 (1): 121–134, arXiv:1803.08530, doi:10.1107/s2053273318014481, MR 3896412, PMID 30575590, S2CID 4553572, archived from the original (PDF) on 2022-02-17, retrieved 2021-06-18
Ressouche, E.; Simonet, V.; Canals, B.; Gospodinov, M.; Skumryev, V. (December 2009), "Magnetic frustration in an iron-based Cairo pentagonal lattice", Physical Review Letters, 103 (26): 267204, arXiv:1001.0710, Bibcode:2009PhRvL.103z7204R, doi:10.1103/physrevlett.103.267204, PMID 20366341, S2CID 20752605

books.google.com

Conway, John H.; Burgiel, Heidi; Goodman-Strauss, Chaim (2008), The Symmetries of Things, AK Peters, p. 288, ISBN 978-1-56881-220-5
Steurer, Walter; Dshemuchadse, Julia (2016), Intermetallics: Structures, Properties, and Statistics, International Union of Crystallography Monographs on Crystallography, vol. 26, Oxford University Press, p. 42, ISBN 9780191023927
Alsina, Claudi; Nelsen, Roger B. (2010), Charming proofs: a journey into elegant mathematics, Dolciani mathematical expositions, vol. 42, Mathematical Association of America, p. 164, ISBN 978-0-88385-348-1.
Martin, George Edward (1982), Transformation Geometry: An Introduction to Symmetry, Undergraduate Texts in Mathematics, Springer, p. 119, ISBN 978-0-387-90636-2.

bridgesmathart.org

archive.bridgesmathart.org

Thomas, B.G.; Hann, M.A. (2008), "Patterning by projection: Tiling the dodecahedron and other solids", in Sarhangi, Reza; Séquin, Carlo H. (eds.), Bridges Leeuwarden: Mathematics, Music, Art, Architecture, Culture, London: Tarquin Publications, pp. 101–108, ISBN 9780966520194

doi.org

O'Keeffe, M.; Hyde, B. G. (1980), "Plane nets in crystal chemistry", Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 295 (1417): 553–618, Bibcode:1980RSPTA.295..553O, doi:10.1098/rsta.1980.0150, JSTOR 36648, S2CID 121456259.
Schattschneider, Doris (1978), "Tiling the plane with congruent pentagons", Mathematics Magazine, 51 (1): 29–44, doi:10.1080/0025570X.1978.11976672, JSTOR 2689644, MR 0493766
Macmillan, R. H. (December 1979), "Pyramids and pavements: Some thoughts from Cairo", The Mathematical Gazette, 63 (426): 251–255, doi:10.2307/3618038, JSTOR 3618038, S2CID 125608794
Kovács, Gergely; Nagy, Benedek; Turgay, Neşet Deniz (May 2021), "Distance on the Cairo pattern", Pattern Recognition Letters, 145: 141–146, Bibcode:2021PaReL.145..141K, doi:10.1016/j.patrec.2021.02.002, S2CID 233375125
Goodman-Strauss, C.; Sloane, N. J. A. (2019), "A coloring-book approach to finding coordination sequences" (PDF), Acta Crystallographica Section A, 75 (1): 121–134, arXiv:1803.08530, doi:10.1107/s2053273318014481, MR 3896412, PMID 30575590, S2CID 4553572, archived from the original (PDF) on 2022-02-17, retrieved 2021-06-18
Rollett, A. P. (September 1955), "2530. A pentagonal tessellation", Mathematical Notes, The Mathematical Gazette, 39 (329): 209, doi:10.2307/3608750, JSTOR 3608750, S2CID 250439435
Chung, Ping Ngai; Fernandez, Miguel A.; Li, Yifei; Mara, Michael; Morgan, Frank; Plata, Isamar Rosa; Shah, Niralee; Vieira, Luis Sordo; Wikner, Elena (2012), "Isoperimetric pentagonal tilings", Notices of the American Mathematical Society, 59 (5): 632–640, doi:10.1090/noti838, MR 2954290
Dunn, J. A. (December 1971), "Tessellations with pentagons", The Mathematical Gazette, 55 (394): 366–369, doi:10.2307/3612359, JSTOR 3612359, S2CID 118680100. Although Dunn writes that the equilateral form of the tiling was used in Cairo, this appears to be a mistake.
Morgan, Frank (2019), "My undercover mission to find Cairo tilings", The Mathematical Intelligencer, 41 (3): 19–22, doi:10.1007/s00283-019-09906-7, MR 3995312, S2CID 198468426
Banaru, A. M.; Banaru, G. A. (August 2011), "Cairo tiling and the topology of layered hydrates", Moscow University Chemistry Bulletin, 66 (3), Article 159, doi:10.3103/S0027131411030023, S2CID 96002269
Ressouche, E.; Simonet, V.; Canals, B.; Gospodinov, M.; Skumryev, V. (December 2009), "Magnetic frustration in an iron-based Cairo pentagonal lattice", Physical Review Letters, 103 (26): 267204, arXiv:1001.0710, Bibcode:2009PhRvL.103z7204R, doi:10.1103/physrevlett.103.267204, PMID 20366341, S2CID 20752605
Zhang, Shunhong; Zhou, Jian; Wang, Qian; Chen, Xiaoshuang; Kawazoe, Yoshiyuki; Jena, Puru (February 2015), "Penta-graphene: A new carbon allotrope", Proceedings of the National Academy of Sciences of the United States of America, 112 (8): 2372–2377, Bibcode:2015PNAS..112.2372Z, doi:10.1073/pnas.1416591112, PMC 4345574, PMID 25646451

