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