Editing Cube (section)

== References ==
{{reflist|refs=

<ref name=alexandrov>{{cite book
 | last = Alexandrov | first = A. D. | author-link = Aleksandr Danilovich Aleksandrov
 | contribution = 8.1 Parallelohedra
 | contribution-url = https://books.google.com/books?id=R9vPatr5aqYC&pg=PA349
 | pages = 349–359
 | publisher = Springer
 | title = Convex Polyhedra | title-link = Convex Polyhedra (book)
 | year = 2005
}}</ref>

<ref name=an>{{cite book
 | last1 = Alsina | first1 = Claudi
 | last2 = Nelsen | first2 = Roger B.
 | year = 2015
 | title = A Mathematical Space Odyssey: Solid Geometry in the 21st Century
 | publisher = [[Mathematical Association of America]]
 | url = https://books.google.com/books?id=FEl2CgAAQBAJ&pg=PA85
 | page = 85
 | isbn = 978-1-61444-216-5
 | volume = 50
}}</ref>

<ref name=aw>{{cite book
 | last1 = Aldous | first1 = Joan
 | last2 = Wilson | first2 = Robin
 | year = 2000
 | title = Graphs and Applications: An Introductory Approach
 | url = https://books.google.com/books?id=1qRvTI_oWUAC&pg=PA382
 | publisher = Springer
 | isbn = 978-1-85233-259-4
}}</ref>

<ref name=ball>{{cite book
 | last = Ball | first = Keith
 | year = 2010
 | editor-last = Gowers | editor-first = Timothy | editor-link = Timothy Gowers
 | contribution = High-dimensional geometry and its probabilistic analogues
 | title = The Princeton Companion to Mathematics | title-link = The Princeton Companion to Mathematics
 | publisher = Princeton University Press
 | isbn = 9781400830398
 | page = [https://books.google.com/books?id=ZOfUsvemJDMC&pg=PA671 671]
}}</ref>

<ref name=barnes>{{cite book
 | last = Barnes | first = John
 | year = 2012
 | title = Gems of Geometry
 | edition = 2nd
 | url = https://books.google.com/books?id=7YCUBUd-4BQC&pg=PA82
 | page = 82
 | publisher = Springer
 | isbn = 978-3-642-30964-9
 | doi = 10.1007/978-3-642-30964-9
}}</ref>

<ref name=barrow>{{cite book|title= Impossibility: The Limits of Science and the Science of Limits|author=John D. Barrow|author-link=John D. Barrow|publisher=Oxford University Press|year=1999|isbn=9780195130829|page=14|url=https://books.google.com/books?id=0jRa1a4pD5IC&pg=PA14}}</ref>

<ref name=berman-graph>{{cite book
 | last = Berman | first = Leah
 | editor-last1 = Connelly | editor-first1 = Robert
 | editor-last2 = Weiss | editor-first2 = Asia
 | editor-last3 = Whiteley | editor-first3 = Walter
 | title = Rigidity and Symmetry
 | series = Fields Institute Communications
 | contribution = Geometric Constructions for Symmetric 6-Configurations
 | contribution-url = https://books.google.com/books?id=_n4eBAAAQBAJ&pg=PA84
 | page = 84
 | year = 2014
 | volume = 70
 | publisher = Springer
 | doi = 10.1007/978-1-4939-0781-6
 | isbn = 978-1-4939-0781-6
}}</ref>

<ref name=biegasiewicz>{{cite journal| last1 = Biegasiewicz | first1 = Kyle | last2 = Griffiths | first2 = Justin | last3 = Savage | first3 = G. Paul | last4 = Tsanakstidis | first4 = John | last5 = Priefer | first5 = Ronny | year = 2015 | title = Cubane: 50 years later | journal = Chemical Reviews| volume = 115 | issue = 14 | pages = 6719–6745 | doi=10.1021/cr500523x | pmid=26102302}}</ref>

<ref name=calter>{{cite book
 | last1 = Calter | first1 = Paul
 | last2 = Calter | first2 = Michael
 | year = 2011
 | title = Technical Mathematics
 | url = https://books.google.com/books?id=4fHwTZK3JEIC&pg=PA197
 | page = 197
 | publisher = [[John Wiley & Sons]]
| isbn = 978-0-470-53492-2
 }}</ref>

<ref name=cc>{{cite journal
 | last1 = Chilton | first1 = B. L.
 | last2 = Coxeter | first2 = H. S. M. | author2-link = Harold Scott MacDonald Coxeter
 | doi = 10.1080/00029890.1963.11992147
 | journal = [[The American Mathematical Monthly]]
 | jstor = 2313051
 | mr = 157282
 | pages = 946–951
 | title = Polar zonohedra
 | volume = 70
 | year = 1963
}}</ref>

