ε-quasi-twelve-neighbour packings of unit balls in E3

Böröczky, Károly and Szabó, László (2016) ε-quasi-twelve-neighbour packings of unit balls in E3. Acta Mathematica Hungarica, 148 (2). pp. 509-521. ISSN 0236-5294 (print), 1588-2632 (online)

Text art3A10.10072Fs10474_016_0583_4_u.pdf Restricted to Registered users only Download (590kB) | Request a copy

Abstract

Let (Formula presented.) be a (small) positive number. A packing of unit balls in (Formula presented.) is said to be an (Formula presented.)-quasi-twelve-neighbour packing if no two balls of the packing touch each other but for each unit ball B of the packing there are twelve other balls in the packing with the property that the distance of the centre of each of these twelve balls from the centre of B is smaller than (Formula presented.). We construct (Formula presented.)-quasi-twelve-neighbour packings of unit balls in (Formula presented.) for arbitrary small positive (Formula presented.) with some surprising properties. © 2016 Akadémiai Kiadó, Budapest, Hungary

Actions (login required)

Edit Item