  Current understanding of thermal rectification asserts that the rectification
ratio (R), which measures the relative heat flux between two ends of a
nanostructure, is determined by its geometric asymmetry. The higher the
asymmetry, the higher the R. However, by using nonequilibrium molecular
dynamics method we have calculated thermal transport in Si nanocones as an
example, the results show that such an understanding may be incorrect and R may
not increase monotonically with geometric asymmetry. Rather, R exhibits a sharp
reverse when the vertex angle ({\theta}) of the nanocone is approximately
90{\deg}. In other words, when {\theta} > 90{\deg}, R decreases, rather than
increasing. We show that this abnormal behavior is originated from a change in
the thermal transport mechanism. At small {\theta}s, phonon transport is
dominated by localized modes, especially for transport from tip to bottom. At
large {\theta}s, however, these localized modes disappear, leading to R
decrease.
