Periodic planar disc packings | Zendy

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Periodic planar disc packings

Author(s) -

Robert Connelly,

William Dickinson

Publication year - 2013

Publication title -

philosophical transactions of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.074

H-Index - 169

eISSN - 1471-2962

pISSN - 1364-503X

DOI - 10.1098/rsta.2012.0039

Subject(s) - torus , conjecture , quotient , hexagonal lattice , combinatorics , mathematics , lattice (music) , planar , sphere packing , graph , geometry , physics , condensed matter physics , computer science , computer graphics (images) , antiferromagnetism , acoustics

Several conditions are given when a packing of equal discs in a torus is locally maximally dense, where the torus is defined as the quotient of the plane by a two-dimensional lattice. Conjectures are presented that claim that the density of any collectively jammed packing, whose graph does not consist of all triangles, and the torus lattice is the standard triangular lattice, is at most (n/(n + 1))π√12, where n is the number of packing discs in the torus. Several classes of collectively jammed packings are presented where the conjecture holds.

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