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Volumn 46, Issue 4, 2011, Pages 799-818

Upper Bound on the Packing Density of Regular Tetrahedra and Octahedra

Author keywords

Hilbert problem; Octahedron; Packing; Regular solid; Tetrahedron; Upper bound

Indexed keywords


EID: 80053654552     PISSN: 01795376     EISSN: 14320444     Source Type: Journal    
DOI: 10.1007/s00454-010-9304-x     Document Type: Article
Times cited : (22)

References (18)
  • 1
    • 80053627011 scopus 로고    scopus 로고
    • ebooks@adelaide. edu. Translated by J. L. Stocks
    • Aristotle: On the Heavens, vol. III. ebooks@adelaide. edu. Translated by J. L. Stocks.
    • Aristotle: On the Heavens , vol.III
  • 3
    • 52549094495 scopus 로고    scopus 로고
    • A dense packing of regular tetrahedra
    • Chen, E. R.: A dense packing of regular tetrahedra. Discrete Comput. Geom. 40, 214 (2008).
    • (2008) Discrete Comput. Geom. , vol.40 , pp. 214
    • Chen, E.R.1
  • 4
    • 77954865409 scopus 로고    scopus 로고
    • Dense crystalline dimer packings of regular tetrahedra
    • Chen, E. R., Engel, M., Glotzer, S.: Dense crystalline dimer packings of regular tetrahedra. Discrete Comput. Geom. 44, 253 (2010).
    • (2010) Discrete Comput. Geom. , vol.44 , pp. 253
    • Chen, E.R.1    Engel, M.2    Glotzer, S.3
  • 5
    • 33746083618 scopus 로고    scopus 로고
    • Packing, tiling, and covering with tetrahedra
    • Conway, J. H., Torquato, S.: Packing, tiling, and covering with tetrahedra. Proc. Natl. Acad. Sci. USA 103(28), 10612 (2006).
    • (2006) Proc. Natl. Acad. Sci. USA , vol.103 , Issue.28 , pp. 10612
    • Conway, J.H.1    Torquato, S.2
  • 7
    • 72049096936 scopus 로고    scopus 로고
    • Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra
    • Haji-Akbari, A., Engel, M., Keys, A., Zheng, X.: Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra. Nature 462, 773 (2009).
    • (2009) Nature , vol.462 , pp. 773
    • Haji-Akbari, A.1    Engel, M.2    Keys, A.3    Zheng, X.4
  • 8
    • 22044441063 scopus 로고    scopus 로고
    • A proof of the Kepler conjecture
    • Hales, T. C.: A proof of the Kepler conjecture. Ann. Math. Second Ser. 162, 1065 (2005).
    • (2005) Ann. Math. Second Ser. , vol.162 , pp. 1065
    • Hales, T.C.1
  • 11
    • 84966205029 scopus 로고
    • The densest lattice packing of tetrahedra
    • Hoylman, D. J.: The densest lattice packing of tetrahedra. Bull. Am. Math. Soc. 76, 135 (1970).
    • (1970) Bull. Am. Math. Soc. , vol.76 , pp. 135
    • Hoylman, D.J.1
  • 14
    • 77954863997 scopus 로고    scopus 로고
    • Dense periodic packings of tetrahedra with small repeating units
    • Kallus, Y., Elser, V., Gravel, S.: Dense periodic packings of tetrahedra with small repeating units. Discrete Comput. Geom. 44, 245 (2010).
    • (2010) Discrete Comput. Geom. , vol.44 , pp. 245
    • Kallus, Y.1    Elser, V.2    Gravel, S.3
  • 15
    • 0039702930 scopus 로고
    • Which tetrahedra fill space?
    • Senechal, M.: Which tetrahedra fill space? Math. Mag. 54(5), 227 (1981).
    • (1981) Math. Mag. , vol.54 , Issue.5 , pp. 227
    • Senechal, M.1
  • 16
    • 70350075655 scopus 로고    scopus 로고
    • Dense packings of polyhedra: Platonic and archimedean solids
    • 041104
    • Torquato, S., Jiao, Y.: Dense packings of polyhedra: Platonic and archimedean solids. Phys. Rev. E 80, 041104 (2009).
    • (2009) Phys. Rev. E , vol.80
    • Torquato, S.1    Jiao, Y.2
  • 17
    • 68949093616 scopus 로고    scopus 로고
    • Dense packings of the platonic and archimedean solids
    • Torquato, S., Jiao, Y.: Dense packings of the platonic and archimedean solids. Nature 460, 876 (2009).
    • (2009) Nature , vol.460 , pp. 876
    • Torquato, S.1    Jiao, Y.2
  • 18
    • 77951701042 scopus 로고    scopus 로고
    • Exact constructions of a family of dense periodic packings of tetrahedra
    • 041310
    • Torquato, S., Jiao, Y.: Exact constructions of a family of dense periodic packings of tetrahedra. Phys. Rev. E 81, 041310 (2010).
    • (2010) Phys. Rev. E , vol.81
    • Torquato, S.1    Jiao, Y.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.