Now, I have a small piece of calcite that I chipped out of a boulder. Very scrappy and difficult to see through it to get the double image, so thought I'd shine a laser through it, and was surprised to see a pattern like this. What's going on?

Here's an interesting discussion that resulted from someone seeing the same pattern and someone else trying to replicate it:

Unexpected laser pattern through calcite crystal

I've bought a calcite crystal and tried to see birefringence by shining a laser through it. I get a split spot in the centre of a sixfold pattern The hexagonal pattern resembles a diffraction patt...

If the sample is thin, thermal lensing processes would happen right away. Not sure if you saw a delay.. Reported w/details here: www.nature.com/articles/382...#physics#science

diffraction pattern based on the shape of the calcite crystal lattice?