Simulations of scattering and polarization properties for randomly ori
ented polyhedral ice crystals are presented based on the geometric opt
ics and the far-field diffraction approximation. Particle shapes range
from various hexagonal symmetric particles to highly complex shaped d
eterministic and random fractals. All calculations are performed at a
wavelength of 0.55 mu m. Hexagonal symmetric particles show several na
rrow scattering peaks besides the well known 22 degrees and 46 degrees
halos. Column-like ice crystals provide neutral points (NP) at larger
scattering angles than plate-like ice crystals. The ranges of NPs for
column-like and plate-like crystals are separated at a scattering ang
le of about 156 degrees, which may allow a polarimetric distinction be
tween these two crystal types. The effects of particle size are studie
d by applying observationally derived aspect-ratio parameterizations t
o the individual particle types. Differences in the asymmetry paramete
r versus size relations for column-like particle types are basically c
aused by different aspect-ratio parameterizations rather than by the d
ifferent types of columns. Thus, solid hexagonal columns appear repres
entative for all column-like ice crystals. The dependency on crystal t
ype is much stronger for plate-like particles. Increasing distortion o
f the crystal shapes leads to a considerable smoothing of the scatteri
ng signature. Scattering by complex-shaped particles is discussed for
deterministic and randomized triadic Koch-fractals. The scattering sig
nature for disordered fractals converges with increasing distortion an
d may be regarded as characteristic for complex-shaped ice crystals.