تفاوت میان نسخه‌های «چندوجهی»

(خنثی‌سازی ویرایش 33078275 از محمد هادی ۷۷ (بحث) فقط چندوجهى تعريف نشده.)
برچسب‌ها: خنثی‌سازی ویرایش با تلفن همراه ویرایش با مرورگر تلفن همراه ویرایش پیشرفته تلفن همراه
برچسب‌ها: ویرایش با تلفن همراه ویرایش با مرورگر تلفن همراه ویرایش پیشرفته تلفن همراه متن دارای ویکی‌متن نامتناظر
* {{citation|last=Ghomi|first=Mohammad|date=2018-01-01|title=Dürer's Unfolding Problem for Convex Polyhedra|journal=Notices of the American Mathematical Society|language = en|volume=65|issue=1|pages=25–27|doi=10.1090/noti1609|doi-access=free}}
* {{cite journal | title=A class of multi-symmetric polyhedra | language = en| first=Michael | last=Goldberg | journal= [[Tohoku Mathematical Journal]] | year=1937 |url=https://www.jstage.jst.go.jp/article/tmj1911/43/0/43_0_104/_article}}
* {{citation |last=Goldman |first=Ronald N.|author-link=Ron Goldman (mathematician) |editor-last=Arvo |editor-first=James |title=Graphic Gems Package: Graphics Gems II |publisher=Academic Press |language=en |year=1991 |pages=170–171 |chapter=Chapter IV.1: Area of planar polygons and volume of polyhedra}}
* {{citation
| last1 = Grünbaum
| archive-date = 2017-02-22
| url-status = dead
|language=en
}}
* {{citation
| publisher = Kluwer Acad. Publ.
| title = Proceedings of the NATO Advanced Study Institute on Polytopes: Abstract, Convex and Computational
|language=en
| year = 1994}}.
* {{citation
| year = 1994
| pages = 49 - 56
| language=en
}}.
* {{citation
| volume = 223
| year = 1999| isbn = 978-0-8218-0674-6
| language=en
}}
* {{citation
| title = Discrete and Computational Geometry: The Goodman–Pollack Festschrift
| volume = 25
| year = 2003| isbn = 978-3-642-62442-1 | citeseerx = 10.1.1.102.755 }}.
| language=en
}}.
* {{citation
| last = Grünbaum | first = Branko | author-link = Branko Grünbaum
| title-link = Convex Polytopes
| volume = 221
| language=en
| year = 2003}}.
*{{citation
| volume = 64
| year = 2009| doi-access = free
|language=en
}}. Reprinted in {{citation|title=The Best Writing on Mathematics 2010|editor-first=Mircea|editor-last=Pitici|publisher=Princeton University Press|year=2011|language=en|pages=18–31}}.
* {{cite book | last=Haeckel | first=E. | title=Art Forms in Nature | publisher=Dover Publications | series=Dover Pictorial Archive | year=2012 | isbn=978-0-486-15532-6 | url=https://books.google.com/books?id=E1nCAgAAQBAJ | ref=harv | access-date=2018-11-12 | archive-url=https://www.webcitation.org/74iD9CaTh?url=https://books.google.com/books?id=E1nCAgAAQBAJ | archive-date=16 دسامبرDecember 2018 | language=en}}
* {{citation
| last1 = Harris | first1 = J. W.
| location = New York
|publisher = Springer
| title = "Wedge". §4.5.2 in ''Handbook of Mathematics and Computational Science''}}.
|language=en}}.
* {{SpringerEOM|first=M.|last=Hazewinkel|title=Dehn invariant|language=en|id=Dehn_invariant&oldid=35803}}
* {{cite book | last=Henle | first=M. | title=A Combinatorial Introduction to Topology | publisher=Dover | series=Dover Books on Mathematics Series | year=1994 | isbn=978-0-486-67966-2 | url=https://books.google.com/books?id=S0RJYkBxowEC&pg=PA9 | ref=harv | access-date=2018-10-22 | language=en | archive-url=https://www.webcitation.org/74iD9tMla?url=https://books.google.com/books?id=S0RJYkBxowEC | archive-date=16 دسامبر 2018}}
* {{citation
| last = Hopf | first = Henning
| publisher = Wiley VCH
| year = 2000
| language=en
}}.