<ref name=cmsi>{{cite conference
 | last1 = Chin | first1 = Daniel Jie Yuan Chin
 | last2 = Mohamed | first2 = Ahmad Sufril Azlan
 | last3 = Shariff | first3 = Khairul Anuar
 | last4 = Ishikawa | first4 = Kunio
 | editor-last1 = Zaman | editor-first1 = Halimah Badioze
 | editor-last2 = Smeaton | editor-first2 = Alan
 | editor-last3 = Shih | editor-first3 = Timothy
 | editor-last4 = Velastin | editor-first4 = Sergio
 | editor-last5 = Terutoshi | editor-first5 = Tada
 | editor-last6 = Jørgensen | editor-first6 = Bo Nørregaard
 | editor-last7 = Aris | editor-first7 = Hazleen Aris
 | editor-last8 = Ibrahim | editor-first8 = Nazrita Ibrahim
 | date = 23–25 November 2021
 | conference = 7th International Visual Informatics Conference
 | title = Advances in Visual Informatics
 | location = [[Kajang, Malaysia]]
 | contribution = GPU-Accelerated Enhanced Marching Cubes 33 for Fast 3D Reconstruction of Large Bone Defect CT Images
 | contribution-url = https://books.google.com/books?id=GclOEAAAQBAJ&pg=PA376
 | page = 376
}}</ref>

<ref name=coxeter>{{cite book
 | last = Coxeter | first = H.S.M. | author-link = Harold Scott MacDonald Coxeter
 | year = 1973
 | title = Regular Polytopes | title-link = Regular Polytopes (book)
 | publisher = [[Dover Publications]]
 | place = New York
 | edition = 3rd
 | pages = [http://books.google.com/books?id=2ee7AQAAQBAJ&pg=PA122 122–123]
}} See §1.8 Configurations.</ref>

<ref name=cp>{{cite journal
 | last1 = Cunningham | first1 = Gabe
 | last2 = Pellicer | first2 = Daniel
 | year = 2024
 | title = Finite 3-orbit polyhedra in ordinary space, II
 | journal = Boletín de la Sociedad Matemática Mexicana
 | volume = 30 | issue = 32
 | doi = 10.1007/s40590-024-00600-z
| doi-access = free
 }} See p. 276.</ref>

<ref name=cr>{{cite book
 | last1 = Cundy | first1 = H. Martyn | author1-link = Martyn Cundy
 | last2 = Rollett | first2 = A.P.
 | edition = 2nd
 | location = Oxford
 | mr = 0124167
 | publisher = Clarendon Press
 | title = Mathematical models
 | title-link = Mathematical Models (Cundy and Rollett)
 | year = 1961
 | contribution = 3.2 Duality
 | pages = 78–79
}}</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/309
 | page = 309
 | isbn = 978-0-521-55432-9
}}</ref>

<ref name=cundy>{{cite journal
 | last = Cundy | first = H. Martyn
 | year = 1956
 | title = 2642. Unitary Construction of Certain Polyhedra
 | journal = [[The Mathematical Gazette]]
 | volume = 40 | issue = 234 | pages = 280&ndash;282
 | jstor = 3609622
 | doi = 10.2307/3609622
}}</ref>

<ref name=cz>{{cite book
 | last1 = Chartrand | first1 = Gary
 | last2 = Zhang | first2 = Ping
 | year = 2012
 | title = A First Course in Graph Theory
 | publisher = [[Dover Publications]]
 | url = https://books.google.com/books?id=zA_CAgAAQBAJ&pg=PA25
 | page = 25
| isbn = 978-0-486-29730-9
 }}</ref>

