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The Translative Kissing Number of Tetrahedra Is 18
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  • Published: September 1999

The Translative Kissing Number of Tetrahedra Is 18

  • I. Talata1 

Discrete & Computational Geometry volume 22, pages 231–248 (1999)Cite this article

Abstract.

We show that the maximum number of mutually nonoverlapping translates of any tetrahedron T which touch T is 18. Moreover, in the case of 18 touching translates the arrangement turns out to be unique. We also give a description of all possible arrangements of 17 touching translates. Finally, we apply these results to determine the minimum and maximum densities of 17 + -neighbor translative packings of tetrahedra.

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Authors and Affiliations

  1. Department of Mathematics, Auburn University, 218 Parker Hall, Auburn, AL 36849-5310, USA talatis@mail.auburn.edu, , , , , , US

    I. Talata

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  1. I. Talata
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Received November 4, 1997, and in revised form February 5, 1998.

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Talata, I. The Translative Kissing Number of Tetrahedra Is 18 . Discrete Comput Geom 22, 231–248 (1999). https://doi.org/10.1007/PL00009457

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  • Issue Date: September 1999

  • DOI: https://doi.org/10.1007/PL00009457

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Keywords

  • Maximum Density
  • Translative Packing
  • Nonoverlapping Translate
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