* {{citation
| last=Hopkins | first=Brian
|title= Resources for Teaching Discrete Mathematics: Classroom Projects, History, modules, and articles| language=en}}
* {{cite journal | last=Johnson | first=Norman W. | author-link=Norman Johnson (mathematician) | title=Convex Solids with Regular Faces | journal=Canadian Journal of Mathematics | volume=18 | year=1966 | zbl=0132.14603 | issn=0008-414X | doi=10.4153/cjm-1966-021-8| language=en}}
* {{cite book|title=Nanostructured materials for solar energy conversion|editor=Sōga, Tetsuo |chapter=Fullerene Thin Films as Photovoltaic Material|author=Katz, E. A.|year=2006 |isbn=978-0-444-52844-5|publisher=Elsevier|pages= 361–443|language=en|chapter-url=https://books.google.com/books?id=GmQR1tuk5IgC&pg=PA361|ref=Katz}}
* {{cite book | last=Kotrč | first=Ronald F. | title=THE DODECAHEDRON IN PLATO'S "TIMAEUS" | publisher=J.D. Sauerländers Verlag | journal=Rheinisches Museum für Philologie | language=en | year=1981 | 7= | url=https://www.jstor.org/stable/41245051?seq=1#page_scan_tab_contents | ref=harv | access-date=2018-10-22 | archive-url=https://www.webcitation.org/74iD9cVWk?url=https://www.jstor.org/stable/41245051?seq=1#page_scan_tab_contents | archive-date=16 دسامبر 2018}}
* {{Cite journal |title=The Topology and Combinatorics of Soccer Balls |first1=Dieter |author1-link=Dieter Kotschick |last1=Kotschick |journal=American Scientist |year=2006 |volume=94 |issue=4 |doi=10.1511/2006.60.350| language=en}}
* {{Citation
| last=Lakatos
| title=Proofs and Refutations
| publisher=[[Cambridge Technology Press]]
| year=1976}}
| language=en}}
* {{cite book | last=Lewars | first=Errol G. | title=Modeling Marvels | publisher=Springer Netherlands | publication-place=Dordrecht | year=2008 | isbn=978-1-4020-6972-7 | doi=10.1007/978-1-4020-6973-4 | ref=harv}}
* {{cite book | last=MacLeanLewars | first=K.J.MErrol G. | title=AModeling Geometric Analysis of the Platonic Solids and Other Semi-Regular PolyhedraMarvels | publisher=LovingSpringer Healing PressNetherlands | seriespublication-place=Geometric explorations seriesDordrecht | year=20072008 | isbn=978-1-9326904020-996972-67 | urldoi=https://books.google10.com1007/books?id=vINuAwAAQBAJ | ref=harv | access978-date=20181-114020-106973-4 | archive-urlref=https://www.webcitation.org/74iCuWAgX?url=https://books.google.com/books?id=vINuAwAAQBAJ harv| archive-datelanguage=16 دسامبر 2018en}}
* {{cite book | last=SenechalMacLean | first=K.J.M. | title=ShapingA Space:Geometric ExploringAnalysis Polyhedraof inthe Nature,Platonic Art,Solids and theOther GeometricalSemi-Regular ImaginationPolyhedra | publisher=SpringerLoving NewHealing YorkPress | series=EBSCOhostGeometric ebooksexplorations onlineseries | year=20132007 | isbn=978-01-387932690-9271499-56 | url=https://books.google.com/books?id=kZtCAAAAQBAJvINuAwAAQBAJ | ref=harv | access-date=2018-11-10 | archive-url=https://www.webcitation.org/74iCm8uGF74iCuWAgX?url=https://books.google.com/books?id=kZtCAAAAQBAJvINuAwAAQBAJ | language=en| archive-date=16 دسامبر 2018}}
* {{Cite book|url=https://books.google.com/books?id=nNVsHwAACAAJ |author=Mark Lehner |title= The Complete Pyramids: Solving the Ancient Mysteries |publisher=Thames & Hudson|isbn=978-0-500-28547-3|date=2008|language=en}}
* {{SpringerEOM|title=Polyhedron, abstract|id=Polyhedron,_abstract&oldid=25452|first=S.V.|last=MatveevMatvee|language=en}}
* {{citation|title=Solid Geometry|first=Joseph P.|last=McCormack|publisher=D. Appleton-Century Company| language=en|year=1931}}
* {{citation
| last1 = Meserve | first1 = B. E.
|publisher=The Mathematics Teacher
| volume = 45
| year = 1952}}.
| language=en}}.