<ref name=erdahl>{{cite journal
 | last = Erdahl | first = R. M.
 | doi = 10.1006/eujc.1999.0294
 | issue = 6
 | journal = European Journal of Combinatorics
 | mr = 1703597
 | pages = 527–549
 | title = Zonotopes, dicings, and Voronoi's conjecture on parallelohedra
 | volume = 20
 | year = 1999| doi-access = free
 }}. Voronoi conjectured that all tilings of higher dimensional spaces by translates of a single [[convex polytope]] are combinatorially equivalent to Voronoi tilings, and Erdahl proves this in the special case of [[zonotope]]s. But as he writes (p.&nbsp;429), Voronoi's conjecture for dimensions at most four was already proven by Delaunay. For the classification of three-dimensional parallelohedra into these five types, see {{cite journal
 | last1 = Grünbaum | first1 = Branko | author1-link = Branko Grünbaum
 | last2 = Shephard | first2 = G. C. | author2-link = Geoffrey Colin Shephard
 | doi = 10.1090/S0273-0979-1980-14827-2
 | issue = 3
 | journal = [[Bulletin of the American Mathematical Society]]
 | mr = 585178
 | pages = 951–973
 | series = New Series
 | title = Tilings with congruent tiles
 | volume = 3
 | year = 1980| doi-access = free
}}</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=fowler>{{cite journal|title=Mathematics in Science Fiction: Mathematics as Science Fiction|first=David|last=Fowler|journal=World Literature Today|volume=84|issue=3|year=2010|pages=48–52|doi=10.1353/wlt.2010.0188 |jstor=27871086|s2cid=115769478 |quote=Robert Heinlein's "And He Built a Crooked House," published in 1940, and Martin Gardner's "The No-Sided Professor," published in 1946, are among the first in science fiction to introduce readers to the Moebius band, the Klein bottle, and the hypercube (tesseract).}}</ref>

<ref name=french>{{cite journal
 | last = French | first = Doug
 | year = 1988
 | title = Reflections on a Cube
 | journal = Mathematics in School
 | volume = 17 | issue = 4 | pages = 30&ndash;33
 | jstor = 30214515
}}</ref>

<ref name=fuchs>{{cite journal
 | last = Fuchs | first1 = Dmitry
 | last2 = Fuchs | first2 = Ekaterina
 | journal = Moscow Mathematical Journal
 | volume = 7 | issue = 2 | year = 2007 | pages = 265–279
 | title = Closed Geodesics on Regular Polyhedra
 | doi = 10.17323/1609-4514-2007-7-2-265-279
}}</ref>

<ref name=fuller>{{cite book
 | last = Fuller | first = Buckimster
 | title = Synergetics: Explorations in the Geometry of Thinking
 | year = 1975
 | publisher = MacMillan Publishing
 | url = https://books.google.com/books?id=AKDgDQAAQBAJ&pg=PA173
 | page = 173
| isbn = 978-0-02-065320-2
 }}</ref>

<ref name=greene>{{cite journal | last = Greene | first = N | year = 1986 | title = Environment mapping and other applications of world projections | journal = IEEE Computer Graphics and Applications | volume = 6 | issue = 11| pages = 21–29 | doi = 10.1109/MCG.1986.276658 | s2cid = 11301955 }}</ref>

<ref name=gruber>{{cite book
 | last = Gruber | first = Peter M.
 | contribution = Chapter 16: Volume of Polytopes and Hilbert's Third Problem
 | doi = 10.1007/978-3-540-71133-9
 | isbn = 978-3-540-71132-2
 | mr = 2335496
 | pages = 280–291
 | publisher = Springer, Berlin
 | series = Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]
 | title = Convex and Discrete Geometry
 | volume = 336
 | year = 2007
}}</ref>

<ref name=grunbaum-1997>{{cite journal
 | last = Grünbaum | first = Branko | authorlink = Branko Grünbaum 
 | year = 1997
 | title = Isogonal Prismatoids
 | journal = Discrete & Computational Geometry
 | volume = 18 | issue = 1 | pages = 13&ndash;52
 | doi = 10.1007/PL00009307
}}</ref>

<ref name=grunbaum-2003>{{cite book
 | 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=haeckel>{{cite book
 | last = Haeckel | first = E. | author-link = Ernst Haeckel
 | year = 1904
 | title = [[Kunstformen der Natur]]
 | language = de
}} See [http://www.biolib.de/haeckel/kunstformen/index.html here] for an online book.</ref>

<ref name=hall>{{cite journal
 | last = Hall | first = T. Proctor | authorlink = T. Proctor Hall
 | year = 1893
 | jstor = 2369565
 | title = The projection of fourfold figures on a three-flat
 | journal = [[American Journal of Mathematics]]
 | volume = 15
 | issue = 2 | pages = 179–189
| doi = 10.2307/2369565 }}</ref>

<ref name=hart>{{cite conference
 | last = Hart | first = George
 | editor-last1 = Goldstein | editor-first1 = Susan
 | editor-last2 = McKenna | editor-first2 = Douglas
 | editor-last3 = Fenyvesi | editor-first3 = Kristóf
 | date = 16–20 July 2019
 | location = [[Linz, Austria]] 
 | title = Bridges 2019 Conference Proceedings
 | contribution = Max Brücknerʼs Wunderkammer of Paper Polyhedra
 | contribution-url = https://archive.bridgesmathart.org/2019/bridges2019-59.pdf
 | isbn =  978-1-938664-30-4
 | publisher = Tessellations Publishing, [[Phoenix, Arizona]]
}}</ref>