ens-lyon.fr

perso.ens-lyon.fr

Rao, Michaël (2017), Exhaustive search of convex pentagons which tile the plane (PDF), arXiv:1708.00274

handle.net

hdl.handle.net

Haag, F. (1911), "Die regelmäßigen Planteilungen", Zeitschrift für Kristallographie, Kristallgeometrie, Kristallphysik, Kristallchemie, 49: 360–369, hdl:2027/uc1.b3327994 See in particular Figures 2b, p. 361, and 4a, p. 363.

harvard.edu

ui.adsabs.harvard.edu

O'Keeffe, M.; Hyde, B. G. (1980), "Plane nets in crystal chemistry", Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 295 (1417): 553–618, Bibcode:1980RSPTA.295..553O, doi:10.1098/rsta.1980.0150, JSTOR 36648, S2CID 121456259.
Kovács, Gergely; Nagy, Benedek; Turgay, Neşet Deniz (May 2021), "Distance on the Cairo pattern", Pattern Recognition Letters, 145: 141–146, Bibcode:2021PaReL.145..141K, doi:10.1016/j.patrec.2021.02.002, S2CID 233375125
Ressouche, E.; Simonet, V.; Canals, B.; Gospodinov, M.; Skumryev, V. (December 2009), "Magnetic frustration in an iron-based Cairo pentagonal lattice", Physical Review Letters, 103 (26): 267204, arXiv:1001.0710, Bibcode:2009PhRvL.103z7204R, doi:10.1103/physrevlett.103.267204, PMID 20366341, S2CID 20752605
Zhang, Shunhong; Zhou, Jian; Wang, Qian; Chen, Xiaoshuang; Kawazoe, Yoshiyuki; Jena, Puru (February 2015), "Penta-graphene: A new carbon allotrope", Proceedings of the National Academy of Sciences of the United States of America, 112 (8): 2372–2377, Bibcode:2015PNAS..112.2372Z, doi:10.1073/pnas.1416591112, PMC 4345574, PMID 25646451