* {{cite journal |vauthors=Mettenleiter TC, Klupp BG, Granzow H | title = Herpesvirus assembly: a tale of two membranes | journal = Curr. Opin. Microbiol. | volume = 9 | issue = 4 | year = 2006 | pmid = 16814597 | language=en | doi = 10.1016/j.mib.2006.06.013}}
* {{citation|url=http://www.openproblemgarden.org/op/d_urers_conjecture|title=Dürer's conjecture|work=Open Problem Garden|first=D. |last=Moskovich|language=en|date=June 4, 2012}}
* {{cite book | last=Nayudu | first=M.V. | title=Plant Viruses | publisher=Tata McGraw-Hill | year=2008 | language=en| isbn=978-0-07-065660-4 | url=https://books.google.com/books?id=w11opH8eqY8C&pg=PA50 | ref=harv | access-date=2018-11-12 | archive-url=https://www.webcitation.org/74iCpOLjD?url=https://books.google.com/books?id=w11opH8eqY8C | archive-date=16 دسامبر 2018}}
* {{citation
| last = Needham | first = Joseph
| publisher = Caves Books Ltd.
| year = 1986
|language=en
}}
* {{citation|title=Computational Geometry in C|journal=Computers in Physics|volume=9|issue=1|first=Joseph|last=O'Rourke|author-link=Joseph O'Rourke (professor)|year=1993|bibcode=1995ComPh...9...55O|doi=10.1063/1.4823371|language=en}}
* {{cite news| url=http://news.bbc.co.uk/1/hi/world/africa/3641516.stm | work=BBC News | title=Sudan's past uncovered | date=2004-09-09 | access-date=2010-04-12 | first=Lawrence | last=Pollard}}
* {{cite book | last=Pottmann | first=Helmut | title=Architectural geometry | publisher=Bentley Institute Press | publication-place=Exton, Pa | year=2007 | isbn=978-1-934493-04-5 | oclc=180177477 | language=en| ref=harv}}
* {{cite book | last=Pottmann | first=Helmut | last2=Asperl | first2=Andreas | last3=Hofer | first3=Michael | last4=Kilian | first4=Axel | last5=Bentley | first5=Daril | title=Architectural geometry | publisher=Bentley Institute Press | year=2007 | isbn=1-934493-04-X | language=en | oclc=180177477 | ref=harv}}
* {{citation
| last = Richeson | first = David S. | author-link = David Richeson
| title = Euler's Gem: The polyhedron formula and the birth of topology
| title-link = Euler's Gem
| year = 2008}}.
|language=en}}.
* {{cite web | first=Michael | last=Ritter | date=2003 | url=http://www.uwsp.edu/geo/faculty/ritter/geog101/textbook/connections/connections_dating_pyramids.html |language=en|title=Dating the Pyramids |url-status=dead |archive-url=https://web.archive.org/web/20080511163647/http://www.uwsp.edu/geo/faculty/ritter/geog101/textbook/connections/connections_dating_pyramids.html |archive-date=11 May 2008| access-date=15 May 2008}}
* {{Cite book |title=Art, Mathematics and Architecture for Humanistic Renaissance: the Platonic Solids|last=Sala|first=Nicoletta |year=2004|publisher=University of Italian Switzerland, Academy of Architecture, Switzerland | language=en| ref=harv | url = http://math.unipa.it/~grim/SiSala2.PDF}}
* {{cite journal | last=Sarhangi | first=Reza | title=Illustrating Abu al-Wafā' Būzjānī: Flat Images, Spherical Constructions | journal=Iranian Studies | publisher=Informa UK Limited | volume=41 | issue=4 | year=2008 | issn=0021-0862 | language=en | doi=10.1080/00210860802246184 | pages=511–523 | ref=harv}}
