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Tr. Mat. Inst. Steklova, 2002, Volume 239, Pages 146–169 (Mi tm365)  

This article is cited in 7 scientific papers (total in 7 papers)

Extension Theorem in the Theory of Isohedral Tilings and Its Applications

N. P. Dolbilina, V. S. Makarovb

a Steklov Mathematical Institute, Russian Academy of Sciences
b Peoples Friendship University of Russia

Abstract: A detailed proof is given for one of the basic theorems in the theory of isohedral tilings, the extension theorem, which describes necessary and sufficient conditions under which a given polyhedron admits an isohedral tiling of a space of constant curvature.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2002, 239, 136–158

Bibliographic databases:
UDC: 514.174+514.87+512.817.7
Received in March 2002

Citation: N. P. Dolbilin, V. S. Makarov, “Extension Theorem in the Theory of Isohedral Tilings and Its Applications”, Discrete geometry and geometry of numbers, Collected papers. Dedicated to the 70th birthday of professor Sergei Sergeevich Ryshkov, Tr. Mat. Inst. Steklova, 239, Nauka, MAIK Nauka/Inteperiodika, M., 2002, 146–169; Proc. Steklov Inst. Math., 239 (2002), 136–158

Citation in format AMSBIB
\Bibitem{DolMak02}
\by N.~P.~Dolbilin, V.~S.~Makarov
\paper Extension Theorem in the Theory of Isohedral Tilings and Its Applications
\inbook Discrete geometry and geometry of numbers
\bookinfo Collected papers. Dedicated to the 70th birthday of professor Sergei Sergeevich Ryshkov
\serial Tr. Mat. Inst. Steklova
\yr 2002
\vol 239
\pages 146--169
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm365}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1975141}
\zmath{https://zbmath.org/?q=an:1068.52027}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2002
\vol 239
\pages 136--158


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Dolbilin N., Schulte E., “The local theorem for monotypic tilings”, Electron. J. Combin., 11:2 (2004), R7, 19 pp.  mathscinet  zmath  isi
    2. N. P. Dolbilin, “Properties of Faces of Parallelohedra”, Proc. Steklov Inst. Math., 266 (2009), 105–119  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    3. L. N. Romakina, “Simple partitions of a hyperbolic plane of positive curvature”, Sb. Math., 203:9 (2012), 1310–1341  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. N. P. Dolbilin, “Parallelohedra: a retrospective and new results”, Trans. Moscow Math. Soc., 73 (2012), 207–220  mathnet  crossref  mathscinet  zmath  elib
    5. M. Deza, M. Dutour Sikirić, M. I. Shtogrin, “Fullerenes and disk-fullerenes”, Russian Math. Surveys, 68:4 (2013), 665–720  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. A. A. Gavrilyuk, “A Class of Affinely Equivalent Voronoi Parallelohedra”, Math. Notes, 95:5 (2014), 625–633  mathnet  crossref  crossref  mathscinet  isi  elib
    7. Dolbilin N., “Delone sets with congruent clusters”, Struct. Chem., 27:6, SI (2016), 1725–1732  crossref  isi  elib  scopus
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