2 New Palindromes
1- Was it a car or a cat I saw?
and
2- 1122211
The symmetry behind this one is interesting because while it is a fairly simple palindrome, it is the
solution of a palindrome divided by ANOTHER palindrome. Specifically, 12344321 / 11. These divided are both palindromic numbers, simple ones, and their result after division is another palindrome, so I thought that was kind of interesting. Also while researching I ran across a hypothesis that any palindromic number with an even number of digits is divisible by 11, so think on that as well.
Sources:
http://www.rinkworks.com/words/palindromes.shtml