* {{cite book | last=Senechal | first=M. | title=Shaping Space: Exploring Polyhedra in Nature, Art, and the Geometrical Imagination | publisher=Springer New York | series=EBSCOhost ebooks online | year=2013 | isbn=978-0-387-92714-5 | url=https://books.google.com/books?id=kZtCAAAAQBAJ | ref=harv | access-date=2018-11-10 | archive-url=https://www.webcitation.org/74iCm8uGF?url=https://books.google.com/books?id=kZtCAAAAQBAJ | archive-date=16 دسامبر 2018}}
* {{cite book | last=Senechal | first=M. | title=Shaping Space: Exploring Polyhedra in Nature, Art, and the Geometrical Imagination | publisher=Springer New York | language=en | series=EBSCOhost ebooks online | year=2013 | isbn=978-0-387-92714-5 | url=https://books.google.com/books?id=kZtCAAAAQBAJ | ref=harv | access-date=2018-11-10 | archive-url=https://www.webcitation.org/74iCm8uGF?url=https://books.google.com/books?id=kZtCAAAAQBAJ | archive-date=16 دسامبر 2018}}
* {{citation| last = Shephard | first = G. C. | author-link = Geoffrey Colin Shephard| issue = 3| journal = Mathematical Proceedings of the Cambridge Philosophical Society| mr = 0390915| pages = 389–403| title = Convex polytopes with convex nets| language=en| volume = 78| year = 1975 |doi=10.1017/s0305004100051860| bibcode = 1975MPCPS..78..389S}}
* {{cite book |editor-first=F. Arthur |editor-last=Sherk |editor2-first=Peter |editor2-last=McMullen |editor3-first=Anthony C. |editor3-last=Thompson |editor4-first=Asia Ivic |editor4-last=Weiss |title=Kaleidoscopes: Selected Writings of H.S.M. Coxeter |publisher=Wiley |year=1995 |language=en |isbn=978-0-471-01003-6 |url=https://archive.org/details/kaleidoscopessel0000coxe |url-access=registration}}
** (Paper 10) {{cite journal |first=H.S.M. |last=Coxeter |title=Star Polytopes and the Schlafli Function f(α,β,γ) |journal=Elemente der Mathematik |volume=44 |issue=2 |pages=25–36 |year=1989 |url=https://eudml.org/doc/141447}}
** (Paper 2210) [https://books.google.com/books?id=fUm5Mwfx8rAC&pg=PA251 pp. 251–278] {{cite journal |first=H.S.M. |last=Coxeter |title=RegularStar Polytopes and Semithe RegularSchlafli PolytopesFunction If(α,β,γ) |journal=Math.Elemente Zeit.der Mathematik |volume=4644 |yearlanguage=1940en |doiissue=10.1007/BF011814492 |zblpages=002225–36 |year=1989 |url=https://eudml.38305org/doc/141447}} MR 2,10
** (Paper 2322) [https://books.google.com/books?id=fUm5Mwfx8rAC&pg=PA279PA251 pp. 279–312251–278] {{cite journal |author-mask=1 |first=H.S.M. |last=Coxeter |title=Regular and Semi- Regular Polytopes III |journal=Math. Zeit. |volume=18846 |issuelanguage=4en |year=19851940 |doi=10.1007/BF01161657BF01181449 |zbl=05470022.5200538305}} MR 2,10
** (Paper 2423) [https://books.google.com/books?id=fUm5Mwfx8rAC&pg=PA313PA279 pp. 313–358279–312] {{cite journal |author-mask=1 |first=H.S.M. |last=Coxeter |title=Regular and Semi-Regular Polytopes IIIII |journal=Math. Zeit. |volume=200188 |issue=14 |year=19881985 |doi=10.1007/BF01161745BF01161657 | language=en| zbl=06330547.5200652005}}
** (Paper 24) [https://books.google.com/books?id=fUm5Mwfx8rAC&pg=PA313 pp. 313–358] {{cite journal |author-mask=1 |first=H.S.M. |last=Coxeter |title=Regular and Semi-Regular Polytopes III |journal=Math. Zeit. |volume=200 |issue=1 |year=1988 |doi=10.1007/BF01161745 | language=en| zbl=0633.52006}}
* {{cite news |last=Slackman |first=Michael |date=16 November 2007 |title=In the Shadow of a Long Past, Patiently Awaiting the Future |work=The New York Times|url=https://www.nytimes.com/2008/11/17/world/middleeast/17cairo.html |access-date=17 November 2008 |quote=Deep below the Egyptian desert, archaeologists have found evidence of yet another pyramid, this one constructed 4,300 years ago to store the remains of a pharaoh’s mother. That makes 138 pyramids discovered here so far, and officials say they expect to find more.}}
