This paper discusses the role of symmetry-breaking in biometric recognition. Using publicly available databases, we investigate three kinds of broken symmetries in iris patterns: binocular, monocular, and monozygotic. We report a small but statistically significant difference in similarities between the ipsilateral and the contralateral eyes of twins, and also between genetically identical and nonidentical eyes. Another new finding is a doubling in the variance of Hamming distance scores under a simple monocular mirror transformation, which is consistent with an assessment of entropy.