Permuting words and and enumerating poems

Caleb Emmons teaches mathematics at Pacific University.  Here is his very-clever description of the requirements for a poem to be a sestina -- spelled out in a poem that is itself a sestina.  (A sestina has 39 lines and its form depends on 6 words -- arrangements of which are the end-words of 6 6-line stanzas; these same words also appear, 2 per line, in the final 3-line stanza.)