Phase functions have been calculated using the Monte Carlo;geometric r
ay tracing method for single hexagonal pyramidal ice crystals (such as
solid and hollow bullets) randomly oriented in space and horizontal p
lane, in order to study the concentric halo formations. Results from t
hree dimensional model calculations show that 9 degrees halo can be as
bright as the common 22 degrees halo for pyramidal angle of 28 degree
s, and the 18 degrees, 20 degrees, 23 degrees and 35 degrees halos can
not be seen due to the strong 22 degrees halo domination in the scatte
ring phase function between 18 degrees and 35 degrees. For solid pyram
idal ice crystals randomly oriented horizontally, the 35 degrees are c
an be produced and its intensity depends on the incident ray solar ang
le and the particle aspect ratio.