Final answer:
Dylan Thomas' poem 'Do not go gentle into that good night' is a vilanelle, an uncommon formal structure in English poetry due to its demanding pattern of repetition and rhyme.
Step-by-step explanation:
The poetic form of Dylan Thomas' 'Do not go gentle into that good night' is known as a vilanelle, which is a rare form in English poetry. A vilanelle consists of 19 lines with a strict pattern of repetition and a rhyme scheme of ABA. This form is known for its two repeating refrains and two repeating rhymes, making the structure exceptionally challenging for poets to write, contributing to its scarcity in English poetry. The vilanelle is uncommon because it requires a high level of precision and often a strong emotional or thematic reason for the repetition that is inherent to the form.