Creating a 3D model of a constellation

Hello,

At school we we were given the assignment to create a 3D model of a
constellation. We were quite lucky as we got the constellation of Orion.
As all stars of Orion are very clear loads of information was
available. To create the 3D model we used the RA, the Declination and
the distance to the star. By using some trigonometry we converted these
values (after some a correction of 85 degrees in the RA to get the
constellation right in front of us) into a 3D grid.
Having calculated this we used very small lights to represent the stars
and placed them in a box of 40x40x40 cm, at the positions we calculated
earlier. The only problem was that the bunch of lights that were visible
were almost not recognisable as representing orion. The teachers were
unable to provide us with a reason why Orion wasn't visible. But I am
still curious about why it didn't work out so that's why I post this
message. I don't exactly know if this is the right newsgroup but it
seemed the most logical one to pick. And by the way if my explanation of
the calculation wasn't clear enough (was can be quite easy possible as I
have looped through that calculation numorous times and know about every
bit of it) just drop a message and I'll post the entire calculation.

Thanks in advance,
Wouter Lueks