<ref name=heath>{{cite book
 | last = Heath | first = Thomas L. | authorlink = 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
 | pages = 262, 478, 480
}}</ref>

<ref name=helvajian>{{cite book|editor1-last= Helvajian|editor1-first= Henry|title= Small Satellites: Past, Present, and Future|year= 2008|publisher= Aerospace Press|location= El Segundo, Calif.|isbn= 978-1-884989-22-3|editor2-first= Siegfried W.|editor2-last= Janson|page=159}}</ref>

<ref name=hh>{{cite journal
 | last1 = Harary | first1 = F. | authorlink1 = Frank Harary
 | last2 = Hayes | first2 = J. P. | last3 = Wu | first3 = H.-J.
 | title = A survey of the theory of hypercube graphs
 | journal = Computers & Mathematics with Applications
 | volume = 15
 | issue = 4
 | pages = 277–289
 | year = 1988
 | doi = 10.1016/0898-1221(88)90213-1| hdl = 2027.42/27522
 | hdl-access = free
}}</ref>

<ref name=hhlnqr>{{cite arXiv
 | last1 = Hasan | first1 = Masud 
 | last2 = Hossain | first2 = Mohammad M.
 | last3 = López-Ortiz | first3 = Alejandro
 | last4 = Nusrat | first4 = Sabrina
 | last5 = Quader | first5 = Saad A.
 | last6 = Rahman | first6 = Nabila
 | title = Some New Equiprojective Polyhedra
 | date = 2010 
 | class = cs.CG 
 | eprint = 1009.2252 
 }}</ref>

<ref name=hoffmann>{{cite book
 | last = Hoffmann | first = Frank
 | year = 2020
 | title = Introduction to Crystallography
 | url = https://books.google.com/books?id=16H0DwAAQBAJ&pg=PA35
 | page = 35
 | publisher = Springer
 | doi = 10.1007/978-3-030-35110-6
 | isbn = 978-3-030-35110-6
}}</ref>

<ref name=holme>{{cite book
 | last = Holme | first = A.
 | year = 2010
 | title = Geometry: Our Cultural Heritage
 | publisher = [[Springer Science+Business Media|Springer]]
 | url = https://books.google.com/books?id=zXwQGo8jyHUC
 | isbn = 978-3-642-14441-7
 | doi = 10.1007/978-3-642-14441-7
}}</ref>

<ref name=hp>{{cite journal
 | last1 = Horvat | first1 = Boris
 | last2 = Pisanski | first2 = Tomaž | author2-link = Tomaž Pisanski
 | doi = 10.1016/j.disc.2009.11.035 | doi-access = free
 | issue = 12
 | journal = [[Discrete Mathematics (journal)|Discrete Mathematics]]
 | mr = 2610282
 | pages = 1783–1792
 | title = Products of unit distance graphs
 | volume = 310
 | year = 2010
}}</ref>

<ref name=hr-w>{{cite book
 | title = Geometry: Reteaching Masters
 | publisher = Holt Rinehart & Winston
 | isbn = 9780030543289
 | year = 2001
 | page = 74
}}</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="hut">{{cite arXiv
 | last1 = Diaz | first1 = Giovanna
 | last2 = O'Rourke | first2 = Joseph | author2-link = Joseph O'Rourke (professor)
 | title = Hypercube unfoldings that tile <math>\mathbb{R}^3</math> and <math>\mathbb{R}^2</math>
 | year = 2015
 | class = cs.CG
 | eprint = 1512.02086
}}</ref>

<ref name=inchbald>{{cite journal
 | last = Inchbald | first = Guy
 | year = 2006
 | title = Facetting Diagrams
 | journal = [[The Mathematical Gazette]]
 | volume = 90 | issue = 518 | pages = 253&ndash;261
 | doi = 10.1017/S0025557200179653
 | jstor = 40378613
}}</ref>

<ref name=jessen>{{cite journal
 | last = Jessen | first = Børge | author-link = Børge Jessen
 | issue = 2
 | journal = Nordisk Matematisk Tidskrift
 | jstor = 24524998
 | mr = 0226494
 | pages = 90–96
 | title = Orthogonal icosahedra
 | volume = 15
 | year = 1967
}}</ref>

<ref name=jeon>{{cite journal
 | last = Jeon | first = Kyungsoon
 | year = 2009
 | title = Mathematics Hiding in the Nets for a CUBE
 | journal = Teaching Children Mathematics
 | volume = 15 | issue = 7 | pages = 394&ndash;399
 | doi = 10.5951/TCM.15.7.0394
 | jstor = 41199313
}}</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
}} See table II, line 3.</ref>

