Not the original poster but a big fan of this app.
I have seen a lot of dice variants out there. The rhomboid d6 and diamond d12 seem to be pretty popular with many makers. Also, dice with clipped corners are common.
For new dice, there are d2s, d3s, and (my personal favorite) triangular d5s - though I believe the latter is a patented design. They're not too commonly used but are just fun to have around sometimes.