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== References == {{reflist|refs= <ref name=ak>{{cite book | last1 = Alexander | first1 = Daniel C. | last2 = Koeberlin | first2 = Geralyn M. | year = 2014 | title = Elementary Geometry for College Students | url = https://books.google.com/books?id=EN_KAgAAQBAJ&pg=PA403 | edition = 6th | publisher = Cengage Learning | page = 403 | isbn = 978-1-285-19569-8 }}</ref> <ref name=berman>{{cite journal | last = Berman | first = Martin | year = 1971 | title = Regular-faced convex polyhedra | journal = Journal of the Franklin Institute | volume = 291 | issue = 5 | pages = 329–352 | doi = 10.1016/0016-0032(71)90071-8 | mr = 290245 }}</ref> <ref name=cromwell>{{cite book | last = Cromwell | first = Peter R. | year = 1997 | title = Polyhedra | publisher = Cambridge University Press | url = https://archive.org/details/polyhedra0000crom/page/55 | page = 55 | isbn = 978-0-521-55432-9 }}</ref> <ref name=erickson>{{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&pg=PA62 | page = 62 | isbn = 978-1-61444-509-8 }}</ref> <ref name=fhnp>{{cite journal | last1 = Finbow | first1 = Arthur S. | last2 = Hartnell | first2 = Bert L. | last3 = Nowakowski | first3 = Richard J. | last4 = Plummer | first4 = Michael D. | author4-link = Michael D. Plummer | doi = 10.1016/j.dam.2009.08.002 | issue = 8 | journal = Discrete Applied Mathematics | mr = 2602814 | pages = 894–912 | title = On well-covered triangulations. III | volume = 158 | year = 2010 | doi-access = free }}</ref> <ref name=grunbaum-2003>{{citation | last = Grünbaum | first = Branko | author-link = Branko Grünbaum | contribution = 13.1 Steinitz's theorem | edition = 2nd | isbn = 0-387-40409-0 | pages = 235–244 | publisher = Springer-Verlag | series = [[Graduate Texts in Mathematics]] | title = Convex Polytopes | title-link = Convex Polytopes | volume = 221 | year = 2003 }}</ref> <ref name=hs>{{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 = Taylor & Francis | isbn = 978-1-4665-5464-1 | url = https://books.google.com/books?id=b2fjR81h6yEC&pg=PA252 | page = 252 }}</ref> <ref name=johnson>{{cite journal | last = Johnson | first = Norman W. | authorlink = Norman W. Johnson | year = 1966 | title = Convex polyhedra with regular faces | journal = [[Canadian Journal of Mathematics]] | volume = 18 | pages = 169–200 | doi = 10.4153/cjm-1966-021-8 | mr = 0185507 | s2cid = 122006114 | zbl = 0132.14603| doi-access = free }}</ref> <ref name=kappraff>{{cite book | last = Kappraff | first = Jay | year = 1991 | edition = 2nd | title = Connections: The Geometric Bridge Between Art and Science | publisher = [[World Scientific]] | url = https://books.google.com/books?id=tz76s0ZGFiQC&pg=PA475 | page = 475 | isbn = 978-981-281-139-4 }}</ref> <ref name=livio>{{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-year = 2002 | edition = First trade paperback | year = 2003 | publisher = [[Random House|Broadway Books]] | location = New York City | isbn = 0-7679-0816-3 | pages = 70–71 }}</ref> <ref name=maekawa>{{cite book | last = Maekawa | first = Jun | year = 2022 | title = Art & Science of Geometric Origami: Create Spectacular Paper Polyhedra, Waves, Spirals, Fractals, and More! | url = https://books.google.com/books?id=Kq-kEAAAQBAJ&pg=PA42 | page = 42 | publisher = [[Tuttle Publishing|Tuttle]] | isbn = 978-1-4629-2398-4 }}</ref> <ref name=mclean>{{cite journal | last = McLean | first = K. Robin | year = 1990 | title = Dungeons, dragons, and dice | journal = The Mathematical Gazette | volume = 74 | issue = 469 | pages = 243–256 | doi = 10.2307/3619822 | jstor = 3619822 | s2cid = 195047512 }}</ref> <ref name=negami>{{cite book | last = Negami | first = S. | year = 2016 | contribution = Faithful Embeddings of Planar Graphs on Orientable Closed Surfaces | contribution-url = https://books.google.com/books?id=HarWCwAAQBAJ&pg=PA250 | page = 250 | editor-last1 = Širáň | editor-first1 = Jozef | editor-last2 = Jajcay | editor-first2 = Robert | title = Symmetries in Graphs, Maps, and Polytopes: 5th SIGMAP Workshop, West Malvern, UK, July 2014 | series = Springer Proceedings in Mathematics & Statistics | volume = 159 | publisher = Springer | doi = 10.1007/978-3-319-30451-9 | isbn = 978-3-319-30451-9 }}</ref> <ref name=oh>{{cite book | last1 = O'Keeffe | first1 = Michael | last2 = Hyde | first2 = Bruce G. | title = Crystal Structures: Patterns and Symmetry | year = 2020 | url = https://books.google.com/books?id=_MjPDwAAQBAJ&pg=PA141 | page = 141 | publisher = [[Dover Publications]] | isbn = 978-0-486-83654-6 }}</ref> <ref name=polya>{{cite book | last = Polya | first = G. | year = 1954 | title = Mathematics and Plausible Reasoning: Induction and analogy in mathematics | url = https://books.google.com/books?id=-TWTcSa19jkC&pg=PA138 | page = 138 | publisher = Princeton University Press | isbn = 0-691-02509-6 }}</ref> <ref name=radii>{{harvtxt|Coxeter|1973}} Table I(i), pp. 292–293. See the columns labeled <math>{}_0\!\mathrm{R}/\ell</math>, <math>{}_1\!\mathrm{R}/\ell</math>, and <math>{}_2\!\mathrm{R}/\ell</math>, Coxeter's notation for the circumradius, midradius, and inradius, respectively, also noting that Coxeter uses <math>2\ell</math> as the edge length (see p. 2).</ref> <ref name=smith>{{cite book | last = Smith | first = James | year = 2000 | title = Methods of Geometry | url = https://books.google.com/books?id=B0khWEZmOlwC&pg=PA392 | page = 392 | publisher = [[John Wiley & Sons]] | isbn = 978-1-118-03103-2 }}</ref> <ref name=timofeenko-2010>{{cite journal | last = Timofeenko | first = A. V. | year = 2010 | title = Junction of Non-composite Polyhedra | journal = St. Petersburg Mathematical Journal | volume = 21 | issue = 3 | pages = 483–512 | doi = 10.1090/S1061-0022-10-01105-2 | url = https://www.ams.org/journals/spmj/2010-21-03/S1061-0022-10-01105-2/S1061-0022-10-01105-2.pdf }}</ref> <ref name=trigg>{{cite journal | last = Trigg | first = Charles W. | author-link = Charles W. Trigg | issue = 1 | journal = Mathematics Magazine | jstor = 2689647 | pages = 55–57 | title = An Infinite Class of Deltahedra | volume = 51 | year = 1978 | doi = 10.1080/0025570X.1978.11976675 }}</ref> <ref name=wd>{{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 }}</ref> <ref name=ziegler>{{cite book | last = Ziegler | first = Günter M. | author-link = Günter M. Ziegler | contribution = Chapter 4: Steinitz' Theorem for 3-Polytopes | isbn = 0-387-94365-X | pages = 103–126 | publisher = Springer-Verlag | series = [[Graduate Texts in Mathematics]] | title = Lectures on Polytopes | volume = 152 | year = 1995 }}</ref> }}
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