<ref name=joyner>{{cite book
 | last = Joyner | first = David
 | year = 2008
 | title = Adventures in Group Theory: Rubik's Cube, Merlin's Machine, and Other Mathematical Toys
 | url = https://books.google.com/books?id=6an_DwAAQBAJ&pg=PA76
 | page = 76
 | edition = 2nd
 | isbn = 978-0-8018-9012-3
 | publisher = The Johns Hopkins University Press
}}</ref>

<ref name=jwy>{{cite journal
 | last1 = Jerrard | first1 = Richard P.
 | last2 = Wetzel | first2 = John E.
 | last3 = Yuan | first3 = Liping
 | title = Platonic passages
 | journal = [[Mathematics Magazine]]
 | date = April 2017
 | volume = 90 | issue = 2 | pages = 87–98
 | publisher = [[Mathematical Association of America]]
 | location = Washington, DC
 | doi = 10.4169/math.mag.90.2.87
 | s2cid = 218542147
}}</ref>

<ref name=kane>{{cite book
 | last = Kane | first = Richard
 | year = 2001
 | title = Reflection Groups and Invariant Theory
 | url = http://books.google.com/books?id=KmL1uuiMyFUC&pg=PA16
 | page = 16
}}</ref>

<ref name=kemp>{{cite journal|title=Dali's dimensions|first=Martin|last=Kemp|journal=[[Nature (journal)|Nature]]|volume=391|issue=27|date=1 January 1998|page=27|doi=10.1038/34063|bibcode=1998Natur.391...27K|doi-access=free}}</ref>

<ref name=khattar>{{cite book
 | last = Khattar | first = Dinesh
 | year = 2008
 | title = Guide to Objective Arithmetic
 | url = https://books.google.com/books?id=BoBCOYuOlzkC&pg=PA377
 | page = 377
 | publisher = [[Pearson Education]]
 | edition = 2nd
 | isbn = 978-81-317-1682-3
}}</ref>

<ref name=kl>{{cite book
 | last1 = Kitaev | first1 = Sergey
 | last2 = Lozin | first2 = Vadim
 | title = Words and Graphs
 | url = https://books.google.com/books?id=EXH_CgAAQBAJ&pg=PA171
 | page = 171
 | year = 2015 
 | doi = 10.1007/978-3-319-25859-1
 | isbn = 978-3-319-25859-1
}}</ref>

<ref name=knstv>{{cite journal
 | last1 = Kov´acs | first1 = Gergely
 | last2 = Nagy | first2 = Benedek Nagy
 | last3 = Stomfai | first3 = Gergely
 | last4 = Turgay | first4 = Nes¸et Deni̇z
 | last5 = Vizv´ari | first5 = B´ela
 | year = 2021
 | title = On Chamfer Distances on the Square and Body-Centered CubicGrids: An Operational Research Approach
 | doi = 10.1155/2021/5582034
 | journal = Mathematical Problems in Engineering
 | pages = 1&ndash;9
 | doi-access = free
}}</ref>

<ref name=kozachok>{{cite conference
 | last = Kozachok | first = Marina
 | contribution = Perfect prismatoids and the conjecture concerning with face numbers of centrally symmetric polytopes
 | pages = 46–49
 | publisher = P.G. Demidov Yaroslavl State University, International B.N. Delaunay Laboratory
 | title = Yaroslavl International Conference "Discrete Geometry" dedicated to the centenary of A.D.Alexandrov (Yaroslavl, August 13-18, 2012)
 | url = https://www.dcglab.uniyar.ac.ru/sites/default/files/papers/Alexandrov2012Thesis.pdf#page=46
 | year = 2012
}}</ref>

<ref name=linti>{{cite book
 | last = Linti | first = G.
 | editor-last1 = Reedijk | editor-first1 = J.
 | editor-last2 = Poeppelmmeier | editor-first2 = K.
 | year = 2013
 | title = Comprehensive Inorganic Chemistry II: From Elements to Applications
 | contribution = Catenated Compounds - Group 13 [Al, Ga, In, Tl]
 | publisher = Newnes
 | url = https://books.google.com/books?id=_4C7oid1kQQC&pg=RA7-PA41
 | page = 41
| isbn = 978-0-08-096529-1
 }}</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 = 1st trade paperback
 | year = 2003
 | publisher = [[Random House|Broadway Books]]
 | location = New York City
 | isbn = 978-0-7679-0816-0
 | page = 147
}}</ref>

