Occurrences of D. H. Lehmer's 10-th degree polynomial 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.
 A: 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
A: well, this link will direct you to just under 300 scholarly articles on Lehmer's polynomial:
http://scholar.google.com/scholar?q=polynomial+lehmer&btnG=&hl=en&as_sdt=2005&sciodt=0%2C5&cites=18047953845360790641&scipsc=1
(oh, and I added the big-list tag to this question, I guess that is appropriate :)

a small selection:


*

*The
Lehmer polynomial and pretzel links

*What is Lehmer's Number?

*Heights of polynomials and entropy in algebraic dynamics

*On the
distribution of the roots of a polynomial with integral
coefficients

*Primes in sequences associated to polynomials (after Lehmer)

*Lehmer's
problem for compact Abelian groups

*Higher
Mahler measure for cyclotomic polynomials and Lehmer's question

*Lehmer's Conjecture for
Hermitian Matrices over the Eisenstein and Gaussian Integers

*Solved
and unsolved problems on polynomials

*Polynomials with restricted coefficients and prescribed noncyclotomic factors

*A seventeenth-order polylogarithm ladder

*Lehmer's question, knots and surface dynamics
