  We study the level statistics (second half moment $I_0$ and rigidity
$\Delta_3$) and the eigenfunctions of pseudointegrable systems with rough
boundaries of different genus numbers $g$. We find that the levels form energy
intervals with a characteristic behavior of the level statistics and the
eigenfunctions in each interval. At low enough energies, the boundary roughness
is not resolved and accordingly, the eigenfunctions are quite regular functions
and the level statistics shows Poisson-like behavior. At higher energies, the
level statistics of most systems moves from Poisson-like towards Wigner-like
behavior with increasing $g$. Investigating the wavefunctions, we find many
chaotic functions that can be described as a random superposition of regular
wavefunctions. The amplitude distribution $P(\psi)$ of these chaotic functions
was found to be Gaussian with the typical value of the localization volume
$V_{\rm{loc}}\approx 0.33$. For systems with periodic boundaries we find
several additional energy regimes, where $I_0$ is relatively close to the
Poisson-limit. In these regimes, the eigenfunctions are either regular or
localized functions, where $P(\psi)$ is close to the distribution of a sine or
cosine function in the first case and strongly peaked in the second case. Also
an interesting intermediate case between chaotic and localized eigenfunctions
appears.