<ref name=lm>{{cite journal
 | last1 = Lagarias | first1 = J. C. | author1-link = Jeffrey Lagarias
 | last2 = Moews | first2 = D.
 | doi = 10.1007/BF02574064
 | issue = 3–4
 | journal = [[Discrete & Computational Geometry]]
 | mr = 1318797
 | pages = 573–583
 | title = Polytopes that fill <math>\mathbb{R}^n</math> and scissors congruence
 | volume = 13
 | year = 1995| doi-access = free
}}</ref>

<ref name=ls>{{cite journal
 | last1 = Langer | first1 = Joel C.
 | last2 = Singer | first2 = David A.
 | journal = [[Milan Journal of Mathematics]]
 | title = Reflections on the Lemniscate of Bernoulli: The Forty-Eight Faces of a Mathematical Gem
 | volume = 78 | pages = 643–682 | year = 2010
 | doi = 10.1007/s00032-010-0124-5
}}</ref>

<ref name=lunnon>{{cite book
 | last = Lunnon | first = W. F.
 | contribution = Symmetry of Cubical and General Polyominoes
 | editor-last = Read | editor-first = Ronald C.
 | title = Graph Theory and Computing
 | place = New York
 | publisher = [[Academic Press]]
 | year = 1972
 | pages = 101–108
 | isbn = 978-1-48325-512-5
 | url = https://books.google.com/books?id=ja7iBQAAQBAJ&pg=PA101
}}</ref>

<ref name=lutzen>{{cite journal
 | last = Lützen | first = Jesper
 | year = 2010
 | title = The Algebra of Geometric Impossibility: Descartes and Montucla on the Impossibility of the Duplication of the Cube and the Trisection of the Angle
 | url = https://onlinelibrary.wiley.com/doi/10.1111/j.1600-0498.2009.00160.x
 | journal = Centaurus
 | language = en
 | volume = 52 | issue = 1 | pages = 4–37
 | doi = 10.1111/j.1600-0498.2009.00160.x
}}</ref>

<ref name=ly>{{cite book
 | last1 = Gross | first1 = Jonathan L.
 | last2 = Yellen | first2 = Yellen
 | year = 2006
 | title = Graph Theory and Its Applications, Second Edition
 | url = https://books.google.com/books?id=-7Q_POGh-2cC?&pg=PA273
 | page = 273
 | publisher = Taylor & Francis
}}</ref>

<ref name=marar>{{cite book
 | last = Marat | first = Ton
 | title = A Ludic Journey into Geometric Topology
 | year = 2022
 | url = https://books.google.com/books?id=aPGGEAAAQBAJ&pg=PA112
 | page = 112
 | publisher = Springer
 | doi = 10.1007/978-3-031-07442-4
 | isbn = 978-3-031-07442-4
}}</ref>

<ref name=march>{{cite journal
 | last = March | first = Lionel
 | title = Renaissance mathematics and architectural proportion in Alberti's De re aedificatoria
 |journal=Architectural Research Quarterly
 |date=1996
 |volume=2 |issue=1 |pages=54–65
 |doi=10.1017/S135913550000110X
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}}</ref>

<ref name=masalski>{{cite journal
 | last = Masalski | first = William J.
 | title = Polycubes
 | journal = The Mathematics Teacher
 | volume = 70 | issue = 1 | year = 1977 | pages = 46–50
 | doi = 10.5951/MT.70.1.0046
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<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
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 | s2cid = 195047512
}} See p. 247.</ref>

<ref name=moore>{{cite journal
 | last = Moore | first = Kimberly
 | year = 2018
 | title = Minecraft Comes to Math Class
 | journal = Mathematics Teaching in the Middle School
 | volume = 23 | issue = 6 | pages = 334–341
 | doi = 10.5951/mathteacmiddscho.23.6.0334
 | jstor = 10.5951/mathteacmiddscho.23.6.0334
}}</ref>

<ref name=mk>{{cite book
 | last1 = Mills | first1 = Steve
 | last2 = Kolf | first2 = Hillary
 | year = 1999
 | title = Maths Dictionary
 | publisher = Heinemann
 | url = https://books.google.com/books?id=dvFfTAR6XwEC&pg=PA16
 | isbn = 978-0-435-02474-1
 | page = 16
}}</ref>

<ref name=ns>{{cite journal
 | last1 = Nelson | first1 = Roice
 | last2 = Segerman | first2 = Henry
 | title = Visualizing hyperbolic honeycombs
 | journal = Journal of Mathematics and the Arts
 | year = 2017
 | volume = 11 | issue = 1 | pages = 4–39
 | doi = 10.1080/17513472.2016.1263789
| arxiv = 1511.02851
 }}</ref>

<ref name=padmanabhan>{{cite book |title=Sleeping Beauties in Theoretical Physics |last=Padmanabhan |first=Thanu |chapter=The Grand Cube of Theoretical Physics |publisher=Springer |year=2015 |pages=1–8 |isbn=978-3319134420 }}</ref>