* {{cite news |last=Slackman |first=Michael |date=1716 November 20082007 |title=In the Shadow of a Long Past, Patiently Awaiting the Future |work=The New York Times |url=https://www.nytimes.com/2008/11/17/world/middleeast/17cairo.html |access-date=117 MayNovember 20102008 |language=en |quote=Deep below the Egyptian desert, archaeologists have found evidence of yet another pyramid, this one constructed 4,300 years ago to store the remains of a pharaoh’s mother. That makes 138 pyramids discovered here so far, and officials say they expect to find more.}}
* {{cite news |last=Slackman |first=Michael |language=en |date=1617 November 20072008 |title=In the Shadow of a Long Past, Patiently Awaiting the Future |work=The New York Times |url=https://www.nytimes.com/2008/11/17/world/middleeast/17cairo.html |access-date=171 NovemberMay 2008 |quote=Deep below the Egyptian desert, archaeologists have found evidence of yet another pyramid, this one constructed 4,300 years ago to store the remains of a pharaoh’s mother. That makes 138 pyramids discovered here so far, and officials say they expect to find more.2010}}
* {{citation |title=An Etruscan dodecahedron|first=Amelia Carolina|last=Sparavigna|year=2012|arxiv=1205.0706}}
* {{citation
| year=2009
|url=https://books.google.com/books?id=nVx-tu596twC&pg=PA18
|language=en
}}
* {{citation|first=B. M.|last=Stewart|title=Adventures Among the Toroids: A Study of Orientable Polyhedra with Regular Faces|title-link= Adventures Among the Toroids |edition=2nd|language=en|year=1980|isbn=978-0-686-11936-4|publisher=B. M. Stewart}}
* {{cite book | last=Tanna | first=S. | title=Amazing Math: Introduction to Platonic Solids | publisher=CreateSpace Independent Publishing Platform | year=2014 | language=en| isbn=978-1-5030-8485-8 | url=https://books.google.com/books?id=8-nVrQEACAAJ | ref=harv | access-date=2018-09-15 | archive-url=https://www.webcitation.org/74iCq0awA?url=https://books.google.com/books?id=8-nVrQEACAAJ | archive-date=16 دسامبر 2018}}
* {{citation
| last = Trigg | first = Charles W.
| volume = 51
| year = 1978| doi = 10.1080/0025570X.1978.11976675
| language=en
}}.
* {{citation
| title=Monohedral idemvalent polyhedra that are toroids
| volume=67
| year=1997| s2cid=117884274
| s2cid=117884274
| language=en
}}
* {{Mathworld|urlname=EulerCharacteristic|title=Euler Characteristic|language=en|mode=cs2}}
* {{Mathworld|urlname=Polyhedron|title=Polyhedron|language=en|mode=cs2}}
* {{Mathworld|urlname=Prism|title=Prism|language=en|mode=cs2}}
* {{Mathworld|urlname=Pyramid|title=Pyramid|language=en|mode=cs2}}
* {{Mathworld|urlname=PyramidalFrustum|title=Pyramidal Frustum|language=en|mode=cs2}}
* {{Mathworld|urlname=RegularPolyhedron|title=Regular Polyhedron|language=en|mode=cs2}}
* {{Mathworld|urlname=ShephardsConjecture|title=Shephard's Conjecture|language=en|mode=cs2}}
* {{citation
| last = Wells | first = A.F.
| isbn = 0-19-855370-6
| year = 1984
|language=en
}}.
}}.