jstor.org

O'Keeffe, M.; Hyde, B. G. (1980), "Plane nets in crystal chemistry", Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 295 (1417): 553–618, Bibcode:1980RSPTA.295..553O, doi:10.1098/rsta.1980.0150, JSTOR 36648, S2CID 121456259.
Schattschneider, Doris (1978), "Tiling the plane with congruent pentagons", Mathematics Magazine, 51 (1): 29–44, doi:10.1080/0025570X.1978.11976672, JSTOR 2689644, MR 0493766
Macmillan, R. H. (December 1979), "Pyramids and pavements: Some thoughts from Cairo", The Mathematical Gazette, 63 (426): 251–255, doi:10.2307/3618038, JSTOR 3618038, S2CID 125608794
Rollett, A. P. (September 1955), "2530. A pentagonal tessellation", Mathematical Notes, The Mathematical Gazette, 39 (329): 209, doi:10.2307/3608750, JSTOR 3608750, S2CID 250439435
Dunn, J. A. (December 1971), "Tessellations with pentagons", The Mathematical Gazette, 55 (394): 366–369, doi:10.2307/3612359, JSTOR 3612359, S2CID 118680100. Although Dunn writes that the equilateral form of the tiling was used in Cairo, this appears to be a mistake.

maa.org

Schattschneider, Doris (1978), "Tiling the plane with congruent pentagons", Mathematics Magazine, 51 (1): 29–44, doi:10.1080/0025570X.1978.11976672, JSTOR 2689644, MR 0493766

neilsloane.com

Goodman-Strauss, C.; Sloane, N. J. A. (2019), "A coloring-book approach to finding coordination sequences" (PDF), Acta Crystallographica Section A, 75 (1): 121–134, arXiv:1803.08530, doi:10.1107/s2053273318014481, MR 3896412, PMID 30575590, S2CID 4553572, archived from the original (PDF) on 2022-02-17, retrieved 2021-06-18

nih.gov

pubmed.ncbi.nlm.nih.gov

Goodman-Strauss, C.; Sloane, N. J. A. (2019), "A coloring-book approach to finding coordination sequences" (PDF), Acta Crystallographica Section A, 75 (1): 121–134, arXiv:1803.08530, doi:10.1107/s2053273318014481, MR 3896412, PMID 30575590, S2CID 4553572, archived from the original (PDF) on 2022-02-17, retrieved 2021-06-18
Ressouche, E.; Simonet, V.; Canals, B.; Gospodinov, M.; Skumryev, V. (December 2009), "Magnetic frustration in an iron-based Cairo pentagonal lattice", Physical Review Letters, 103 (26): 267204, arXiv:1001.0710, Bibcode:2009PhRvL.103z7204R, doi:10.1103/physrevlett.103.267204, PMID 20366341, S2CID 20752605
Zhang, Shunhong; Zhou, Jian; Wang, Qian; Chen, Xiaoshuang; Kawazoe, Yoshiyuki; Jena, Puru (February 2015), "Penta-graphene: A new carbon allotrope", Proceedings of the National Academy of Sciences of the United States of America, 112 (8): 2372–2377, Bibcode:2015PNAS..112.2372Z, doi:10.1073/pnas.1416591112, PMC 4345574, PMID 25646451

ncbi.nlm.nih.gov

Zhang, Shunhong; Zhou, Jian; Wang, Qian; Chen, Xiaoshuang; Kawazoe, Yoshiyuki; Jena, Puru (February 2015), "Penta-graphene: A new carbon allotrope", Proceedings of the National Academy of Sciences of the United States of America, 112 (8): 2372–2377, Bibcode:2015PNAS..112.2372Z, doi:10.1073/pnas.1416591112, PMC 4345574, PMID 25646451

oeis.org

Coordination sequences for the Cairo pentagonal tiling in the On-Line Encyclopedia of Integer Sequences: A219529 for pentagons, A296368 for degree-three vertices, and A008574 for degree-four vertices, retrieved 2021-06-17

patents.google.com

Moore, H. C. (July 20, 1909), Tile (US Patent 928,320)

