This paper introduces, describes, exemplifies and tells the story of two new poetic forms based on permutations. Braided Bellringing PH4 poems use permutations at the level of words and phrases, while Anagrammatic, Anglo Saxon-inspired poems use permutations at the level of letters and spellings. The author discusses formal poetry in terms of an optimal balance between enabling constraints and creative freedom, and contextualizes rule-based mathematical poetry and wordplay. There is a discussion of opportunities for embodied, movement-based learning experiences supporting the development of mathematical understanding through collaborative performances of PH4 poems.