* {{citation|first=Magnus J.|last=Wenninger|author-link=Magnus Wenninger|title=Polyhedron Models|publisher=Cambridge University Press|language=en|year=1971}}
* {{citation
| last=Whiteley | first=Walter | authorlink=Walter Whiteley
| mr=621628
| title=Realizability of polyhedra
|language=en
| url=http://www.iri.upc.edu/people/ros/StructuralTopology/ST1/st1-07-a4.pdf
| year=1979}}.
| location=Berlin, New York
| series=Graduate Texts in Mathematics
| language=en
| year=1995
| volume=152}}
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* {{cite web | title=Form, Shape, and Space: Teachers' Booklet | date=2008 | url=https://www.ncetm.org.uk/public/files/271019/ULITA+Teachers+booklet.pdf | ref={{sfnref | Form, Shape, and Space: Teachers' Booklet | 2008}} | access-date=2018-10-22 | archive-url=https://www.webcitation.org/74iD6hYpU?url=https://www.ncetm.org.uk/public/files/271019/ULITA+Teachers+booklet.pdf | language=en| archive-date=16 دسامبر 2018 }}
* {{cite web | title=Geometry - mathematics | website=Encyclopedia Britannica | url=https://www.britannica.com/science/geometry | ref={{sfnref | Encyclopedia Britannica - Geometry}} | access-date=2018-09-16 | archive-url=https://www.webcitation.org/74iCmZWN4?url=https://www.britannica.com/science/geometry | language=en| archive-date=16 دسامبر 2018 }}
* {{cite web | title=Phi in Sacred Solids | website=Sacred Geometry | date=2012-11-28 | url=http://www.sacred-geometry.es/?q=en/content/phi-sacred-solids | ref={{sfnref | Sacred Geometry | 2012}} | access-date=2018-11-10 | language=en| archive-url=https://www.webcitation.org/74iCqWJtY?url=http://www.sacred-geometry.es/?q=en%2Fcontent%2Fphi-sacred-solids | archive-date=16 دسامبر 2018 }}
* {{cite web | title="Platonic solid - MATHEMATICS" | website=Encyclopedia Britannica | url=https://www.britannica.com/science/Platonic-solid | ref={{sfnref | Encyclopedia Britannica}} | access-date=2018-09-06 | archive-url=https://www.webcitation.org/74iCuu3ar?url=https://www.britannica.com/science/Platonic-solid | language=en| archive-date=16 دسامبر 2018 }}
* {{cite web | title=Formula Derivations for Polyhedra | website=Whistler Alley Mathematics | date=2016-01-21 | url=http://whistleralley.com/polyhedra/derivations.htm | ref={{sfnref | Whistler Alley Mathematics - Formula Derivations for Polyhedra | 2016}} | access-date=2018-11-24 | language=en | archive-url=https://www.webcitation.org/74iD1cJGx?url=http://whistleralley.com/polyhedra/derivations.htm | archive-date=16 دسامبر 2018 }}
* {{cite web | title=Platonic Solids | website=Whistler Alley Mathematics | date=2011-12-29 | url=http://whistleralley.com/polyhedra/platonic.htm | ref={{sfnref | Whistler Alley Mathematics | 2011}} | access-date=2018-10-22 | archive-url=https://www.webcitation.org/74iD4BC54?url=http://whistleralley.com/polyhedra/platonic.htm | language=en| archive-date=16 دسامبر 2018 }}
* {{cite web | title=The Nobel Moment: Dan Shechtman | language=en | website=NIST | date=2017-05-02 | url=https://www.nist.gov/content/nist-and-nobel/nobel-moment-dan-shechtman | ref={{sfnref | NIST | 2017}} | access-date=2018-11-12 | archive-url=https://www.webcitation.org/74iCwl4sr?url=https://www.nist.gov/content/nist-and-nobel/nobel-moment-dan-shechtman | archive-date=16 دسامبر 2018 }}
* [https://www.math.technion.ac.il/S/rl/docs/uniform.pdf Uniform Solution for Uniform Polyhedra]{{Webarchive|url=https://web.archive.org/web/20151127053535/http://www.math.technion.ac.il/S/rl/docs/uniform.pdf | language=en| date=2015-11-27}}
* {{cite web|url=http://www.orchidpalms.com/polyhedra/cupolas/cupola1.html|title=cupolas|website=www.orchidpalms.com| language=en| access-date=21 April 2018}}
* {{Citation
[http://www.latinamericanstudies.org/aztecs/sacrifice.htm The Enigma of Aztec Sacrifice]". ''Natural History'', April 1977. Vol. 86
|title=The Enigma of Aztec Sacrifice
[ |url=http://www.latinamericanstudies.org/aztecs/sacrifice.htm The Enigma of Aztec Sacrifice]". ''Natural History'', April 1977. Vol. 86
|journal=Natural History
|date=April 1977
|volume=86
|language=en
}}
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