A litany poem is best described as a poem that features a repetitive structure, often using a specific phrase or word at the beginning of each line or stanza. Traditionally, a litany poem consists of a series of lines or phrases that build on each other, creating a cumulative effect.
While your description of having stanzas with specific line counts (like 5, 4, and 6 lines) adds a unique twist, a classic litany typically does not have a fixed rhyme scheme. Instead, it emphasizes the repeated phrasing, which is central to its effectiveness.
In summary, a litany poem tells a story, utilizes repetition, and can vary in structure but is characterized by that recurring element—most commonly starting each line or stanza with the same word or phrase. It does not necessarily have to conform to a strict rhyme scheme or line count.