semanticscholar.org

api.semanticscholar.org

O'Keeffe, M.; Hyde, B. G. (1980), "Plane nets in crystal chemistry", Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 295 (1417): 553–618, Bibcode:1980RSPTA.295..553O, doi:10.1098/rsta.1980.0150, JSTOR 36648, S2CID 121456259.
Macmillan, R. H. (December 1979), "Pyramids and pavements: Some thoughts from Cairo", The Mathematical Gazette, 63 (426): 251–255, doi:10.2307/3618038, JSTOR 3618038, S2CID 125608794
Kovács, Gergely; Nagy, Benedek; Turgay, Neşet Deniz (May 2021), "Distance on the Cairo pattern", Pattern Recognition Letters, 145: 141–146, Bibcode:2021PaReL.145..141K, doi:10.1016/j.patrec.2021.02.002, S2CID 233375125
Goodman-Strauss, C.; Sloane, N. J. A. (2019), "A coloring-book approach to finding coordination sequences" (PDF), Acta Crystallographica Section A, 75 (1): 121–134, arXiv:1803.08530, doi:10.1107/s2053273318014481, MR 3896412, PMID 30575590, S2CID 4553572, archived from the original (PDF) on 2022-02-17, retrieved 2021-06-18
Rollett, A. P. (September 1955), "2530. A pentagonal tessellation", Mathematical Notes, The Mathematical Gazette, 39 (329): 209, doi:10.2307/3608750, JSTOR 3608750, S2CID 250439435
Dunn, J. A. (December 1971), "Tessellations with pentagons", The Mathematical Gazette, 55 (394): 366–369, doi:10.2307/3612359, JSTOR 3612359, S2CID 118680100. Although Dunn writes that the equilateral form of the tiling was used in Cairo, this appears to be a mistake.
Morgan, Frank (2019), "My undercover mission to find Cairo tilings", The Mathematical Intelligencer, 41 (3): 19–22, doi:10.1007/s00283-019-09906-7, MR 3995312, S2CID 198468426
Banaru, A. M.; Banaru, G. A. (August 2011), "Cairo tiling and the topology of layered hydrates", Moscow University Chemistry Bulletin, 66 (3), Article 159, doi:10.3103/S0027131411030023, S2CID 96002269
Ressouche, E.; Simonet, V.; Canals, B.; Gospodinov, M.; Skumryev, V. (December 2009), "Magnetic frustration in an iron-based Cairo pentagonal lattice", Physical Review Letters, 103 (26): 267204, arXiv:1001.0710, Bibcode:2009PhRvL.103z7204R, doi:10.1103/physrevlett.103.267204, PMID 20366341, S2CID 20752605

tess-elation.co.uk

Bailey, David, "Cairo tiling", David Bailey's World of Escher-like Tessellations, retrieved 2020-12-06

uab.cat

ddd.uab.cat

Ressouche, E.; Simonet, V.; Canals, B.; Gospodinov, M.; Skumryev, V. (December 2009), "Magnetic frustration in an iron-based Cairo pentagonal lattice", Physical Review Letters, 103 (26): 267204, arXiv:1001.0710, Bibcode:2009PhRvL.103z7204R, doi:10.1103/physrevlett.103.267204, PMID 20366341, S2CID 20752605

uni-goettingen.de

resolver.sub.uni-goettingen.de

Reinhardt, Karl (1918), Über die Zerlegung der Ebene in Polygone (Doctoral dissertation) (in German), Borna-Leipzig: Druck von Robert Noske, "Vierter Typus", p. 78, and Figure 24, p. 81

web.archive.org

Goodman-Strauss, C.; Sloane, N. J. A. (2019), "A coloring-book approach to finding coordination sequences" (PDF), Acta Crystallographica Section A, 75 (1): 121–134, arXiv:1803.08530, doi:10.1107/s2053273318014481, MR 3896412, PMID 30575590, S2CID 4553572, archived from the original (PDF) on 2022-02-17, retrieved 2021-06-18