<ref name=poo-sung>{{cite journal
 | last = Poo-Sung
 | first = Park, Poo-Sung
 | year = 2016
 | title = Regular polytope distances
 | journal = [[Forum Geometricorum]]
 | volume = 16
 | pages = 227–232
 | url = http://forumgeom.fau.edu/FG2016volume16/FG201627.pdf
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 | access-date = 2016-05-24
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 }}</ref>

<ref name=popko>{{cite book|title=Divided Spheres: Geodesics and the Orderly Subdivision of the Sphere|first=Edward S.|last=Popko|publisher=CRC Press|year=2012|isbn=9781466504295|pages=100–101|url=https://books.google.com/books?id=WLAFlr1_2S4C&pg=PA100}}</ref>

<ref name=ps>{{cite book
 | last1 = Pisanski | first1 = Tomaž
 | last2 = Servatius | first2 = Brigitte
 | title = Configuration from a Graphical Viewpoint
 | year = 2013
 | url = https://books.google.com/books?id=3vnEcMCx0HkC&pg=PA21
 | page = 21
 | publisher = Springer
 | isbn = 978-0-8176-8363-4
 | doi = 10.1007/978-0-8176-8364-1
}}</ref>

<ref name="pucc">{{cite conference
 | contribution = Polycube unfoldings satisfying Conway's criterion
 | last1 = Langerman | first1 = Stefan | author1-link = Stefan Langerman
 | last2 = Winslow | first2 = Andrew
 | title = 19th Japan Conference on Discrete and Computational Geometry, Graphs, and Games (JCDCG^3 2016)
 | year = 2016
 | contribution-url = http://andrewwinslow.com/papers/polyunfold-jcdcggg16.pdf
}}</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=rajwade>{{cite book
 | last = Rajwade | first = A. R.
 | title = Convex Polyhedra with Regularity Conditions and Hilbert's Third Problem
 | series = Texts and Readings in Mathematics
 | year = 2001
 | url = https://books.google.com/books?id=afJdDwAAQBAJ&pg=PA84
 | publisher = Hindustan Book Agency
 | page = 84&ndash;89
 | isbn = 978-93-86279-06-4
 | doi = 10.1007/978-93-86279-06-4
}}</ref>

<ref name=rudolph>{{cite book
 | last = Rudolph | first = Michael
 | year = 2022
 | title = The Mathematics of Finite Networks: An Introduction to Operator Graph Theory
 | url = https://books.google.com/books?id=NIdoEAAAQBAJ&pg=PA25
 | page = 25
 | publisher = [[Cambridge University Press]]
 | doi = 10.1007/9781316466919
 | doi-broken-date = 1 November 2024
 | isbn = 9781316466919
}}</ref>

<ref name=rz>{{cite book
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 | last2 = Zeilten | first2 = Steve
 | year = 2006
 | title = Hidden New York: A Guide to Places that Matter
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 | page = 77
 | isbn = 978-0-8135-3890-7
 | publisher = Rutgers University Press
}}</ref>

<ref name=senechal>{{cite book
 | last = Senechal | first = Marjorie
 | year = 1989
 | contribution = A Brief Introduction to Tilings
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 | editor-last = Jarić | editor-first = Marko
 | title = Introduction to the Mathematics of Quasicrystals
 | publisher = [[Academic Press]]
 | page = 12
}}</ref>

<ref name=shephard>In higher dimensions, however, there exist parallelopes that are not zonotopes. See e.g. {{cite journal
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 | doi = 10.1112/S0025579300008652
 | journal = Mathematika
 | mr = 365332
 | pages = 261–269
 | title = Space-filling zonotopes
 | volume = 21
 | year = 1974| issue = 2
 }}</ref>

<ref name=skilling>{{cite journal|first=John|last=Skilling|title=Uniform Compounds of Uniform Polyhedra|journal=[[Mathematical Proceedings of the Cambridge Philosophical Society]]|volume=79|issue=3|pages=447–457|year=1976|doi=10.1017/S0305004100052440|bibcode=1976MPCPS..79..447S |mr=0397554}}</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=sod>{{cite journal
 | last1 = Slobodan | first1 = Mišić
 | last2 = Obradović | first2 = Marija
 | last3 = Ðukanović | first3 = Gordana
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 | year = 2015
 | journal = Journal for Geometry and Graphics
 | volume = 19
 | issue = 1
 | pages = 79–91
 | url = https://www.heldermann-verlag.de/jgg/jgg19/j19h1misi.pdf
}}</ref>

