Snow Math

So all this snow had me thinking about the addage: "no two snowflakes are alike."  Is this really true?  Are there really an infinite amount of snowflakes that never repeat?  Luckily, I have the internet to consult.  After reading a few different reputable websites (http://www.its.caltech.edu/~atomic/snowcrystals/alike/alike.htm
http://www.sciencebase.com/science-blog/are-all-snowflakes-different.html)

The answer appears to be that no two larger snowflakes are alike.  Wow!  That really boggles the mind!