I will give a brief overview of sonnets, citing some examples, and describe a notation for the grouping structure and end rhyme pattern types of individual poems and sonnet sequences. Then I construct the sets of rhyme patterns of poems with even rhymes and compute their counts. Cascading this construction over rhyme groupings leads to counts for a variety of sonnet forms. The structure and counts for two types of sonnets are visualized as trees. I then visualize end rhyme patterns as color bands for two types of patterns: (1) systematically generated rhyme patterns for sections of sonnets, and (2) sonnet sequences from the literature. These bands provide a holistic visual overview that can give insight into the structure of poem sequences that may span hundreds of lines. Different color assignments can also be used to exhibit and enhance the visual beauty inherent in rhyme patterns. Mathematica 7 is used to create counts, summary tables and images of end rhyme patterns.