  Champanerkar, Kofman and Lal\'{i}n conjectured an inequality between
bipyramid volume of links and Mahler measure of associated dimer models induced
from alternating links on torus. Hyperbolic volume and Mahler measure can be
related for isoradial graphs, which allows us to confirm the conjecture for two
examples. By exploiting a connection between perfect matchings of dimer models
and spanning trees on lattices, five more examples are calculated.

Geometric Topology;Combinatorics