<ref name=sriraman>{{cite book
 | last = Sriraman | first = Bharath
 | editor1-first = Bharath | editor1-last = Sriraman
 | editor2-first = Viktor | editor2-last = Freiman
 | editor3-first = Nicole | editor3-last = Lirette-Pitre
 | title = Interdisciplinarity, Creativity, and Learning: Mathematics With Literature, Paradoxes, History, Technology, and Modeling
 | volume = 7 | series = The Montana Mathematics Enthusiast: Monograph Series in Mathematics Education
 | year = 2009
 | isbn = 9781607521013
 | publisher = Information Age Publishing, Inc.
 | contribution = Mathematics and literature (the sequel): imagination as a pathway to advanced mathematical ideas and philosophy
 | pages = 41–54
}}</ref>

<ref name=thomson>{{cite book|first=James|last=Thomson|author-link=James Thomson (mathematician)|title=An Elementary Treatise on Algebra: Theoretical and Practical|year=1845|location=London|publisher=Longman, Brown, Green, and Longmans|page=4|url=https://archive.org/details/anelementarytre01thomgoog/page/n15}}</ref>

<ref name=timofeenko-2010>{{cite journal
 | last = Timofeenko | first = A. V.
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 | 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=tisza>{{cite book
 | last = Tisza | first = Miklós
 | year = 2001
 | title = Physical Metallurgy for Engineers
 | url = https://books.google.com/books?id=y1eTDQRdI2wC&pg=PA45
 | page = 45
 | publisher = [[ASM International (society)|ASM International]]
 | location = [[Materials Park, Ohio]]
 | isbn = 978-1-61503-241-9
}}</ref>

<ref name=trudeau>{{cite book
 | last = Trudeau | first = Richard J.
 | title = Introduction to Graph Theory
 | year = 1976
 | isbn = 978-0-486-67870-2
 | publisher = Dover Publications
 | url = http://books.google.com/books?id=eRLEAgAAQBAJ&pg=PA122
 | page = 122
}}</ref>

<ref name=twelveessay>{{cite book
 | last = Coxeter | first = H. S. M. | authorlink = Harold Scott MacDonald Coxeter
 | year = 1968
 | title = The Beauty of Geometry: Twelve Essays
 | url = https://books.google.com/books?id=p4o-Uf-i-IUC&pg=PA212
 | page = 167
 | publisher = [[Dover Publications]]
 | isbn = 978-0-486-40919-1
}} See table III.</ref>

<ref name=vm>{{cite book |title=Infrared Thermal Imaging: Fundamentals, Research and Applications |first1=Michael |last1=Vollmer |first2=Klaus-Peter |last2=Möllmann |publisher=[[John Wiley & Sons]] |date=2011 |isbn=9783527641550 |pages=36–38 |url=https://books.google.com/books?id=b-MqbyPwAuoC&pg=PA36}}</ref>

<ref name=vxac>{{cite book
 | last1 = Viana | first1 = Vera
 | last2 = Xavier | first2 = João Pedro
 | last3 = Aires | first3 = Ana Paula
 | last4 = Campos | first4 = Helena
 | contribution = Interactive Expansion of Achiral Polyhedra
 | editor-last = Cocchiarella | editor-first = Luigi
 | year = 2019
 | title = ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics 40th Anniversary - Milan, Italy, August 3-7, 2018
 | series = Advances in Intelligent Systems and Computing
 | volume = 809
 | publisher = Springer
 | doi = 10.1007/978-3-319-95588-9
 | page = 1123
| isbn = 978-3-319-95587-2
 }} See Fig. 6.</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=yackel>{{cite conference
 | last = Yackel | first = Carolyn
 | title = Proceedings of Bridges 2009: Mathematics, Music, Art, Architecture, Culture
 | editor-last1 = Kaplan | editor-first1 = Craig | editor-link1 = Craig S. Kaplan
 | editor-last2 = Sarhangi | editor-first2 = Reza
 | location = [[Banff, Alberta]], Canada
 | date = 26–30 July 2013
 | contribution = Marking a Physical Sphere with a Projected Platonic Solid
 | contribution-url = https://archive.bridgesmathart.org/2009/bridges2009-123.pdf
 | pages = 123&ndash;130
 | isbn = 978-0-96652-020-0
}}</ref>

<ref name=zeeman>{{cite journal
 | last = Zeeman | first = E. C. | author-link = Christopher Zeeman
 | date = July 2002
 | doi = 10.2307/3621846
 | issue = 506
 | journal = [[The Mathematical Gazette]]
 | jstor = 3621846
 | pages = 241–247
 | title = On Hilbert's third problem
 | volume = 86
}}</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>

}}