  This paper addresses a long standing open problem due to Lehmer in which the
triple 2,3,7 plays a notable role. Lehmer's problem asks whether there is a gap
between 1 and the next smallest algebraic integer with respect to Mahler
measure. The question has been studied in a wide range of contexts including
number theory, ergodic theory, hyperbolic geometry, and knot theory; and
relates to basic questions such as describing the distribution of heights of
algebraic integers, and of lengths of geodesics on arithmetic surfaces. This
paper focuses on the role of Coxeter systems in Lehmer's problem. The analysis
also leads to a topological version of McKay's correspondence.
