Jigsaw puzzle - what is the possible number of combinations?

Hello,

I'm new here, I do hope I've chosen the right sub-forum to post this question. Anyway - I'm a graphic designer, and recently I've 'designed' a sort of a jigsaw puzzle made out of 16 cubes which you have to use to create one character (it's for typography project) in a 4 x 4 grid (you have to use every single cube in a grid specified before).

The question is: what is the approx. number of combination if you have: **16 cubes**, with each side having different geometric shape (6 in total), out of which 2 shapes can be used in 4 different combinations.

So I have: 1 circle, 1 hollow circle, 1 right angle triangle, 1 quarter of a circle (forming sort of an arch), 1 square and 1 'empty' square.

Both right-angle triangle and quarter-of-a-circle can be placed in 4 different ways, therefore I suppose increasing the possible number of combinations.

You can see the typographic puzzle by clicking here.

I know you can have 10,000 combination with a 4 pin number, so I wonder approx. how many combinations you can have with this puzzle?

I did A level maths but I'm afraid I can't think of formula to work it out myself.

Thank you,

Monika