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== References == === Footnotes === {{notelist|group="lower-alpha"}} === Notes === {{reflist|30em}} === Bibliographies === {{refbegin|30em}} * {{cite book | last = Barnes | first = John | year = 2012 | title = Gems of Geometry | edition = 2nd | url = https://books.google.com/books?id=7YCUBUd-4BQC | publisher = Springer | doi = 10.1007/978-3-642-30964-9 | isbn = 978-3-642-30964-9 }} * {{cite book | last1 = Benz | first1 = Klaus-Werner | last2 = Neumann | first2 = Wolfgang | year = 2014 | title = Introduction to Crystal Growth and Characterization | publisher = Wiley | isbn = 978-3-527-31840-7 }} * {{cite journal | last = Berman | first = Martin | doi = 10.1016/0016-0032(71)90071-8 | journal = Journal of the Franklin Institute | mr = 290245 | pages = 329–352 | title = Regular-faced convex polyhedra | volume = 291 | year = 1971| issue = 5 }} * {{cite book | last = Bickle | first = Allan | year = 2020 | title = Fundamentals of Graph Theory | url = https://books.google.com/books?id=2sbVDwAAQBAJ | publisher = [[American Mathematical Society]] | isbn = 978-1-4704-5549-1 }} * {{cite book | last1 = Brigaglia | first1 = Aldo | last2 = Palladino | first2 = Nicla | last3 = Vaccaro | first3 = Maria Alessandra | year = 2018 | editor1-last = Emmer | editor1-first = Michele | editor2-last = Abate | editor2-first = Marco | contribution = Historical notes on star geometry in mathematics, art and nature | doi = 10.1007/978-3-319-93949-0_17 | pages = 197–211 | publisher = Springer International Publishing | title = Imagine Math 6: Between Culture and Mathematics | isbn = 978-3-319-93948-3 }} * {{cite journal | last1 = Buker | first1 = W. E. | last2 = Eggleton | first2 = R. B. | title = The Platonic Solids (Solution to problem E2053) | journal = [[American Mathematical Monthly]] | volume = 76 | issue = 2 | year = 1969 | page = 192 | jstor = 2317282 | doi = 10.2307/2317282}} * {{cite book | last = Cann | first = Alan | year = 2012 | title = Principles of Molecular Virology | edition = 5th | url = https://books.google.com/books?id=mDbsN9LvE8gC | isbn = 978-0-12384939-7 | publisher = Academic Press }} * {{cite book | last1 = Chancey | first1 = C. C. | last2 = O'Brien | first2 = M. C. M. | year = 1997 | title = The Jahn-Teller Effect in C<sub>60</sub> and Other Icosahedral Complexes | url = https://books.google.com/books?id=wcQIEAAAQBAJ&pg=PA13 | page = 13 | publisher = [[Princeton University Press]] | isbn = 978-0-691-22534-0 }} *{{cite book | last1 = Chudnovsky | first1 = Maria | author1-link = Maria Chudnovsky | last2 = Seymour | first2 = Paul | author2-link = Paul Seymour (mathematician) | chapter= The structure of claw-free graphs | mr = 2187738 | pages = 153–171 | publisher = Cambridge University Press | series =London Mathematical Society Lecture Note Series (327) |editor=Bridget S. Webb | title = Surveys in combinatorics 2005 |chapter-url = http://www.math.princeton.edu/~mchudnov/claws_survey.pdf | year = 2005 |isbn=978-0-511-73488-5 }} * {{cite book | last = Coxeter | first = H. S. M. | author-link = Harold Scott MacDonald Coxeter | title = [[Regular Polytopes (book)|Regular Polytopes]] | edition = 3rd | year = 1973 | publisher = Dover Publications | isbn = 0-486-61480-8 | pages = 16–17 | contribution = 2.1 Regular polyhedra; 2.2 Reciprocation | contribution-url = https://books.google.com/books?id=iWvXsVInpgMC&pg=PA16 | mr = 0370327 }} * {{cite book | last1 = Coxeter | first1 = H.S.M. | author1-link = Harold Scott MacDonald Coxeter | author-mask1 = 3 | last2 = du Val | first2 = P. | author2-link = Patrick du Val | last3 = Flather | first3 = H. T. | last4 = Petrie | first4 = J. F. | author4-link = John Flinders Petrie | year = 1938 | title = [[The Fifty-Nine Icosahedra]] | publisher = University of Toronto Studies (Mathematical Series) | volume = 6 }} * {{cite book | last1 = Coxeter | first1 = H.S.M. | author-mask1 = 3 | last2 = du Val | first2 = P. | author-mask2 = 3 | last3 = Flather | first3 = H. T. | author-mask3 = 3 | last4 = Petrie | first4 = J. F. | author-mask4 = 3 | title = The Fifty-Nine Icosahedra | title-link = The Fifty-Nine Icosahedra | publisher = Tarquin | edition = 3rd | isbn = 978-1-899618-32-3 | mr = 676126 | year = 1999 | orig-date = 1938 }} * {{cite book | last = Cromwell | first = Peter R. | title = Polyhedra | year = 1997 | url = https://archive.org/details/polyhedra0000crom | publisher = [[Cambridge University Press]] | isbn = 978-0-521-55432-9 }} * {{cite journal | last = Cundy | first = H. Martyn | year = 1952 | title = Deltahedra | journal = The Mathematical Gazette | volume = 36 | issue = 318 | pages = 263–266 | doi = 10.2307/3608204 | jstor = 3608204 | s2cid = 250435684 }} * {{cite book | last1 = Dennis | first1 = L. | last2 = McNair | first2 = J. Brender | last3 = Woolf | first3 = N. J. | last4 = Kauffman | first4 = L. H. | year = 2018 | editor-last1 = McNair | editor-first1 = Jytte Brender | editor-last2 = Dennis | editor-first2 = Lynnclaire | editor-last3 = Kauffman | editor-first3 = Louis H. | title = Mereon Matrix, The: Everything Connected Through (K)nothing | chapter = The Context – Form Informing Function | chapter-url = https://books.google.com/books?id=4hVeDwAAQBAJ&pg=PA143 | publisher = [[World Scientific]] | isbn = 978-981-323-357-7 }} * {{cite book | last1 = Dronskowski | first1 = Richard | last2 = Kikkawa | first2 = Shinichi | last3 = Stein | first3 = Andreas | year = 2017 | title = Handbook of Solid State Chemistry, 6 Volume Set | publisher = John Sons & Wiley | url = https://books.google.com/books?id=e0VBDwAAQBAJ | isbn = 978-3-527-69103-6 }} * {{cite book | last = Erickson | first = Martin | year = 2011 | title = Beautiful Mathematics | publisher = [[Mathematical Association of America]] | url = https://books.google.com/books?id=LgeP62-ZxikC | isbn = 978-1-61444-509-8 }} * {{cite book | last1 = Fallat | first1 = Shaun M. | last2 = Hogben | first2 = Lesley | editor-last = Hogben | editor-first = Leslie | year = 2014 | title = Handbook of Linear Algebra | url = https://books.google.com/books?id=8hnYCwAAQBAJ | contribution = Minimum Rank, Maximum Nullity, and Zero Forcing Number of Graphs | contribution-url = https://books.google.com/books?id=8hnYCwAAQBAJ&pg=SA46 | publisher = CRC Press | isbn = 978-1-4665-0728-9 }} * {{cite book | last1 = Flanagan | first1 = Kieran | last2 = Gregory | first2 = Dan | year = 2015 | title = Selfish, Scared and Stupid: Stop Fighting Human Nature and Increase Your Performance, Engagement and Influence | publisher = [[John Wiley & Sons]] | url = https://books.google.com/books?id=hViuEAAAQBAJ | isbn = 978-0-7303-1279-6 }} * {{cite journal | last1 = Gallardo | first1 = J. | last2 = Pérez-Illana | first2 = M. | last3 = Martín-González | first3 = N. | last4 = San Martín | first4 = C. | title = Adenovirus Structure: What Is New? | journal = International Journal of Molecular Sciences | volume = 22 | issue = 10 | date = May 2021 | page = 5240 | pmid = 34063479 |pmc=8156859 | doi = 10.3390/ijms22105240 | doi-access = free }} * {{cite book | last = Gray | first = Hermann | year = 2018 | title = A History of Abstract Algebra: From Algebraic Equations to Modern Algebra | url = https://books.google.com/books?id=gl1oDwAAQBAJ | publisher = Springer | isbn = 978-3-319-94772-3 | doi = 10.1007/978-3-319-94772-3 | doi-broken-date = 14 March 2025 }} * {{cite book | last = Haeckel | first = E. | author-link = Ernst Haeckel | year = 1904 | title = [[Kunstformen der Natur]] | lang = de }} See [http://www.biolib.de/haeckel/kunstformen/index.html here] for an online book. * {{cite book | last1 = Herrmann | first1 = Diane L. | last2 = Sally | first2 = Paul J. | year = 2013 | title = Number, Shape, & Symmetry: An Introduction to Number Theory, Geometry, and Group Theory | publisher = CRC Press | isbn = 978-1-4665-5464-1 | url = https://books.google.com/books?id=b2fjR81h6yEC }} * {{cite book | last = Heath | first = Thomas L. | author-link = Thomas Little Heath | year = 1908 | title = The Thirteen Books of Euclid's Elements | edition = 3rd | publisher = [[Cambridge University Press]] | url = https://archive.org/details/thirteenbookseu03heibgoog/page/480 }} * {{cite book | last = Herz-Fischler | first = Roger | title = A Mathematical History of the Golden Number | publisher = Courier Dover Publications | year = 2013 | isbn = 978-0-486-15232-5 | url = https://books.google.com/books?id=aYjXZJwLARQC }} * {{cite journal | last = Hofmeister | first = H. | year = 2004 | title = Fivefold Twinned Nanoparticles | journal = Encyclopedia of Nanoscience and Nanotechnology | volume = 3 | pages = 431–452 }} * {{cite journal | last = Hopkins | first = Brian | year = 2004 | title = Hamiltonian paths on Platonic graphs | journal = [[International Journal of Mathematics and Mathematical Sciences]] | volume = 2004 | issue = 30 | pages = 1613–1616 | doi = 10.1155/S0161171204307118 | doi-access = free }} * {{cite journal | last = Inchbald | first = Guy | year = 2006 | title = Facetting Diagrams | journal = [[The Mathematical Gazette]] | volume = 90 | issue = 518 | pages = 253–261 | doi = 10.1017/S0025557200179653 | jstor = 40378613 }} * {{cite journal | last = Johnson | first = Norman W. | author-link = Norman Johnson (mathematician) | doi = 10.4153/cjm-1966-021-8 | journal = [[Canadian Journal of Mathematics]] | mr = 0185507 | pages = 169–200 | title = Convex polyhedra with regular faces | volume = 18 | year = 1966 | zbl = 0132.14603 }} * {{cite journal | last = Gallian | first = Joseph A. | author-link = Joseph Gallian | journal = Electronic Journal of Combinatorics | mr = 1668059 | page = Dynamic Survey 6, 43 pp. (389 pp. in 18th ed.) (electronic) | title = A dynamic survey of graph labeling | url = http://www.combinatorics.org/ojs/index.php/eljc/article/viewFile/DS6/pdf | volume = 5 | year = 1998 }} * {{cite book | last = Kappraff | first = Jay | year = 1991 | edition = 2nd | title = Connections: The Geometric Bridge Between Art and Science | publisher = [[World Scientific]] | isbn = 978-981-281-139-4 }} * {{cite journal | last = Kotschick | first = Dieter | date = 2006 | title = The Topology and Combinatorics of Soccer Balls | url = https://www.americanscientist.org/article/the-topology-and-combinatorics-of-soccer-balls | journal = [[American Scientist]] | volume = 94 | issue = 4 | page = 350 | doi = 10.1511/2006.60.350 }} * {{cite book | last = Klein | first = Felix | author-link = Felix Klein | title = Lectures on the ikosahedron and the solution of equations of the fifth degree | year = 1888 | publisher = Courier Corporation | url = http://digital.library.cornell.edu/cgi/t/text/text-idx?c=math;cc=math;view=toc;subview=short;idno=03070001 | isbn = 978-0-486-49528-6 | postscript =,}} Dover edition, translated from {{cite book |last =Klein |first =Felix |title =Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen vom fünften Grade |url =https://archive.org/details/vorlesungenberd00kleigoog |publisher =Teubner |year =1884 }} * {{cite book | last = Livio | first = Mario | author-link = Mario Livio | title = The Golden Ratio: The Story of Phi, the World's Most Astonishing Number | url = https://books.google.com/books?id=bUARfgWRH14C | orig-date = 2002 | edition = 1st trade paperback | year = 2003 | publisher = [[Random House|Broadway Books]] | location = New York City | isbn = 978-0-7679-0816-0 }} * {{cite book | last = MacLean | first = Kenneth J. M. | year = 2007 | title = A Geometric Analysis of the Platonic Solids and Other Semi-Regular Polyhedra | publisher = Loving Healing Press | isbn = 978-1-932690-99-6 }} * {{cite journal | last = Minas-Nerpel | first = Martina | year = 2007 | title = A Demotic Inscribed Icosahedron from Dakhleh Oasis | journal = The Journal of Egyptian Archaeology | volume = 93 | issue = 1 | pages = 137–148 | jstor = 40345834 | doi = 10.1177/030751330709300107 }} * {{cite book | last = Pugh | first = Anthony | year = 1976a | title = Polyhedra: A Visual Approach | url = https://books.google.com/books?id=IDDxpYQTR7kC | publisher = University of California Press | isbn = 978-0-520-03056-5 }} * {{cite book | last = Pugh | first = Anthony | author-mask = 3 | isbn = 978-0-520-03055-8 | publisher = University of California Press | title = An Introduction to Tensegrity | url = https://books.google.com/books?id=McEOfJu3NQAC | year = 1976b }} * {{cite book | last = Rotman | first = Joseph | year = 1998 | title = Galois Theory | series = Universitext | url = https://books.google.com/books?id=0kHhBwAAQBAJ | publisher = Springer | edition = 2nd | isbn = 978-1-4612-0617-0 | doi = 10.1007/978-1-4612-0617-0 }} * {{cite book | last = Shavinina | first = Larisa V. | year = 2013 | title = The Routledge International Handbook of Innovation Education | publisher = Routledge | isbn = 978-0-203-38714-6 }} * {{cite book | last = Seidel | first = J. J. | editor-last1 = Corneil | editor-first1 = D. G. | editor-last2 = Mathon | editor-first2 = R. | year = 1991 | title = Geometry and Combinatorics | url = https://books.google.com/books?id=brziBQAAQBAJ | publisher = Academic Press | isbn = 978-1-4832-6800-2 }} * {{cite book | last = Senechal | first = Marjorie | year = 1989 | contribution = A Brief Introduction to Tilings | contribution-url = https://books.google.com/books?id=OToVjZW9CKMC | editor-last = Jarić | editor-first = Marko | title = Introduction to the Mathematics of Quasicrystals | publisher = [[Academic Press]] | page = 12 }} * {{cite book | last = Silvester | first = John R. | year = 2001 | title = Geometry: Ancient and Modern | publisher = Oxford University Publisher }} * {{cite book | last = Simmons | first = George F. | title = Calculus Gems: Brief Lives and Memorable Mathematics | publisher = Mathematical Association of America | year = 2007 | isbn = 978-0-88385-561-4 }} * {{cite book | last = Smith | first = David E. | year = 1958 | title = History of Mathematics | volume = 2 | publisher = Dover Publications | isbn = 0-486-20430-8 | url = https://books.google.com/books?id=uTytJGnTf1kC }} * {{cite journal | last = Spokoyny | first = A. M. | author-link = Alexander M. Spokoyny | year = 2013 | title = New Ligand Platforms Featuring Boron-Rich Clusters as Organomimetic Sbstituents | journal = Pure and Applied Chemistry | volume = 85 | issue = 5 | pages = 903–919 | doi = 10.1351/PAC-CON-13-01-13 | pmc = 3845684 | pmid=24311823 }} * {{cite book | last = Stillwell | first = John | editor-last1 = Axler | editor-first1 = S. | editor-last2 = Ribet | editor-first2 = K. A. | year = 2005 | title = The Four Pillars of Geometry | series = Undergraduate Texts in Mathematics | contribution = Transformations | contribution-url = https://books.google.com/books?id=I1QPQic_PxwC | publisher = Springer | doi = 10.1007/0-387-29052-4 | isbn = 978-0-387-29052-2 }} * {{cite book | last1 = Strauss | first1 = James H. | last2 = Strauss | first2 = Ellen G. | title = Viruses and Human Disease | chapter = The Structure of Viruses | publisher = Elsevier | year = 2008 | pages = 35–62 | doi = 10.1016/b978-0-12-373741-0.50005-2 | pmc = 7173534 | isbn = 978-0-12-373741-0 | s2cid = 80803624 }} * {{cite book | last = Sutton | first = Daud | title = Platonic & Archimedean Solids | series = Wooden Books | publisher = Bloomsbury Publishing USA | year = 2002 | isbn = 978-0-8027-1386-5 | url = https://books.google.com/books?id=vgo7bTxDmIsC }} * {{cite book | last1 = Steeb | first1 = Willi-hans | last2 = Hardy | first2 = Yorick | last3 = Tanski | first3 = Igor | title = Problems And Solutions For Groups, Lie Groups, Lie Algebras With Applications | date = 2012 | publisher = World Scientific Publishing Company | isbn = 978-981-310-411-2 | url = https://books.google.com/books?id=UdI7DQAAQBAJ | language = en }} * {{cite conference | last = Tsuruta | first = Naoya | year = 2024 | editor-last = Takenouchi | editor-first = Kazuki | title = ICGG 2024 - Proceedings of the 21st International Conference on Geometry and Graphics | series = Lecture Notes on Data Engineering and Communications Technologies | contribution = Polyhedral Realization as Deltahedra Using Subgroup Isomorphism Test | contribution-url = https://books.google.com/books?id=kLckEQAAQBAJ&pg=PA108 | volume = 1 | publisher = Springer | isbn = 978-3-031-71225-8 | doi = 10.1007/978-3-031-71225-8 }} * {{cite journal | last = Verheyen | first = H. F. | doi = 10.1016/0898-1221(89)90160-0 | doi-access = | issue = 1–3 | journal = [[Computers and Mathematics with Applications]] | mr = 0994201 | pages = 203–250 | title = The complete set of Jitterbug transformers and the analysis of their motion | volume = 17 | year = 1989 }} * {{cite book | last1 = Walter | first1 = Steurer | last2 = Deloudi | first2 = Sofia | year = 2009 | title = Crystallography of Quasicrystals: Concepts, Methods and Structures | series = Springer Series in Materials Science | volume = 126 | url = https://books.google.com/books?id=nVx-tu596twC&pg=PA50 | page = 50 | isbn = 978-3-642-01898-5 | doi = 10.1007/978-3-642-01899-2 }} * {{cite book | last = Wells | first = David | location = London | page = 161 | publisher = Penguin | title = The Penguin Dictionary of Curious and Interesting Geometry | year = 1991 }} * {{cite book | last = Wenninger | first = Magnus J. | year = 1971 | title = Polyhedron Models | publisher = [[Cambridge University Press]] }} * {{cite journal | last = Whyte | first = L. L. | doi = 10.1080/00029890.1952.11988207 | journal = [[The American Mathematical Monthly]] | jstor = 2306764 | mr = 50303 | pages = 606–611 | title = Unique arrangements of points on a sphere | volume = 59 | year = 1952| issue = 9 }} {{refend}}
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