  We successfully synthesized a verdazyl-based complex,
($p$-Py-V-$p$-CN)$_2$[Cu(hfac)$_2$]. Molecular orbital calculations reveal that
three types of antiferromagnetic (AF) interactions are involved in the
formation of a spin-1/2 distorted octagonal lattice composed of the verdazyl
radical and Cu spins. The magnetic properties of the compound exhibited
contributions from AF correlations and a phase transition to an AF ordered
state at approximately $T_{\rm{N}}$ = 2.5 K. Below $T_{\rm{N}}$, we observed a
$T^2$ dependence of the specific heat, indicating dominant two-dimensional AF
correlations within the octagonal lattice. The magnetization curve in the
low-temperature region exhibited a low-field linear increase, subsequent
bending at 1/3 magnetization, and high-field nonlinear increase. We reproduced
the observed unique magnetic behavior through the numerical analysis based on
the octagonal lattice. These results demonstrate that the present compound
exhibits magnetic properties characteristic of octagonal lattice topology.
