Salem numbers and Lehmer's minimum height problem are venerated not only in number theory and diophantine analysis, where they are considered naturally interesting for their own sake, but also in fields such as hyperbolic geometry and holomorphic dynamics. As is so well known, the least known Salem number is a root $1.176280\ldots$ of the following monic reciprocal $10$-th degree $\{-1,0,1\}-$polynomial discovered way back in 1933 by D. H. Lehmer in his work on primality testing:
$$
x^{10} + x^9 - x^7 - x^6 - x^5 - x^4 - x^3 + x + 1.
$$


I am interested in seeing any mathematical contexts or computations through which this particular polynomial shows up, apparently accidental occurrences included (not to say preferred). 


Here is an example from topology: this is the Alexander polynomial of infinitely many knots, including the $(-2,3,7)$-pretzel knot.



Occurrences of D. H. Lehmer's 10-th degree polynomial
Here's a paper of McMullen where the Lehmer polynomial shows up (see Theorem 1.2 there): 


<http://www.math.harvard.edu/~ctm/papers/home/text/papers/blowup/blowup.pdf>


