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Sphere Packings, V. Pentahedral Prisms
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  • Published: 27 February 2006

Sphere Packings, V. Pentahedral Prisms

  • Samuel P. Ferguson1 

Discrete & Computational Geometry volume 36, pages 167–204 (2006)Cite this article

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Abstract

This paper is the fifth in a series of papers devoted to the proof of the Kepler conjecture, which asserts that no packing of congruent balls in three dimensions has density greater than the face-centered cubic packing. In this paper we prove that decomposition stars associated with the plane graph of arrangements we term pentahedral prisms do not contravene. Recall that a contravening decomposition star is a potential counterexample to the Kepler conjecture. We use interval arithmetic methods to prove particular linear relations on components of any such contravening decomposition star. These relations are then combined to prove that no such contravening stars exist.

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  1. 5960 Millrace Court B-303, Columbia, MD 21045, USA

    Samuel P. Ferguson

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  1. Samuel P. Ferguson
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Correspondence to Samuel P. Ferguson.

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Ferguson, S. Sphere Packings, V. Pentahedral Prisms. Discrete Comput Geom 36, 167–204 (2006). https://doi.org/10.1007/s00454-005-1214-y

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  • Received: 11 November 1998

  • Revised: 25 July 2005

  • Published: 27 February 2006

  • Issue Date: July 2006

  • DOI: https://doi.org/10.1007/s00454-005-1214-y

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Keywords

  • Computational Mathematic
  • Linear Relation
  • Plane Graph
  • Interval Arithmetic
  • Sphere Packing
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